Troubleshoot of Pharmaceutical Calculations [2 ed.] 9789843378736

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TROUBLESHOOT OF

PHARMACEUTICAL CALCULATIONS A guidebook of Pharmaceutical Calculations (by Howard C. Ansel (14th Edition))

MD. SOHEL RANA Department of Pharmacy UNIVERSITY OF ASIA PACIFIC

"Troubleshoot of Pharmaceutical Calculations" Md. Sohel Rana Publisher: Md. Sohel Rana (+88 01734-118315) [email protected] Typing: Md. Zahid Hasan & Cover Photo designed by: Jitu Shahed All right reserved by the Author Price: Taka 450 , US$. 10 Sole distributor: KEYA MEDICAL BOOK CENTRE 136, Islamia Market, Nilkhet , Dhaka-1205 Mobile: 01716-213616 Phone: 8622245

ISBN: 978-984-33-7873-6

Dedicated to Parents and all of my teachers

INTRODUCTION

“Troubleshoot of Pharmaceutical Calculation” is a book in which solutions of almost all the pharmaceutical mathematics calculation (by Howard C. Ansel 13th edition) is available. This is the second edition of the 14th edition (Howard C.Ansel). I Hope that it will be helpful and very effective for all the students of Pharmacy department as well as in health practice. Each chapter contains basic concept and solution of problems. In basic concept, there are some primary definitions and equations that are required to solve the common problems, and questions with solutions are also available. Chapter 1 to 24 contains queries and answers based on the book pharmaceutical calculation (by Howard C. Ansel 13th edition). There are additional two new chapters named “Capsule related calculation: selection of shell size, weight capacity and minims per gram calculation” and “Molarity, Normality and Molality”. That will be also helpful and very effective for Pharmacy students as well as in case of Pharmaceutical production. To calculate the drug quantity, the specification of drugs, and required amount of drugs for the individual, for different dosage forms like, tablet, capsule, solution, suspension intravenous infusion etc. this book will be very effective and helpful. Best of hap from the core of the author’s heart goes to the buyer of this book. If any mistakes are found, like, typing, calculation related mistakes etc. please inform page number and problem number to the author via email ([email protected]). Insha Allah all the mistakes will be overcome in next edition. Author Md. Sohel Rana Student, Pharmacy Department University of Asia Pacific

Acknowledgments The author gratefully professes the contribution for revision and associated help of this book: Ikramul Hassan (Lecturer, DU) and Dr. Abdul Mazid (Professor, University of Dhaka). I want to especially thank my advisor Ms. Sayeeda Fahmee Chowdhury for her continuous support. Also, thanks to my teacher, parents and friends for encouraging me in completing such a huge task. Novel additional chapter named @Capsule related Calculation: selection of capsule shell, weight capacity and minims per gram calculation@ I want to especially thank my honorable teacher SM Ashraful Islam, Associate prof. , UAP. His excellent advice has helped me to compile everything necessary. I am grateful to my head of the dept. Prof. Dr. Swarnali Islam Khandaker, and Professor Dr. Muhiuddin Ahmed Bhuiyan, a great mentor and has always inspired me behind writing this book.

Author Md. Sohel Rana

Contents CHAPTER NO

CHAPTER NAME

PAGE NO

01

FUNDAMENTALS OF PHARMACEUTICAL CALCULATION

01-19

02

INTERNATIONAL SYSTEM OF UNIT

20-46

03

PHARMACEUTICALMEASUREMENT

47--53

04

INTERPRETATION OF PRESCRIPTIONS AND MEDICATION ORDERS

54--57

05

DENSITY, SPECIFIC GRAVITY AND SPECIFIC VOLUME

58-72

06

PERCENTAGE, RATIO STRENGTH, AND OTHER EXPRESSION OF CONCENTRATION

73-116

07

CALCULATION OF DOSES: GENRAL CONSIDERATION

117-136

08

CALCULATION OF DOSES: PATIENT PARAMETERS

137-173

09

SOME CALCULATIONS INVOLVING MEASURES OF POTENCY

174-189

10

SELECTED CLINICAL CALCULATIONS

190-201

11

ISOTONIC AND BUFFER SOLUTION

202-222

12

ELECTROLYTE SOLUTION: MILLIEQUIVALENT, MILLIMOLES, AND MILLIOSMOLES

223-264

13

INTRAVENOUS INFUSION, PARENTERAL ADMIXTURES, AND RATE OF FLOW CALCULATION

265-292

14

ENTERAL AND PARENTERAL NUTRITION , BODY MASS INDEX AND THE FOOD NUTRION LABEL

293-315

15

ALTERING PRODUCT STRENGTH, USE OF STOCK, AND PROBLEM SOLVING BY ALLIGATION

316-354

16

REDUCING AND ENLARGING FORMULA

355-368

17

SELECTED CALCULATION IN CONTEMORARY COMPOUNDS

369-406

18

SELECTED CALCULATIONS INVOLVING VETERINARY PHARMACEUTICALS

407-417

19

SELECTED CALCULATIONS ASSOCIATED WITH PLANT EXTRACTIVES

318-425

20

CALCULATION OF ACTIVE DRUG MOIETY

426-434

21

SELECTED CALCULATIONS INVOLVING RADIOPHARMACEUTICALS

435-450

22

BIOAVAILABILITY AND PHARMACOKINETICS CALCULATIONS

451-459

23

SELECTED PHARMACOECONOMICS CALCULATIONS 460-470

24 Apendix-A

COMMON SYSTEM OF MEASUREMENT AND CONVERSION

471-480

25

CAPSULE RELATED CALCULATION: SELECTION OF SHELL SIZE, WEIGHT CAPACITY AND MINIMS PER GRAM CALCULATION

481-487

26

MOLARITY, NORMALITY AND MOLALITY

488-491

Success, getting fast is serendipity, but getting last is achievement. (Sohel Rana)

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION CHAPTER: 01 FUNDAMENTALS OF PHARMACEUTICAL CALCULATION Basic concept: Decimal Fractions : A decimal fraction is a fraction where the denominator (the bottom number) is power of ten. (such as 10, 100, 1000 etc) . You can write decimal fraction with a decimal point (and no denominator) , which make easier to do calcation like addition and multiplication on fractions. Example: 43/100 is a decimal fraction and it can be shown as 0.43 51/1000 is a decimal fraction and it can be shown as 0.051 Percent : A percentage is a number or ratio as a fraction of 100. It is often denoted using the percent sign, “%”, or the abbreviation “pct.” For example, 45% (read as “fortyfive percent”) is equal to 45/100, or 0.45. Example: Convert 3/8 as a percentage. 3/8 × 100 = 37.5 % (answer) Exponential Notation: The exponential notation (sometimes called the "scientific" notation) greatly simplifies calculations, especially with very large and very small numbers. It uses positive and negative exponents to write multiples and submultiples of 10: Any number raised to the 1000 = 10 x 10 x 10 = 103 zeroth power equals one. 100 = 10 x 10 = 102 10 = 10 = 101 1 = 100 0.1 = 1/10 = 10-1 0.01 = 1/100 = 10-2 Ratio proportion and variation: A ratio is a comparison of two similar quantity by the other. Ratio are written with the : symbol Example: the ratio of 6 to 3 is 6÷ 3 = 6/3 = 6: 3 = 2 The ratio of 3 to 6 is 3÷6 = 3/6 = 3:6 = 1/2 A proportion is the expression of the equality of two ratios. It may be written in any one of 1

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION three standard forms: (1) a:b=c:d (2) a :b::c:d (3) a/b=c/d SOLUTIONS OF THE PROBLEMS: 1(A) Common and Decimal Fraction and Percent: 1. How many 0.000065-gram doses can be made from 0.130 gram of a drug? 0.000065 g of drugs present in 0.130 g

of drugs present in

= 1 dose =

dose

= 2000 dose (answer) 02. Give the decimal fraction and percent equivalents for each of the following common fractions: (a) 1⁄35 (b) 3⁄7 (c) 1⁄250 (d)1⁄400 a) Decimal Faction = = 0.0285 (Ans.) %

= = 2.85% (ans)

b) Decimal Faction

=

= 0.4285 (ans) % = 2

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION =42.85%(ans) c) Decimal Faction

=

= 0.004 (ans) %= = 0.4% (ans) d) Decimal Faction

=

= 0.0025 (ans) % = =0.25%(ans) 03. If a clinical study of a new drug demonstrated that the drug met the effectiveness criteria in 646 patients of the 942 patients enrolled in the study, express these results as a decimal fraction and as a percent. Decimal Faction

= = 0.6857 (ans)

%

= = 68.57% (ans)

04. . A pharmacist had 3 ounces of hydromorphone hydrochloride. He used the following: 1/8 ounce ¼ ounce 1.5 ounce How many ounces of hydromorphone hydrochloride were left? Pharmacist had 3 ounces of hydromorphine hydrocloride. He used = ( ) Ounce 3

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 1.875 Ounce Amount of ounce of hydromorphore hydrocloride were left = 3 - 1.875 =1.125 Ounce (answer) 05. A pharmacist had 5 grams of codeine sulfate. He used it in preparing the fol lowing: 8 capsules each containing 0.0325 gram 12 capsules each containing 0.015 gram 18 capsules each containing 0.008 grams How many grams of codeine sulfate were left after he had prepare the capsules? Pharmecist has 5 g of codeire sulfate. ) He used it = ( = 2.204 gm ) gm Amount of codeire sulfate were left = ( = 2.796 gm (ans) 06. The literature for a pharmaceutical product states that 26 patients of the 2,103 enrolled in a clinical study reported headache after taking the prod uct. Calculate (a) the decimal fraction and (b) the percentage of patients re porting this adverse response. a) = 0.0123 (ans) b) % = = 1.236 % (ans) 1(B): Expotential Notetion: 01. Write each of the following in exponential form: (a) 12,650 (b) 0.0000000055 (c) 451 (d) 0.065 (e) 625,000,000 a) 12650 =

(ans) 4

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION b) 0.0000000055 =

(ans)

c) 451 =

(ans)

d) 0.065 = e) 625000000 =

(ans)

02. Write each of the following in the usual numeric form: (a) 4.1 × 106 (b) 3.65 × 10-2 (c)

( d)

(e) 8.6956 a)

= 4100000 (ans)

b)

= 0.0365 (ans)

c)

= 0.00000513 (ans)

d)

= 250000 (ans)

e) 8.6956

= 8695.6 (ans)

03. Find the product: ) ( a) ( ) ( b) ( ) ( c) ( d) (

)

(

e) (

)

(

a) (

) ) ) ) ) )

(

)=

(ans) 5

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION b) (

)

(

c) (

)

(

)=

d) (

)

(

)=

e) (

)

(

04. Find the quotient: ) ( a) ( ) ( b) ( ( ) ( c) a) ( b) ( c) (

)

(ans)

)=

( )

)

)= )= )=

( (

(ans)

(ans) (ans) (ans)

) ) )

)

( )

)

( (

)

)= )= )=

(ans) (ans) (ans)

)= )= )=

(ans) (ans) (ans)

) ) ) (

) )

(ans)

) )

06. Find the difference: ) ( a) ( ) ( b) ( ) ( c) ( a) ( b) ( c) (

(ans)

)

05. Find the sum: ) ( a) ( ) ( b) ( ) ( c) ( a) ( b) ( c) (

)=

( (

6

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1(C): Ratio, Proportion, Variation and Dimentional analysis: 1. If an insulin injection contains 100 units of insulin in each millilitre, how many millilitres should be injected to receive 40 units of insulin? 100 Units of insulin present in

= 1ml of injection

40 units of insulin present in =

= 0.4 ml of injection (ans)

2. Digoxin (LANOXIN) pediatric elixir contains 0.05 mg of digoxin in each milliliter of elixir. How many milligrams of digoxin would be administered with a dose of 0.6 mL? 1 ml of elixir contain = 0.05 mg of digoxin 0.6 ml of elixir contain = 0.6 x 0.05 mg digoxin = 0.03 mg digoxin (ans) 03. In a clinical study , a drug produced drowsiness in 30 of the 1500 patientsstudied . How many patients of the certain pharmacy could expect similareffeccts, based on a patient count of 100? In a clinical study of 1500 patients, drowsiness develop in 30 patient In a clinical study of 100 patients, drowsiness develop in =

patient

= 2 patients Ans: 2 patients 4. A formula for 1250 tablets contains 6.25 grams (g) of diazepam. How many grams of diazepam should be used in preparing 350 tablets? 1250 tablets contain

= 6.25 g of diazepam

350 tablets contain

= = 1.75 g of diazepam (ans)

7

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 5. If 100 capsules contain 500 mg of an active ingredient, how many milligrams of the ingredient will 48 capsules contain? 100 capsules contain

= 500 mg of active ingredient

48 capsules contain

=

mg of active ingredient = 2.4 mg of active ingredient

(answer)

6. Each tablet of TYLENOL WITH CODEINE contains 30 mg of codeine phosphate and 300 mg of acetaminophen by taking two tablets daily for a week, how many milligrams of each drug would the patient take? Daily = 2 tablets 1 week = 7 days = 7 x 2 tablets = 14 tablets 1 tablets of TYLENOL WITH CODEINE Phosphate contain= 30 mg of codeine and 300 mg of acetaminophen 14 tablets of TYLENOL WITH CODEINE Phosphate contain= 14 x 30 mg of codeine and 300 x 14 mg of acetaminophen = 420 mg of codeine and 4200 mg of acetaminophen (answer) 7. A cough syrup contains 10 mg of dextromethorphan hydrobromide per 5 mL. How many milligrams of the drug are contained in a 120-mL container of the syrup?

5 ml cough syrup contain

= 10 mg of dextromethorphan hydrobromide

120 ml cough syrup contain = hydrobromide = 240 mg

mg

of

dextromethorphan

(ans)

8

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 8. If an intravenous fluid is adjusted to deliver 15 mg of medication to a patient perhour, how many milligrams of medication are delivered per minute? By 1 hour = 60 min deliver = 15 mg of medication 1 min deliver

=

mg of medication

= 0.25 mg (ans) 9. The biotechnology drug filgrastim (NEUPOGEN) is available in vials containing 480 micrograms (mcg) of filgrastim per 0.8 mL. How many micrograms of the drug would be administered by each 0.5 mL injection? 0.8 ml of vial contain

= 480 μg of filgrastin

0.5 ml of vial contain

=

μg of filgrastin

= 300 μg of filgrastin

(ans)

10. A prescription drug cost the pharmacist $42.00 for a bottle of 100 tablets. What would be the cost for 24 tablets? 100 tablets cost

= $ 42.00

24 tablets cost

= = $ 10.08 (ans)

11. How many 0.1-mg tablets will contain the same amount of drug as 50 tablets, each of which contains 0.025 mg of the identical drug? 1 tablets contain

= 0.025 mg of the identified drug

50 tablets contain

= 50 x 0.025 mg of the identified drug = 1.25 mg of the identified drug

Number of the tablet will contain the same amount of drug as 50 tablet each of the tablet contain 0.025 mg of identified drug = tablets 9

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 12.5 tablets (ans) 12. Acyclovir (ZOVIRAX) suspension contains 200 mg of acyclovir in each 5 mL. How many milligrams of acyclovir are contained in a pint (473 mL) of suspension? 1 pint = 16 Fl.oz = 16 x 29.57 ml = 473 ml 5 ml of acyclovir suspession contain = 200 mg of acyclovir 473 ml of acyclovir suspession contain =

mg of acyclovir

= 18920 mg (ans) 13. A metered dose inhaler contains 225 mg of metaproterenol sulfate, which is sufficient for 300 inhalations. How many milligrams of metaproterenol sulfate would be administered in each inhalation? 1 metered inhaler deliver

= 300 inhalations

1 metered inhaler contain = 225 mg of metaprotereot sulfate So, 300 inhalation deliver 225 mg of metaprotereot sulfate 1 inhelation deliver

mg of metaprotereot sulfate

= 0.75 mg of metaprotereot sulfate

(ans)

14. A pediatric vitamin drug product contains the equivalent of 0.5 mg of fluoride ion in each milliliter. How many milligrams of fluoride ion would be provided by a dropper that delivers 0.6 mL? 1 ml of pediatric vitamin drug product contain

= 0.5 mg of fluoride ion

0.6 ml of pediatric vitamin drug product contain

= 0.5 x 0.6 mg of flooride ion = 0.3 mg of flooride ion

0.6 ml deliver by 1 dropper 10

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION So, 1 dropper provide= 0.3 mg of flooride ion (ans) 15. If a pediatric vitamin contains 1500 units of vitamin A per milliliter of solution,how many units of vitamin A would be administered to a child given 2 drops of thesolution from a dropper calibrated to deliver 20 drops per milliliter of solution? 20 dropss of drug (vitamin) delivered by

= 1 ml of solution

2 dropss of drug (vitamin) delivered by

=

ml of solution

= 0.1 ml of solution 1 ml of solution contain

= 1500 units of pediatric solution

0.1 ml of solution contain

= 1500 x 0.1 units of pediatric solution = 150 units of pediatric solution

(ans)

16. An elixir contains 40 mg of drug in each 5 mL. How many milligrams of the drug would be used in preparing 4000 mL of the elixir? 5 ml of elixir contain = 40 mg of drugs 4000 ml of elixir contain

=

mg of drugs

= 32000 mg of drugs Ans: 32000 mg of drugs should be used in preparing 400 ml of elixir 17. An elixir of ferrous sulfate contains 220 mg of ferrous sulfate in each 5 mL. If each milligram of ferrous sulfate contains the equivalent of 0.2 mg of elemental iron, how many mg of elemental ion would be represented in each 5 ml of the elixir?

5 ml of ferrous sulfate elixir contain = 220 mg of ferrous sulfate 1 mg of ferrous sulfate contains

= 0.2 mg of elemental ion

220 mg of ferrous sulfate contains

= 200 x 0.2 mg of elemental ion = 44 mg of elemental ion 11

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 5 ml of elixir contain 44 mg od elemental ion (ans) 18. At a constant temperature, the volume of a gas varies inversely with the pres sure. If a gas occupies a volume of 1000 mL at a pressure of 760 mm, what is its volume at a pressure of 570 mm? At 760 mm of presure volume occupies

1000 ml

At 760 mm of presure volume occupies

ml

= 750 ml (ans) 19. If an ophthalmic solution contains 1 mg of dexamethasone phosphate in each milliliter of solution, how many milligrams of dexamethasone phosphate would be contained in 2 drops if the eyedropper used delivered 20 drops per milliliter? 20 drops is delivered by 2 drops is delivered by =

= 1 ml of solution ml of solution of solution:

= 0.1 ml ………. 1 ml of solution contain

= 1 mg of dexamethesone phosphate

0.1 ml of solution contain

= 0.1 x 1 mg of dexamethesone phosphate

= 0.1 mg of dexamethesone phosphate 20. A 15-mL package of nasal spray delivers 20 sprays per milliliter of solution, with each spray containing 1.5 mg of drug. (a) How many total sprays will the package deliver? (b) How many milligrams of drug are contained in the 15-mL package of the spray? a) 1 ml of solution deliver 15 ml of solution deliver

= 20 sprays = 20 x 15 sprays

= 300 sparys Ans: 15 ml packing of sosal spray delivers 300 sprays b) 1 spray contain

= 1.5 mg of drugs 12

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 300 spray contain

= 1.5 x 300 mg of drugs = 450 mg of drugs (ans)

21. A penicillin V potassium preparation provides 400,000 units of activity in each 250mg tablet. How many total units of activity would a patient receive from taking four tablets a day for 10 days? Total tablets receiving by the petient 4 x 10 = 40 tablets 1, 250 mg of tablets of penicillin deliver

= 400000 unit of activity

40, 250 mg of tablets of penicillin deliver

= 40 x 400000 unit of activity

= 16000000 units of activity (ans) 22. If a 5-g packet of a potassium supple ment provides 20 milliequivalents of potassium ion and 3.34 milliequivalents of chloride ion, (a) how many grams of the powder would provide 6 milliequivalents of potassium ion, and ? (b) how many milliequivalents of chloride ion would be provided by this amount of powder? a) 20 milliequivalents of potossium delivered by supplement

= 5 g packet of potassium

6 milliequivalents of potossium delivered by supplement

=

g packet of potassium

= 1.5 g packet of potassium supplement 5 g of packet of a potassium supplement provide = 3.34 milliequivalent of chloride ion 1.5 g of packet of a potassium supplement provide = chloride ion

milliequivalent of

= 1.02 milliequivalent of chloride ion (ans) 23. If a potassium chloride elixir contains 20 milliequivalents of potassium ion in each 15 mL of elixir, how many milliliters will provide 25 milliequivelents of potassium ion to the patient?

13

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 20 milliequivalents of potossium ion present in

=15 ml of elixir

25 milliequivalents of potossium ion present in

=

ml of elixir

= 18.75 ml of elixir (ans) 24. The blood serum concentration of the antibacterial drug ciprofloxacin in creases proportionately with the dose of drug administered. If a 250 mg dose of the drug results in a serum concentration of 1.2 micrograms of drug per milliliter of serum, how many micrograms of drug would be expected per milliliter of serum following a dose of 500 mg of drug? 250 mg dose of the drug result in a serum conc. of 1.2 μg of drug per ml 500 mg dose of the drug result in a serum conc. of

μg of drug per ml

= 2.4 μg of drug per ml

(ans)

25. The dosage of the drug thiabendazole (MINTEZOL) is determined in direct proportion to a patient's weight. If the dose of the drug for a patient weighing 150 pounds is 1.5 grams, what would be the dose for a patient weighing 110 pounds? 150 pound of petient weight require 1.5 g of the drug thibendazole 110 pound of petient weight require

g of the drug thibendazole = 1.1 g of the drug thai bendazole (ans)

26. If 0.5 mL of a mumps virus vaccine contains 5000 units of antigen, how many units would be present in each milliliter if the 0.5 mL of vaccine was diluted to 2 mL with water for injection?

0.5 ml of a mumps virus vaccine contain = 5000 units of antigen After dilution the volume of vaccine is

2ml

2 ml of vaccine contain

=5000 units of antigen

1 ml of vaccine contain

=

units of antigen 14

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 2500 units of antigen

(ans)

27. A sample of Oriental ginseng contains 0.4 mg of active constituents in each 100 mg of powdered plant. How many milligrams of active constituents would be present in 15 mg of powdered plant? 100 mg of powdered plant contain 15 mg of powdered plant contain =

= 0.4 mg of oriental ginseng =

mg of oriental ginseng

0.06 mg of oriental ginseng (ans)

1(D) : Significance figure: 1.State the number of significance figures in each of the italicized quantities. (a) One fluidounce equals 29.57 ml (b) One liter equals 1000 milliliters (c) One inch equals 2.54 cm (d) The chemical costs 1.05 USD per pound (e) One gram equals 1000000 mcg (f) One mcg equals 0.01 mg Ans: a. Four b. Four c. Three d. Three e. Seven f. Four 2.Round each of the following to three significance figures: (a) 32.75 (b) 200.39 (c) 0.03629 (d) 21.635 (e) 0.00944 Ans: a. 32.7 b. 200 c. 0.04

d. 21.6 e. 0.00944

15

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 3.Round each of the following to three decimal places: a. 0.00083 b. 34.79502 c. 0.00494 d. 6.12963 Ans: a. 0.001 b. 34.795 c. 0.005 d. 6.130 4. If a mixture of seven ingredients contains the following approximate weights, what can you validly record as the approximately total combined weight of the ingredients? 26.83 g, 275.3 g, 2.752 g, 4.04 g, 5.197 g, 16.64 g and 0.085 g.

Total = (26.83+275.3+2.752+4.04+5.197+16.64+0.085)g = 330.844 g Ans: 330.844 g 5. Perform the following computations, and retain only significant figures in the results: a. 6.39-0.008

b. 7.01-6.0 c. 5.0×48.3 g d. 24×0.25 g e. 56.824/0.0905

f.

250/1.109

a. 6.39-0.008

= 6.382

b. 7.01-6.0 = 1.01 c. 5.0×48.3 g = 241.6 g d. 24×0.25 g = 6 g 16

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION e. 56.824/0.0905 = 621.922 f. 250/1.109 = 225.42

CALCQUIZ 1.A Digoxin (lanoxin) pediaric elixir contains 0.05 mg of digoxin in each ml of elixir. If there are 1000 mcg in each mg, how many mcg of digoxin would be delivered in each dose of 0.6 ml?

1 mg = 1000 mcg So, 0.05 mg = 1000×0.05 mcg = 50 mcg So, we can say that, 1 ml of elixir contain = 50 mcg of digoxin 0.6 ml of elixir contain = 50×0.6 = 30 mcg of digoxin Ans: 30 mcg of digoxin. 1.B A probiotic colon health product contains, in each capsule, 3 billion viable clls of Lactobacillus acidophilus and Bifidobacterium longum. Express, by exponential notation, the number of viable cells in a container of 30 capsules. We know that 1 billion = 1000,000,000 = 109 17

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION So, 3 billion

= 3×109

1 capsule contain = 3×109 So, 3 capsule contain = 30×3×109 = 90×109 = 9×1010 Ans: 9×1010

1.C. A liquid dietary supplement is packaged in 10 ml dropper containers to deliver 2000 international units of vitamin D3 in each drop (0.027 ml). Calculate the number of drops delivered per milliliter. 0.027 ml contain = 1 drop So, 10 ml contain = 10/0.027 = 370 drops Ans: 370 drops 1.D. The drug pramlintide (SYMLIN) is an antihyperglycemic agent for use in patients with diabetes treated with insulin. A 5 ml vial contains 600 mcg of pramlintide per milliliter. A 0.05 ml dose measures 5 insulin units on the syringe used for injection and provides 30 mcg of pramlintide. Calculate the number of micrograms of pramlintide and corresponding measurement of insulin units on the syringe with the administration of 0.075 ml of injection. 0.05 ml dose measures 5 unit insulin and 30 mcg of pramlintide So, 0.075 ml measures =

×0.075 unit insulin and

×0.075 mcg of Pramlintide

= 7.5 unit insulin and 45 mcg of pramlintide And: 7.5 unit insulin and 45 mcg of pramlintide 18

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1.E. A physician prescribed mometasone furoate monohydrate (NASONEX) nasal spray for a patient with directions to administer two sprays into each nostril once daily. If each spray contains 50 mcg of drug and the containers can deliver a total of 120 sprays how many mcg of drug would the patient receive daily, and how many days of use will the prescription last the patient? Number of micrograms of drug would the patient receive daily = 50×2 = 100 mcg Number of days of use will the prescription last the patient = 120/2 = 60 days Ans: 100 mcg and 60 days.

19

CHAPTER :02 INTERNATIONAL SYSTEM OF UNIT Basic concept: Equivalent of volume: 1 fluidounce (fl.oz) =29.57 ml 1 pint (16 fl.oz) = 473 ml 1 quart (32 fl.oz) = 946 ml 1 gallon, us (128 fl.oz) = 3785 ml 1 gallon uk = 4545ml

Some useful equivalent: Equivalent of lenghth 1 inch = 2.54 cm 1 meter (m) = 39.37 inch 1 pound = 454 g Equivalent of volume: 1 fluidounce (fl.oz) =29.57 ml 1 pint (16 fl.oz) = 473 ml 1 quart (32 fl.oz) =946 ml 1 gallon, us (128 fl.oz) = 3785 ml 1 gallon uk =4545ml Equivalent of weight: 1 pound = 0.454 gm 1 kilogram (kg) = 2.2 pound

1 kilogram = 103 g 1 hectogram = 102 g 1 dekagram = 101 g 1 gram 1 decigram = 10−1 g 1 centigram = 10-2 g 1 miligram = 10-3 1 microgram = 10-6 1 nano-gram = 10-9 g 1 peko-gram = 10-12 1 pentagram = 10-15 Measure of Volume : The liter is the primary unit of volume. It represents the volume of the cube of one tenth of a meter, that is, of 1 dm3. The table of metric volume: 1kiloliter (kL) = 1000 liters 1hectoliter (hL) = 100liters 1dekaliter (daL) = 10liters 1liter (L) =1liter 1 deciliter (dL) = 0.100 liter

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 centiliter (cL) =0.010 liter 1 milliliter (mL) =0.001 liter 1 microliter ( L) = 0.000,001 liter

Measure of length: 1 decimeter (dm) = 0.100 meter 1 centimeter (cm) = 0.010 meter 1 millimeter (mm) = 0.001 meter 1 micrometer = 0.000001 meter 1 nanometer

= 0.000000001 meter

1 meter = 0.001 kilometer = 0.01 hectometer = 0.1 dekameter = 10 decimeter = 100 centimeter = 1000 millimeters = 1000000 µm = 1000000000 nanometer

SOLUTION OF PROBLEMS 1. Add 0.5 kg, 50 mg, and 2.5 dg. Reduce the result to grams. In case of 0.5 kg: 1

kg = 1000 g

so 0.5 kg = 500 g In case of 50 mg∶ 1 mg = 10-3 g 50 mg = 50 × 10-3 = 0.05 g In case of

2.5 dg∶

1 decigram = 10-1g 2.5 decigram = 2.5 × 10-1 g 21

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 0.25 g Total = (500 + 0.25 + 0.05) g

= 500.3 g

Ans∶ 500.3 g 2. Add 7.25 L and 875 cL. Reduce the result to milliliters. 7.25 L: 1 litter = 103 mL 7.25 L = 7.25 × 103 mL = 7250 mL 875 Centilitre : 1 Centilitre = 10-2 L 875 Centilitre = 10-2 × 875 L = 8.75 L = 8.75 × 103 mL = 8750 mL ∴ Total = (8750 + 7250) = 16,000 mL Ans∶ 16,000 mL 3. Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 µg, and express the answer in grams. 0.0025 kg : 1 kg = 103 g 0.0025 kg = 0.0025 × 103 g = 2.5 g 1750 mg: 1 mg = 10-3 g 1750 mg = 1750 × 10-3 g = 1.75 g 22

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 825,000µg: 1 µg = 10-6 g 825,000 µg = 825,000 × 10-6 g = 0.825 g ∴ Total = (0.825 + 1.75 + 2.5) g = 5.075 g

(ans)

4. Reduce 1.256 g to micrograms, to milligrams, and to kilograms. 1.265 g to (µg, mg, kg): 1 g = 10-3 kg So, 1.256 g = 1.256 × 10-3kg

= 1.256×10-3 kg (ans)

Again 1 g = 103 mg 1.256 g = 1.256 × 103 mg = 1256 mg Ans∶ 1256 mg Again,

1 g = 106 µg 1.256 g = 1.256 × 106 µg = 1256000 µg

Ans∶ 1256000 µg 5. Are the terms mcg/mL and mg/L equivalent or not equivalent? =

= 10-6 g/mL = 10-6 g/mL g/mL = g/mL ∴ Equivalent 23

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 6. A low-strength aspirin tablet contains 81 mg of aspirin per tablet. How many tablets may be prepared from 1 kg of aspirin? 1 tablet contain 81 mg 1 kg = 1000 gm = 1000 × 1000 mg ∴

= 12,345 Tablets

Ans∶ 12 , 345 tablets 07. Adhesive tape made from fabric has a tensile strength of not less than 20.41 kg/2.54 cm of width . reduce this quantity to grams and millimeters. =20.41 kg/2.54 cm = 20.41×103g/2.54 ×10—2×103 mm = 20410 g/25.4 mm (ans) 8. A liquid contains 0.25 mg of a substance per milliliter. How many grams of the substance will 3.5 L contain? 0.25 mg/ 1mL 3.5 L 1 mL contain 0.25 mg = 0.25 × 10-3 g of substance 3.5 × 103mL contain = 0.25 × 10-3 × 3.5 ×103 = 0.875 g Ans∶ 0.875 g 9. An inhalation aerosol contains 225 mg of metaproterenol sulfate, which is sufficient for 300 inhalations. How many micrograms of metaproterenol sulfate would be contained in each inhalation? 300 inhalation contain = 225 mg = 225 × 103 µg = 225000 µg 24

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 inhalation contain =

µg

= 750 µg Ans∶ 750 µg

10. TRIPHASIL-28 birth control tablets are taken sequentially, 1 tablet per day for 28 days, with the tablets containing the following: Phase 1 - 6 tablets, each containing 0.050 mg levonorgestrel and 0.030 mg ethinyl estradiol; Phase 2 – 5 0.075 mg levonorgestrel and 0.040 mg ethinyl estradiol; Phase 3 - 10 tablets, each containing 0.125 mg levonorgestrel and 0.030 mg ethinyl estradiol; then, 7 inert tablets (no drug). How many total milligrams each of levonorgestrel and ethinyl estradiol are taken during the 28day period? Phase 1∶ Levonorgestrel = 6 × 0.050 mg = 0.3 mg Ethinyl estradiol = 6 × 0.030 mg = 0.18 mg Phase 2∶ Levonorgestrel = 5 × 0.075 mg = 0.375 mg Ethinylnorgestrel = 5 × 0.040 mg = 0.2 mg Phase 3∶ Levonorgestrel = 10 × 0.125 = 1.25 mg Ethinynorgestrell = 10 × 0.030 mg 25

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 0.3 mg Total Levonorgestrel = (1.25 + 0.375 + 0.3) mg = 1.925 mg (ans) Total Ethinylnorgestrel = (0.3 +0.2 + 0.18) mg = 0.68 mg

(ans)

11. How many colchicine tablets, each containing 600 mcg, may be prepared from 30 g of colchicine? 1 tablet = 600 mcg Total colchicine = 30 g = 30 × 106µg So, = = 50,000 Tablets Ans∶ 50,000 Tablets 12. The following clinical laboratory data are within normal values for an adult. Convert each value to mcg/mL: (a) ammonia, 30 mcg/dL (b) folate, 18 pg/mL (c) serum creatinine, 1.0 mg/dL (d) prostate specific antigen (PSA), 3 ng/mL (e) cholesterol, total, 150 mg/dL (a) =

30

Ammonia = Ammonia = Ammonia = Ammonia = 0.3 µg/mL Ans∶ 0.3 µg/mL (b) 26

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Folate , 18pg/mL = = = 1.8 × 10-5 µg/mL = 0.000018 µg/mL Ans∶ 0.000018 µg/mL (c) Serum contain = 1.0 mg/dl =

(

)

= = 10µg/mL (d) Prostate specific antigen (PSA), 33 = = = 3 × 10-3 = 0.003 Ans∶ 0.003 (e) Cholesterol total, 150 mg/dl =

(

)

= 27

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 1500 Ans∶ 1500 13. The package insert for DONNATAL EXTENTABS indicates the amount of phenobarbital present in each tablet, in milligrams and in the equivalent weight (3/4 grains) in the apothecary system. Refer to Appensix A and calculate the milligrams of phenobarbital present in each tablet. We know from Apendix A that, 1 grain = 0.065 g or 65 mg So ¾=0.75 grain= 65×0.75 = 48.75 mg of Phenobarbital Ans: 48.75 mg of Phenobarbital 14. Levothyroxine sodium tablets (SYNTHROID) are available in 12 different strengths ranging from 25 to 300 mcg. Express this range in (a) mg and (b) ng.

(a) 25 mcg = 25 ×10-3 = 0.025 mg 300 mcg = 300 ×10-3 = 0.3 mg Ans: 0.025-0.3 mg (b)

25 mcg = 25× 103 =25000 ng 300 mcg = 300× 103 =300000 ng

Ans: 25,000 – 300,000 ng 15. Norgestrel and ethinyl estradiol tablets are available containing 0.5 mg of norgestrel and 50 µg of ethinyl estradiol. How many grams of each ingredient would be used in making 10,000 tablets? 1 Norgestrel tablet contain = 0.5 mg of Norgesterl 1 Norgestrel tablet contain = 0.5 × 10-3 g of Norgestrel 10,000 Norgestrel tablet contain = 0.5 × 10-3 × 10,000 g of Norgestrel = 5 g of Norgestrel 28

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 Ethinyl estradiol tablet contains = 50 µg of ethinyl estradiol 1 ethinyl estradiol tablet contains = 50 × 10-6 g of ethinyl estradiol 10,000 ethinyl estradiol tablet contains = 50 × 10-6 × 10,000 g = 0.5 g of ethinyl estradiol Ans: 5 g of Norgesterl and 0.5 g of ethinyl estradiol 16. Approximately 0.02% of a 100-mg dose of the drug miglitol (GLYSET) has been shown to appear in human breast milk. Calculate the quantity of drug detected, in milligrams, following a single dose. 100g = 100 × 103 mg of human breast milk contain 0.02 g of drug miglitol = 0.02 × 103 mg of drug miglitol 1 mg of human breast contain =

.

mg = 2 × 10-4 mg of drug migitol

100 mg of human breast contain = 2 × 10-4 × 100 mg of drug migitol = 0.02 mg of drug migitol Ans∶ 0.02 mg of drug migitol 17. How many grams of digoxin (LANOXIN) would be required to make 25,000 tablets each containing 250 mcg of digoxin? 1 tablet contain 250 µg of digoxin 25000 tablets contain = 250 × 25000 µg of digoxin = 6250000 µg of digoxin = 6250 mg of digoxin =6.250 g of digoxin Ans∶ 6.250 g of digoxin 18. Adalimumab (HUMIRA), a recombinant human monoclonal antibody, is available in a prefilled syringe containing 40 mg/0.8 mL of injection. Calculate the concentration of drug on a mg/ mL basis. 0.8 mL of injection contain 40 mg of Adalimumab 29

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 mL of injection contain

.

= 50 mg of Adalimumab ∴ 50 mg/mL Ans∶ 50 mg/mL 19. If an injectable solution contains 25 mcg of a drug substance in each 0.5 mL, how many milliliters would be required to provide a patient with 0.25 mg of the drug substance? 25 µg of drug substance present in = 0.5 mL of injectable solution 25 × 10-3 mg of drug substance present in 0.5 mL of injection solution 1 mg of drug substance present in

.

mL of injection solution

= 20 ml of……………………. 0.25 mg of drug substance present in 20

0.25

of injection solution

= 5 mL of injection solution Ans∶ 5 mL of injection solution 20. A patient is instructed to take one 50-mcg tablets of pergolide mesylate (PERMAX) a day for the first two days of treatment; 150 mcg/day on the third, fourth and fifth days of treatment; 250 mcg/day on the sixth, seventh and eighth days; and 350 mcg on the ninth day and return to the physician for assessment. During this treatment period, . How many milligrams of the drug were taken? For first two days: 50 mcg × 2 = 100 mcg × 10-3 = 0.1 mg For day 3 to 5: 150 mcg×3 = 450 mcg ×10-3 = 0.45 mg For day 6 to 8 = 250 mcg ×3 = 750 mcg ×10-3 = 0.75 mg For ninth day = 350 mcg ×1 = 350 mcg ×10-3 = 0.350 mg Total drug patient were taken = 0.1+0.45+0.75+0.35 = 1.65 mg Ans: 1.65 mg 21. An oral liquid concentrate of sertraline hydrochloride (ZOLOFT) contains 20 mg/mL of the drug. How many grams of sertraline hydrochloride are in each 60-mL container of the concentrate? 30

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 mL of oral liquid concentrate of sertraline hydrochloride contain 20 mg of drug 60 mL of liquid concentrate of sertraline hydrochloride contain 60 × 20 mg of drug = 1200 mg of drug = 1.2 g of drug Ans∶ 1.2 g of drug 22. Digoxin (LANOXIN) is available for parenteral pediatric use in a concentration of 0.1 mg/mL. How many milliliters would provide a dose of 40 µg?

0.1 mg of digoxin available in = 1 mL of parenteral paediatric 0.1 × 103=100 µg of digoxin available in= 1 mL of parenteral paediatric So, 40 µg of digoxin available in

40

parenteral paediatric

= 0.4 mL of parenteral paediatric Ans∶ 0.4 mL of parenteral paediatric

23. A liquid oral concentrate of morphine sulfate contains 2.4 g of morphine sulfate in a 120mL bottle. Calculate the concentration of morphine sulfate on a mg/mL basis. 120 mL of bottle contain 2.4 g of morphine sulfate = 2.4 × 103 mg of morphine sulfate 1 mL of bottle contain

.

mg of morphine sulfate

= 20 mg of morphine sulfate Ans∶ 20 mg/mL 24. The starting dose of Sodium Oxybate oral solution (XYREM) is 4.5 g/night divided into two equal doses and administered 2.5 to 4 hr apart. How many milliliters of the oral solution containing sodium oxybate, 500 mg/ml, should be administered in each divided dose? 31

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 4.5 g/night divided into two doses So, each divided dose require =4.5/2 = 2.25 g of Sodium Oxybate 0.5 g of drug present in 1 ml of oral solution So, 2.25 of drug present in = 2.25/0.5 =4.5 ml of oral solution Ans∶ 4.5 mL of solution. 25. An intravenous solution contains 500 µg of a drug substance in each milliliter.How many milligrams of the drug would a patient receive from the intravenousinfusion of a liter of the solution? 1 mL of intravenous solution contain = 500µg of drug substance 1L=1000 mL of intravenous solution contain=500 × 1000 µg of drug substance = 500000µg = 500000 × 10-3 mg of drug substance = 500 mg of drug substance Ans∶ 500 mg of drug substance 26. If an intravenous solution containing 123 mg of a drug substance in each 250-mL bottle is to be administered at the rate of 200 µg of drug per minute, how many milliliters of the solution would be given per hour? Patient should administered 200 µg of drug/minute Patient should administered 200 × 60 µg drug/ hour = 12000 µg drug/hour = 12000 × 10-3 mg drug/hour = 12 mg drug/hour 123 mg of drug substance present in 250 mL bottle 12 mg of drug substance present in

12 mL bottle = 24.39 mL bottle (ans)

32

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 27. An oral inhalation (DULERA) to treat asthma provides, in each inhalation, 100 mcg of mometasone furoate and 5 mcg of formoterol fumarate. The recommended dose is two inhalations twice daily (morning and evening). Calculate the quantity of each drug inhaled daily and express the answers in milligrams. Recommended dose = 2 inhalation twice daily So 4 inhalation is required for each drug. For mometasone furoate = 4×100 mcg = 400 mcg = 0.4 mg For formoterol fumarate = 4×5 mcg = 20 mcg = 0.02 mg Ans: 0.4 mg mometasone furoate and 0.02 mg formoterol fumarate 28. One milligram of streptomycin sulfate contains the antibiotic activity of 650 mcg of streptomycin base. How many grams of streptomycin sulfate would be the equivalent of 1 µg of streptomycin base? 650 µg of streptomycin base present in = 1 mg of streptomycin sulfate 650 × 10-6 g streptomycin base present in= 1 × 10-3 g of streptomycin sulfate So, 1 g of streptomycin base present in

g of streptomycin sulfate

= 1.538 g Ans∶ 1.53 g of streptomycin sulfate 29. A commercial package contains thirty-six 200-mg tablets of ibuprofen. How many kilograms of ibuprofen were used in the manufacture of 1000 packages of the product?

1 commercial package contain = 36 × 200mg of ibuprofen = 7200 mg of ibuprofen 1000 commercial packages contain =1000 × 7200 mg of ibuprofen = 7200000 mg of ibuprofen = 7200000 × 10-3 g of ibuprofen = 7200000 × 10-3 × 10-3 kg of ibuprofen = 7.2 kg of ibuprofen 33

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans∶ 7.2 kg of ibuprofen 30. A gas chromatographic column measures 1.8 m in length and 3 mm in internal diameter. Convert these measurements to inches. A gas chromatographic column measure 1.8 m in length and 3 mm in internal diameter A gas chromatographic column measure 1.8 ×100 cm in length and 3 × 10-3 m in internal diameter A gas chromatographic column measure 180 cm in length and 3 × 10-3 × 100 cm in internal diameter A gas chromatographic column measure 180 × 0.3937 inch in length and 0.3 cm in internal diameter A gas chromatographic column measure 70.86 inch in length and 0.3 × 0.3937 inch in internal diameter A gas chromatographic column measure 70.86 inch in length and 0.11871 inch in internal diameter (ans)

We know 1 cm = 0.3937 inch from scientific calculation 31. A prefilled syringe contains 20 mg of drug in 2 mL of solution. How many micrograms of drug would be administered by an injection of 0.5 mL of the solution? 2 mL of solution contain 20 mg of drug = 20 × 103 µg of drug .

0.5 mL of solution contain

µg of drug

= 5000 µg of drug Ans∶ 5000 µg of drug 32. A vial contains 80 mg of drug in 2 mL of injection. How many milliliters of the injection should be administered to obtain 0.02 g of drug? 80 mg of drug present in 2 mL of vial 0.02 g = 20 mg of drug present in

20

vial

= 0.5 mL vial (ans) 34

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 33. One-half liter of solution for intrave nous infusion contains 2 g of drug. How many milliliters of the solution would contain 0.5 mg of drug? 2 g = 2000 mg of drug present in 500 mL of solution 0.5 mg of drug present in

0.5

of solution

= 0.125 mL of solution Ans∶ 0.125 mL of solution 34. A 125-mL container of amoxicillin contains 600 mg/5 mL. How many milliliters would be used to administer 400 mg of amoxicillin? 5 mL container contain = 600 mg of amoxicillin 125 mL container contain =

125 mg of amoxicillin

= 15000 mg ……….. 1 mL container contain =

mg of amoxicillin

= 120 mg of amoxicillin ∴ 120 mg of amoxicillin present in 1 mL of container 400 mg of amoxicillin present in

400 mL of container

= 3.33 mL of container Ans∶ 3.33 mL of container 35. An effervescent tablet has the follow ing formula: Acetaminophen 325 mg Calcium Carbonate 280 mg Citric Acid 900 mg Potassium Bicarbonate 300 mg Sodium Bicarbonate 465 mg (a) Calculate the total weight, in grams, of the ingredients in each tablet (b) How many tablets could be made with a supply of 5 kg of acetaminophen? (a) Total weight of 1 tablet = (325+ 280 + 900 + 300 + 465) mg 35

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 2270 mg = 2270 × 10-3 g = 2.27 g Ans∶ 2.27 g (b) 325 mg of acetaminophen present in 1 tablet 5 kg = 5 × 103 × 103 mg of acetaminophen

5

10

10

= 15384 tablet Ans∶ 15384 tablet 36. A new analytic instrument is capable of detecting picogram quantities of a chemical substance. How many times more capable is this instrument than one that can detect nanogram quantities of the same chemical? times = 1000 times Ans∶ 1000 times 37. The dimensions of a nicotine transdermal patch system are 4.7 cm by 4.8 cm. Express these dimensions in corresponding inches if 1 inch is equiva lent to 25.4 mm. The dimension of a nicotine transdermal patch system are 4.7 cm by 4.8 cm The dimension of nicotine transdermal patch =

.

.

. .

1000

1000

= 47 mm by 48 mm =

.

.

= 1.85 inch by 1.88 inch Ans∶ 1.85 inch by 1.88 inch

36

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 38. If an albuterol inhaler contains 18 mg of albuterol, how many inhalation doses can be delivered if each inhala tion-dose contains 90 µg?

30 µg of drug delivered by = 1 inhalation 18mg=18×103µg=18000µg of drug delivered by =

18000 inhalation

= 200 inhalation = 200 dose Ans∶ 200 dose 39. Acetaminophen, in amounts greater than 4 g per day, has been associated with liver toxicity. What is the maximum number of 500-mg tablets of acetaminophen that a person may take daily and not reach the toxic level? Acetaminophen, in amount greater than 4g =4000 mg per day has become associated with liver toxicity 1 tablet contain = 500 mg ∴ = 8 tablets Ans∶ 8 tablets 40. Prochlorperazine (COMPAZINE) for injection is available in 10-mL multiple dose vials containing 5 mg/ml. How many 2-mg doses can be with drawn from the vial? 1 mL of vial contain 5 mg of drug 10 mL of vial contain 5 × 10 mg of drug = 50 mg of drug 2 mg dose can be withdrawn from the vial =

dose

= 25 dose Ans∶ 25 dose 37

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 41. The recommended dose for a brand of nicotine patch is one 21-mg dose per day for 6 weeks, followed by 14 mg per day for 2 weeks, and then 7 mg per day for 2 more weeks. What total quantity, in grams, would a patient receive during this course of treatment? Total quantity of drug administered by patent during course of treatment = {(21 × 6 × 7) + (14 × 2 × 7) + ( 7 × 14)} mg = 1176 mg of drug = 1176 × 10-3 g of drug = 1.176 g of drug Ans∶ 1.176 g of drug 42. A medical device is sterilized by gamma radiation at 2.5 megarads (Mrad). Express the equivalent quantity in rads. 1 megarads = 1 × 106 red 2.5 megarads = 2.5 × 106 rad = 2500000 rad Ans∶ 2500000 rad 43. A round transdermal patch measures 4.3 cm in diameter. Convert this dimension to inches and millimeters. 4.3 cm = 4.3 × 0.3937 inch (1 cm = 0.3937 inch) = 1.6929 inch Ans∶ 1.6929 Again, 4.3 cm =

.

10

(100 cm = 1 m)

= 43 mm Ans∶ 43 mm 44. A solution for direct IV bolus injection contains 125 mg of drug in each 25 mL of injection. What is the concen tration of drug in terms of µg/µ L? 38

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 25 mL of injection contain

= 125 mg of drug

25 × 103 µl of injection contain = 125 × 103 µg of drug 1 µL of injection contain

=

of drug

= 5 mcg So, 5 µg/µL Ans∶ 5 µg/µL

45. The total number of human genomic characters is 3.5 billion. Express this quantity numerically without using a decimal point. 3.5 billion: numerically = 3.5 ×1000000000 = 3500000000 (ans) decimal point = 3500000000 = 3.5 ×108 (ans) 46. Conjugated estrogens tablets (PREMARIN) are available in strength of 0.3 mg, 0.45 mg, 0.625 mg, 0.9 mg and 1.25 mg. if patient ―A‖ took one tablet daily of the lowest dose and patient B took one tablet daily in the highest dose, what is the difference in the total quantities taken between patients A and B over a period of 30 days? (a) 2.85 mg (b) 2850 mg (c) 2.85 cg (d) 2.85 dg Patient “A” takes lowest dose = 0.3 mg /day = 0.3 × 30 mg/30days = 9 mg Patient “B” takes lowest dose = 1.25 mg/day = 1.25 × 30 mg/30 days = 37.5 mg Differencw: 37.5 mg-9 mg = 28.5 mg Ans: 28.5 mg 39

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 47. Teratogenic studies of insulin glargine were undertaken in rats at doses up to 0.36 mg/kg/day. This is equivalent to which of the following? (a) 360 cg/lb/day (b) 792 mcg/lb/day (c) 360 mg/lb/day (d) 163.6 mcg/lb/day

(a) 360 cg/lb/day = 360 × 10-2 × 103 mg/0.4535 kg/day = 360 × 10-2 × 103 × 0.4535 kg/µg/day = 3600 mg/kg/day (b) 792 mcg/lb/day = 792 × 10-3 mg /0.4535 kg/day = 792 mg /0.4525kg/day = 792 × 0.4535 mg/kg/day = 359.172 mg/kg/day (c) 360 mg/lb/day = 360 mg/0.4535 kg/day = 360 × 0.4535 mg/kg/day = 163.26 mg/kg/day (d) 163.6 µg/lb/day = 163.6 × 10-3 mg/0.4535 kg/day = 0.163 × 0.4535 mg/kg/day = 0.0741 mg/kg/day 40

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans∶ (d) 163.6 µg/lb/day 48. Pharmacy students, traveling to attend a national pharmacy meeting, were on an airplane with an average air speed of 414 miles per hour. Which is the closest equivalent air speed? (a) 6 mi/min (b) 257 km/h (c) 666 km/h (d) 180 m/sec 1 km = 0.621 miles Average air speed of aeroplane = 414 miles/hour (a )

6 mile/min = 6 × 60 mile/hour = 360 mile/hour

(b) 257 km/h 257 × 0.621 mile/hour = 159.59 mile/hour (c) 666 km/h 666 × 0.621 mile/hour = 413.50 mile/hour (d) 180 m/sec = = 0.18 × 60 × 60 km/h = 648 km/h = 648 × 0.621 mile/h 41

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 402.4 mile/hour Ans∶ (c) 666 km/hour 49. The product of biotechnology, filgrastim (NEUPOGEN), is available in vials containing 0.3 mg of drug in each milliliter. Which choice is equivalent in concentration? (a) 0.03 mg/0.1 dL (b) 300 mcg/0.01 dL (c) 3 mcg/0.01 cL (d) 300 mcg/10 cL

Vial contain 0.3 mg of drug /millilitre (a) 1 dl contain 0.03 mg of drug 10-1 ×103 = 100 mL contain 0.03 mg of drug 1 mL contain

.

of drug

= 3 × 10-4 mg of drug (b) 0.01 dl contain = 300 µg of drug 0.01 × 10-1 × 103 mL contain = 300 × 10-3 mg 1 mL contain 0.3 mg Ans∶ 0.3 mg (c) 0.01 cL contain

= 3 µg of drug

0.01 × 10-2 × 103 mL contain = 2 × 10-3 mg of drug 0.1 mL contain 3× 10-3 mg of drug 1 mL contain

.

mg of drug

= 0.03 mg of drug (d) 42

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 10 cL contain 300 µg of drug 10 × 10-2 × 103 mL contain 300 × 10-3 mg of drug 100 mL contain 0.3 mg of drug 1 mL contain

.

of drug

= 3 × 10-3 mg of drug Ans∶ (b) 300 µg/0.01 dL 50. In a clinical study of finasteride (PROSCAR), a single oral dose of 5 mg resulted in an average blood concentration of 37 ng of drug per milliliter (37 ng/mL) of blood plasma. This is equivalent to which of the following? (a) 37,000 mcg/mL (b) 0.037 mcg/mL (c) 0.000037 mg/cL (d) 0.0037 mcg/dL Dose = 37 ng/mL = 37 × 10-6

mg/mL

= 3.7 × 10-5 mg/mL (a) 1 mL contain 37000µg of drug 1 mL contain 37000 × 10-6 g of drug = 0.037 g of drug = 0.037 × 103 mg of drug = 37 mg of drug ∴ 37 mg/mL

(answer)

CALCQUIZ 2.A. A health-news story that received widespread attention in recent years involved the successful premature birth of octuplets. The eight babies ranged in weight from 1 43

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION lb 8 oz to 3 lb 4 oz. Using the equivalents for the Avoirdupois system given in this chapter, Calculate the babies range in weight, in grams and in kilograms. We know that 1 lb = 0.454 kg 1

ounce = 28.35gm

So, 8 ounce = 8×28.35 = 226.8 g = 226.8×10-3 kg = 0.2268 kg 3lb = 3×0.454 kg = 1.362 kg 4 oz = 4×28.35 g = 113.4 g = 113.4×10-3 kg = 0.1134 kg So, babies range in weight (kg) = (0.454 + 0.2268) kg to (1.362 + 0.1134) kg = 0.680 kg to 1.475 kg So, babies range in weight (g) = 0.680 ×1000 g to 1.475×1000 g = 680 g to 1475 g Ans: babies range in weight (kg) = 0.680 kg to 1.475 kg babies range in weight (g) = 680 g to 1475 g 2.B. Levothyroxine sodium tablets are available in 11 different strengths, ranging from 0.025 mg to 200 mcg. Calculate the difference, in micrograms, between these two strengths.

Strengths of Levothyroxine sodium tablets from 0.025 mg to 200 microgram = 0.025×103 mcg to 200 mcg = 25 mcg to 200 mcg Ans: 25 mcg to 200 mcg 2.C. An inhalation aerosol contains 0.03 g of albuterol sulfate per canister and is labeled to deliver 200 full inhalations. If each inhalation contains 108 mcg of 44

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION albuterol sulfate, how many milligrams of drug would remain in the canister? 1 inhalation contains

= 108 mcg of Albuterol sulfate

So, 200 inhalation contains = 200×108 mcg of ……. = 21600 mcg of ……. = 21600/1000 mg of ……. = 21.6 mg of Albuterol sulfate Ans: Canister contain 21.6 mg of Albuterol sulfate. 2.D. A 0.5 ml container of an investigational ophthalmic solution contains a drug in a concentration of 0.01 mg/ml. How many micrograms of drug would be administered in a 50 µL drop? We know that 1 ml = 1000 microliter 1000 µL ophthalmic solution contain = 0.01 mg of drug So, 50 µL …………………………. =

.

mg of drug

= 0.0005 mg of drug = 0.0005 × 1000 µg of drug = 0.5 mg of drug Ans: 0.5 mg of drug 2.E. A long acting formulation of leuprolide acetate requires injection only once every 3 months. Clinical studies revealed that 4 hours following a single injection. The mean blood plasma level of leuprolide was 36.3 ng/ml and dropped over the next month to a steady level of 23.9 ng/mL. Express the difference between these the two values in µg/dL. Mean blood plasma level = 36.3 ng/ml 45

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION =

.

µg/dL

= 3.63 µg/dL Steady level = 23.9 ng/ml =

.

µg/dL

= 2.39 µg/dL Ans: Mean blood plasma level = 3.63 µg/dL and Steady level = 2.39 µg/dL

46

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

CHAPTER :03 PHARMACEUTICAL MEASUREMENT Basic concept: Weighing by aliquot method:

= smallest quantity Example: On a balance with an SR of 6 mg, and with an acceptable error of no greater than 5%, a quantity of not less than 120 mg must be weighed. = 120 mg

Percentage of error:

Just basic concept: Meassure must be greater than S.M.Q or equivalent to S.M.Q. API= target ×any number that give result greater than measure or equivalent to measure. To Make = measure × number that has been multiplied with API. Dilute with= To Make - API SOLUTION OF PROBLEMS: 01. A prescription calls for 50 milligrams of chlorpheniramine maleate. Using a prescription balance with a sensitivity requirement of 6 milligrams, explain how you would obtain the required amount of chlorpheniramine maleate with an error not greater than 5%. Sensitivity Requirement = 6 mg Target = 50 mg % error = 5 S.M.Q = = 120 API = 50 × 30 = 1500 D.W = 3600 - 1500 = 2100 T.M = 120 × 30 = 3600 measure =120

Here, S.R= sensitivity requirement API = Active Pharmaceutical Ingradient D.W= dilute with T.M= to make S.M.Q= smallest quantity

47

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 02.A prescription balance has a sensitivity requirement of 0.006 gram. Explain how you would weigh 0.012 gram of atropine sulfate with an error not greater than 5%, using lactose as the diluent. Sensitivity requirement = 0.006 gm = 0.006 ×103 mg = 6 mg Target = 0.012 g = 12 mg % of error = 5 S.M.Q = × 100 = 120 API = 12 × 20 D.W = 2400 – 240 = 2160 To make = 120 × 20 = 2400 Measure = 120 03. A torsion prescription balance has a sensitivity requirement of 4 milligrams. Explain how you would weigh 5 milligrams of hydromorphone hydrochloride with an error not greater than 5%. Use lactose as the diluent. S.R = 4 mg Target = 5 mg %=5 S.M. G = = 80 API = 5 × 20 = 100 D.W 6 − 5 T.M = 80 × 20 = 1600 Measure = 80 04. A torsion prescription balance has a sensitivity requirement of 0.004 gram. Explain how you would weigh 0.008 gram of a substance with an error not greater than 5%. S.R = 0.004 g = 4 mg Target = 8 mg %=5 48

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION S.M.Q = = 80 API = 5 × 30 =150 Diw 24 − 5 225 T.M =80 × 30 = 2400 Measure = 80 05. A prescription balance has a sensitivity requirement of 6.5 milligrams. Explain how you would weigh 20 milligrams of a substance with an error not greater than 2%. S.R = 6.5 mg Target = 20 mg %=2 . S.M.Q = = 325 API = 20 × 20 = 400 D.w 65 − 4 6 T.M = 325 × 20 = 6500 Measure = 325 Calculations of Aliquot Parts by Measuring Volume 06. Sodium Citrate 5g Tartar Emetic 0.015 g Cherry Syrup ad 120 mL Using a balance with a sensitivity of 4 mg, an acceptable weighing error of 5% and cherry syrup as the solvent for tartar emetic, how could you obtain the correct quantity of tartar emetic to fill the prescription? Target = 0.4 mL S.M.Q = 1 mL D.W= 10-2 = 8 ml API = 0.4 × 5 = 2 mL T.M – 2 × 5 = 10 Measure = 2 mL 07. A formula calls for 0.6 milliliter of a coloring solution. Using a 10-milliliter graduate calibrated from 2 to 10 milliliters in 1-milliliter units, how could you obtain the desired quantity of the coloring solu- tion by the aliquot method? Use water as the diluent. Target = 0.6 mL 49

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION S.M.Q = 1 mL API = 0.6 × 5 = 3 mL D.w = 10 – 3 =7 mL T.M = 2 × 5 = 10 Measure = 2 mL 08. Using a 10-milliliter graduate calibrated in 1-milliliter units, explain how you would measure 1.25 milliliters of a dye solution by the aliquot method. Use water as the diluent Target = 1.25 S. M. Q = 1 mL API = 1.24 × 4 = 5 mL D.w = 8 – 5 = 3 T.M = 2 × 4 = 8 Measure = 2 mL 09. The formula for 100 milliliters of pentobarbital sodium elixir calls for 0.75 millil- iter oforange oil. Using alcohol as a diluent and a 10-milliliter graduate calibrated in 1milliliter units,how could you obtain the desired quantity of orange oil? Target = 0.75 mL S.M.Q = 1 mL D.W= 8-3 = 5 API = 0.75 × 4 = 3 mL T.M = 2 × 4 = 8 mL Measure = 2 mL 10. A pharmacist attempts to weigh 120 milligrams of codeine sulfate on a balance with a sensitivity requirement of 6 milligrams. Calculate the maximum potential error in terms of percentage. %=? desire = 120 mg S.R = 6 mg S.M.Q = =5% Ans∶ 5 11. In compounding a prescription, a pharmacist weighed 0.050 gram of a substance on a balance insensitive to quantities smaller than 0.004 gram. What was the maximum potential error in terms of percentage? Error in volume = 0.050 – 0.004 50

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 0.046 % of error =

. .

% of error =

. = 92 % (100 – 92) % = 8% (ans)

12. A pharmacist weighed 475 milligrams of a substance on a balance of dubious accuracy. When checked on a balance of high accuracy, the weight was found to be 445 milligrams. Calculate the percentage of error in the first weighing. % of error = = 6.32 % Ans∶ 6.32 % 13. A 10-milliliter graduate weighs 42.745 grams. When 5 milliliters of distilled water are measured in it, the combined weight of graduate and water is 47.675 grams. By definition, 5 milliliters of water should weigh 5 grams. Calculate the weight of the measured water and express any deviation from 5 grams as percentage of error.

47.675 – 43.745 = 4.93 ∴

.

of error

= 1.4 % Ans∶ .4 14. A graduate weighs 35.825 grams. When 10 milliliters of water are measured in it, the weight of the graduate and water is 45.835 grams. Calculate the weight of the water and express any deviation from 10 grams as percentage of error. 45.835 – 35.825 = 10.01 ∴

of error

.

= 0.1 % 51

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans∶ . 15. A pharmacist attempts to weigh 0.375 gram of morphine sulfate on a balance of dubious accuracy. When checked on a highly accurate balance, the weight is found to be 0.400 gram. Calculate the percentage of error in the first weighing.

% of error =

.

.

.375 = 6.66 %

Ans∶ 6.66

CALCQUIZ 3. A. A pharmacist receives a prescription for drops, calling for 0.05 ml of glacial acetic acid, 2ml of glycerin, and 8 ml of purified water . Using a 10 ml graduated cylinder calibrated in 0.5ml units, explain how the required quantity of glacial acetic acid could be obtained.

3.B. A Pharmacist quizzes a pharmacy intern on the aliquot method in the preparation of 12 capsules each to contain 80 mg of morphine sulfate and 3.2mg of naltrexone hydrochloride .Lactose is to be used as a diluent, a prescription balance with a sensitivity of 6 mg is proposed , and a 4% error is acceptable . Provide t. the he relevant calculations.

3.C. The aliquot method was used to obtain 8mg of a drug with a prescription 52

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION balance having a sensitivity of 6 mg . A weighing error of 5% was accepted. If 140 mg of the drug were weighed, added to 2.1 g of lactose, and 120mg of the mixture used to provide the required quantity of drug , were the calculations correct or incorrect ?

3.D. In preparing a zinc oxide ointment, 28.35g of zinc oxide were used rather than the correct quantity, 31.1 g . What percentage error was incurred? All of CALCQUIZ is given for you, try yourself if you need any help then you can contact to me [email protected]

53

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION CHAPTER 04: INTERPRETATION OF PRESCRIPTIONS AND MEDICATION ORDERS TABLE4.1: SELECTED ABBREVIATION, ACRONYMS AND SMBOLS USED IN PRESCRIPTION AND MEDICATION ORDER Abbreviation (latin Meaning Abbreviation Meaning gram origin) (latin origin) Prescription filling Gal Gallon direction aa. or (ana) Of each Gtt (gutt) Drop Ad (ad) Up to; to make Lb (libra) Pound Disp. (dispensatur) Dispense Kg Kilogram Div. (dividatur) Divide L Liter d.t.d (denture tales Give of such does M2 or m2 Square meter doses) Ft (fiat) Make Mcg Microgram M. (mice) Mix mEq Milliequevalent No. (numero) Number Mg Milligram Non rep. or NR (non Do not repeat Mg/kg Milligrams (of drug) repatatur) per kilograms (of body weight) q.s. (quantum sufficit) A sufficient Mg/m2 Milligrams (of quantity drug)per square meter (of body surface area) q.s. ad (quantum A sufficient ml Milliliter sufficiat ad) quantity to make Sig. (signa) Write (directions ml/h Milliliter (of drug on label) administered) per hour (as through intravenous administration) Quantities and mOsm or Milliosmole measurement mOsmol BSA Body surface area Oz. Ounce Cm3 Cubic centimeter Pt. Pint or milliliter (ml) 54

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION F or fl (fluidus) g ss (semissem)

Fluid Gram One half

Qt. t.i.d (ter in die) Ut dict (ut dictum) Wk. Medications: APAP

Quart Three times a day As directed

tbsp.. tsp Signa/ patient instruction a.c.(ante cibos) Ad lib. (ad libitum) Admin

tablespoonful Teaspoonful

Before meals At pleasure, freely Administer

ASA AZT EES

A.M. (ante meridiem) Aq. (aqua) ATC b.i.d (bis in die) c (cum) d (die) Dil. (dilutus) Et h.or hr. (hora)

Morning Water Around the clock Twicw a day With Day Dilute

HC HCTZ MTX NTG Clinical BM BP

Aspirin Zidovudine Erythromycin ethylsuccinate Hydrocortisone Hydrochlorothiazide Methotrexate Nitroglycerin

And Hour

BS CHD

h.s.(hora somnil)

At bedtime

CHF

i.c. (inter)

Betwee meals

GERD

Min. (minutum)

Minute

GI

m& n

Morning and night

GFR

N&V

GU

Noct(nocte)

Nausea vomiting Night

Glomerular filtration rate Genitourinary

HA

Headech

NPO(non per os)

Nothing by mouth

HBP

High blood pressure

p.c(post cibos)

After meals

HRT

PM (post meridiem0

Afternoon;evening

HT OR HTN

Hormone replacement therapy Hypertension

and

Week Acetaminophen

Bowel movement Blood pressure Blood sugar Coronary heart disease Congestive heart failure Gastrointestinal reflux Gastrointestinal

55

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION p.o (per os)

By mouth

LOP

Intraocular pressure

p.r.n (pro re nata)

As needed

MI

q(quaque)

Every

OA

Myocardial infarction Osteoarthritis

qAM

Every morning

Pt

Patient

q4h, q8h,etc

Every__hours

SOB

Shortness of breath

q.i.d (quarter in die)

Four times a day

TPN

res. (repetatur)

Repeat

URI

s (sine)

Without

UTI

Total parenteral nutrition Upper respiratory infection Urinary tract infection

s.i.d (seel in die)

Once a day

s.o.s (si opus sit)

If there is needed

Stat. (statim)

Immediately

Dosage /vehicles amp.

form Ampul

Supp.

Suppository

cap.

Capsule

Susp.

Suspension

D5LR

Dextrose 5% in lactated ringer

Syr

Syrup

D5NS

Dextrose normal (0.9% chloride) Dextrose water Dextrose water

5% in saline sodium

Tab

Tablet

5 % in

IVP

Intravenous push

10 % in

IVPB

Intravenous back

D5W D10W

piggy

Elix

Elixir

NGT

Nasogastric tube

Inj.

Injection

p.o or PO

By mouth

NS

Normal saline

Rect

Rectum or rectal 56

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION ½ NS

Half strength normal saline

SL

Sublingual

Oint or ungt

Ointment

SubQ

Subcutaneously

Pulv

Powder

Top

Topically

RL, R/L OR LR

Ringer’s lactate or lactated ringer’s

V or PV

Vaginally

ROUTES OF ADMINISTRATION: CIVI

ID

Continuous (24 hour) intravenous infusion Intradermal

IM

Intramuscular

IT

Intrathecal

IV

Intravenous

IVB

Intravenous bolus

IV drip

Intravenous infusion

57

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

CHAPTER: 05 DENSITY, SPECIFIC GRAVITY, AND SPECIFIC VOLUME Basic concept: Density: The mass density or density of a material is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho). Mathematically, density is defined as mass divided by volume:

where ρ is the density, m is the mass, and V is the volume. Thus, if 10 ml of sulfuric acid weighs 18 g, it’s density is: Density= =1.8 grams per ml Specific gravity: Specific gravity is the ratio of the density of a substance compared to the density (mass of the same unit volume) of a reference substance. Apparentspecific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. specific gravity = thus if 10 ml of sulfuric acid weighs 18 gm , and 10 ml of water, under similar conditions, weighs 10 gm, the specific gravity of acids is:

Specific gravity = = 1.8 Specific volume: Specific volume = 1/S.G 58

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

SOLUTION OF PROBLEMS:

Calculations of Density 1. If 250 mL of alcohol weighs 203 g, what is its density?

We know that, density = = = 0.812 g/mL Ans∶ .81 g/mL

2. A piece of copper metal weighs 53.6 g, and has a volume of 6 mL Calculate its density. We know that, density =

.

Density

= 8.93 g/mL Ans∶ 8.93 g/mL

Calculations of Specific Gravity 3. If 150 mL of a sorbitol solution weigh 170 g, what is its specific gravity? 150 ml represent = 150 g

1

S.G = = 1.13 Ans∶ 1.13

4. If a liter of a cough syrup weighs 1285 g, what is its specific gravity? 59

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION We know that, specific gravity = 1 L = 1000 ml represent =1000 g S.G = S.G =

1 8

= 1. 285 Ans∶ 1. 285 5. If 500 mL of ferric chloride solution weighs 650 g, what is its specific gravity? S.G =

S.G = = = 1.3 Note: 500 mL represent 500 g Ans∶ 1.3 6. If 2 fl. oz. of glycerol weighs 74.1 g, what is its specific gravity? We know that 1 fl.oz = 29.57 ml So 2 fl.oz = 29.57 ×2 = 59.14 ml 59.14 ml represent = 59.14 g S.G =

S.G =

.

. = 1.252 60

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans∶ 1.252 7. Five pints of diluted hydrochloric acid weighs 2.79 kg. Calculate its specificgravity. 1 pint = 16 fl.oz 5 pint = 80 fl.oz = 80 × 29.5.7 mL = 2365.6 mL that represent 2365.6 g And 2.79 kg = 2.79×103 g S.G =

.

∴ S.G

.

= 1.179 Ans∶ 1.179 08. A pycnometer weighs 21.62 g. filled with water, it weighs 46.71 g; filled with another liquid, it weighs 43.28 g. calculate the specific gravity of the liquid? Specific gravity = = =

.

.

.

.

. .

= 0.893 Ans∶ 0.893 Here,

61

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION W1 = 21.62 g W2 = 46.71 g W3 = 43.38 g 09. A modified Ringer's Irrigation has the following formula: Sodium chloride 8.6 g Potassium chloride 0.3 g Calcium chloride 0.33 g PEG 3350 60 g Water for injection ad 1000 mL Assuming that 980 mL of water is used in preparing the irrigation, calculate its specific gravity.

.

8

.

.

8.

1 1.

Ans∶ 1.049

Calculations of Weight or Volume Using Specific Gravity Note: Use the information in Table 5.1 if necessary. 10. Calculate the weight, in grams, of 100 mL of each of the following: (a) acetone (b) liquid petrolatum (c) syrup (d) nitroglycerin (e) mercury (a) S.G of acetone = 0.79 S.G = weigh = S.G × V = 100 × 0.79 62

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 79 g Ans∶ 79 g (b) S.G of petroleum = 0.87 weigh = 0.87 × 100 = 87 g Ans∶ 87 g (c) S.G of syrup = 1.31 weigh = 1.31 × 100 = 131 g Ans∶ 131 g (d) S.G og nitroglycerin = 1.59 weigh = 1.59 × 100 = 159 g Ans∶ 159 g (e) S.G of Mercury = 13.6 weigh = 13.6 × 100 = 1360 g Ans∶ 1360 g 11. What is the weight, in kilograms, of 5 liters of sulfuric acid with a specific gravity of 1.84?

S.G = weigh = 1.84 × 5000 = 9200 g = 9.2 kg Ans∶ 9.2 kg

63

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 18. What is the weight, in pounds, of 5 pints of nitric acid? 1 pint = 16 FL.OZ 5 pint = 80 FL.OZ = 80 × 29.57 mL = 2365.6 mL S.G of nitric acid = 1.42 weigh = 1.42 × 2365.6 = 3358.3 g 1 pound = 454 g ∴ weigh in pound

.

= 7.3916 Ans∶ 7.3916 pound 13. What is the weight, in kilograms, of 1 gallon of sorbitol solution having a specific gravity of 1.285? 1 gallon = 4545 mL weigh = S.G ×volume in gram weigh = 4545 × 1.285 = 5840 = 5.84 kg Ans∶ 5.84 kg 14. If 500 mL of mineral oil is used to prepare a liter of mineral oil emulsion, how many grams of the oil, having a specific gravity of 0.87, would be used in the preparation of 1 gallon of the emulsion? 1 gallon = 3785 mL To prepare 1000 ml of emulsion = 500 ml of mineral oil is needed. 64

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION So, to prepare 3785 ml of emulsion = = 1892.5 ml S.G = ∴ weigh

. .8 18 . = 1646.47 g

Ans∶ 1646.7 g 15. Calculate the volume, in milliliters, of 100 g of each of the following: (a) peanut oil (b) castor oil (c) polysorbate 80 (d) phosphoric acid (e) mercury (a) S.G of peanut oil = 0.92 volume

=

.

=

. = 108.69 mL

Ans∶ 108.69 mL (b) S.G of castor oil = 0.96 ∴ volume

=

. = 104.16

Ans∶ 104.16 (c) S.G of polysorbate 80 = 1.08 volume =

. 8 = 92.59 mL Ans∶ 92.59 mL 65

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION (d) S.G of phosphoric acid = 1.70 volume =

. = 58.8 mL Ans∶ 58.8 mL

(e) S.G of mercury = 13.6 Volume

=

1 . = 7.35

Ans∶ 7.35 16. What is the volume, in milliliters, of 1 lb of benzyl benzoate having a specific gravity of 1.120? Weight = 1 lb = 454 g S.G = 1.83 Volume =

.8 = 248.08 mL

Ans∶ 248.08 mL 17. What is the volume, in milliliters, of 1 kg of sulfuric acid with a specific gravity of 1.83? Weigh = 1 kg = 1000 g S.G = 1.83 S.G= weigh/volume Volume = Ans∶

1

. = 546.44 mL .44 mL

66

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 18. Calculate the corresponding weights of liquefied phenol and propylene glycol needed to prepare 24 15-mL bottles of the following formula for a cold sore topical liquid: Liquefied phenol 0.4 mL Camphor 0.5 g Benzocaine 2.2 g Ethanol 65 mL Propylene glycol 17 mL Purified water ad 100 mL Total volume 24 × 15 = 360 mL 100 mL of water = 0.4 mL phenol w = S.G × V = 0.4 × 1.07 = 0.428 g Phenol: Now, 100 mL contain 0.428 g phenol . 1 mL contain 1 . 360 mL contain g of phenol = 1.54 g phenol Ans∶ 1.54 g phenol Propylene glycol Again, 17 mL represents 17 g 100 mL contain 17 g Glycol 1 mL contain

1

360 mL contain = 16.2 g Ans∶ 16.2 g

67

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 19. Calculate the total weight of the following formula for a pediatric chewable gummy gel base for medication. Gelatin 43.4 g Glycerin 155 mL Purified Water 21.6 mL

Weight of the Gelatin = 43.4 g Weight of the Glycerin =volume × S.G =155 ×1.25 = 193.79 g Weight of the purified water = 21.6 g ∴ Total weight . 1 . 1. = 258.75 g Ans∶ 258.75 g 20. Calculate the number of milliliters of polysorbate 80 required to prepare 48, 100-g tubes of the following formula for a progesterone vaginal cream. Progesterone, micronized

3g

Polysorbate 80 Methylcellulose 2% Gel

1g 96 g

Total weight of polysorbate 80 = 48 × 1 = 48 g S.G of poiysorbate 80 = 1.03 So, volume = =

= 44.47

.

.

ml answer 68

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 21. If fifty glycerin suppositories are made from the following formula, how many milliliters of glycerin, having a specific gravity of 1.25, would be used in the preparation of 96 suppositories? Glycerin Sodium stearate Purified water

91 g 9g 5g

Weight of 50 glycerin suppositories =91 g volume =

.

=

. = 72.8 mL 50 glycerin suppositories contain 72.8 mL . 1 glycerin suppositories contain mL

96 glycerin suppositories contain

.8

mL

= 139.77 mL Ans∶ 139.77 mL

22. Two 10-mL samples of urine have specific gravities of 1.003 and 1.030. What is the difference in weight, in milligrams, between the two samples? Weigh 1 = 10 × 1.003 = 10.03 Weigh 2 = 10 × 1.030 = 10.30 Difference of weigh = (10.3 – 10.03) = 0.27 g = 270 mg Ans∶ 270 mg

69

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 23.

Testosterone propionate 2 g

Mineral Oil, light 10 g Polysorbate 80 1g Methylcellulose 2% gel 87 g The specific gravity of light mineral oil is 0.85 and that of polysorbate 80 is 1.08. Calculate the milliliters of each needed to fill the prescription. Volume of mineral oil = . = 11.76 mL Volume of polysorbate 80 ml . = 0.93 mL Ans∶ 11.76 ml mineral oil and 0.93 mL polysorbate 80. 24. A formula for an anesthetic ointment is: Benzocaine 200 g Polyethylene glycol400 600g Polyethylene glycol3350 ad 1000 g Polyethylene glycol 400 is a liquid, sp. gr, 1.13, benzocaine and polyethylene glycol 3350 are powders. How many millilitres of polyethylene glycol would be used in the formula? Amount of Polyethylene glycol required = weight/Sp.Gr = 600/1.13 = 530.97 ml Ans: 530.97 ml

Calculations of Drug Costs Using Specific Gravity: 25. The formula for 1000 g of polyethylene glycol ointment calls for 600 g polyethylene glycol 400. At $19.15 per pint, what is the cost of the polyethylene glycol 400, specific gravity 1.140, needed to prepare 4000 g of the ointment? 1000 g of PEG ointment = 600 g PEG 400 1 g of PEG ointment

=

g PEG 400 70

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 4000 g of PEG ointment =

g PEG 400

= 2400 g Volume =

.

=

. = 2105.26 mL 1 pint = 16 Fl.Oz = 16 × 29.57 mL = 473.12 mL 473 mL of the ointment cost = 19.15 USD . 1 mL of the ointment cost = . 2105 mL of the ointment cost =

USD

= 85.22 USD Ans∶ 85.22 USD

CALCQUIZ 5.A. Syrup, USP is prepared by dissolving 850 g of sucrose in sufficient purified water to make 1000 ml of syrup. Syrup has a specific gravity of 1.31. How many milliliters of water are used to prepare a liter of syrup? Sucrose = 850 g, Specific gravity = 1.31 So, volume of sucrose = W/Specific gravity = 850/1.31 = 648.85 ml So, ml of water used to prepare a liter of syrup = 1000-648.85 = 351.15 ml Ans: 351.15 ml of water 5.B. A saturated solution of potassium iodide contains, in each 100 ml, 100 g of potassium iodide. The solubility of potassium iodide is 1 g in 0.7 ml of water. Calculate the specific gravity of the saturated solution. 71

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Specific Gravity = w/v = 100/100 = 1 Ans: 1 5.C. Cocoa butter (Theobroma oil) is used as a suppository base. It is a solid at room temperature, melts at 340 C, and has a specific gravity of 0.86. If a formula for medicated suppositories calls for 48 mL of Theobroma oil, how many grams are equivalent? Specific gravity of Cocoa butter = 0.86 Volume = 48 ml We know that, Specific gravity = w/v So, w = v×specific gravity = 48×0.86 = 41.28 g Ans: 41.28 g

72

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

CHAPTER 06: PERCENTAGE, RATIO STRENGTH, AND OTHER EXPRESSION OF CONCENTRATION Basic concept: Percentage: a percentage is a number or ratio as a fraction of 100. It is often denoted using the percent sign, “%”, or the abbreviation “pct.” For example, 45% (read as “forty-five percent”) is equal to 45/100, or 0.45. Percentage of weight in volume: Another variation on percentage concentration is weight/volume percent or mass/volume percent. This variation measures the amount of solute in grams but measures the amount of solution in milliliters. An example would be a 5%(w/v) NaCl solution. It contains 5 g of NaCl for every 100. mL of solution Volume percentage =

×100

Percentage of volume in volume: Volume-Volume percentage (v/v %) is a measure of concentration of a substance in solution expressed as the ratio of the volume of the solution to the total volume of the solution multiplied by 100%. Volume percentage =

×100

Wine has a typical value of alcohol content v/v % of 12%. This means there is 12 mL of ethanol for every 100 mL of wine. Percentage of weight in weight : Weight percentage =

×100

Ratio strength: 73

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION A ratio is a comparison of two similar quantity by the other. Ratio are written with the : symbol Example: the ratio of 6 to 3 is 6÷ 3 = 6/3 = 6: 3 = 2 The ratio of 3 to 6 is 3÷6 = 3/6 = 3:6 = ½ PARTS PER MILLION (PPM) AND PARTS PER BILLION (PPB): PPM: Parts per million also can beexpressed as milligrams per liter (mg/L). This measurement is the mass of a chemical or contaminate per unit volume of water. Seeing ppm or mg/L on a lab report means the same thing. PPB: measurement is parts per billion (ppb). One ppb is one part in 1 billion. One drop of ink in one of the largest tanker trucks used to haul gasoline would be an ink concentration of 1 ppb. For example: • 1 ppm = 1 mg/L = 1/1 million = 0.000001 • 1 ppb = 1 μg/L =1/1 billion = 0.000000001

SOLUTION OF PROBLEM: Weight-in-Volume Calculations 1.. CLOBEX lotion contains 0.05% w/v clobetasol propionate in 118 ml containers. Calculate the content of drug in milligrams

Content of clobetasol propionate =

×118

=0.059 g = 59 mg Ans: 59 mg Or, 0.05% represent, 100 ml of lotion contain 0.05 g of clobetasol propionate So, 118 ml of lotion contain = 0.05/100 ×118 = 0.059 g = 59 mg Ans: 59 mg 74

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 2.

Ofloxacin Ophthalmic Solution 0.3% Disp. 10 mL Sig: 2 drops into eyes q 4 hours ×2 days; then 2 drops q 6 hours ×4 days. A pharmacist filled the prescription with OCUFLOX. How many milligrams of ofloxacin are contained in the dispensed prescription?

= Or,

=

Or, Weigh = = 0.030 g = 30 mg ofloxacin ( answer) 3.

Dexamethasone Sodium Phosphate 100 mg Sterile Water for Injection ad 100 mL Sig: 2 drops into eyes q 4 hours× 2 days; then 2 drops q 6 hours × 4 days. Calculate the percent strength of dexa methasone sodium phosphate in the pre scription. Volume = 100 ml Weigh = 100 mg = 100 x 10-3 g So, Or, = 0.1 Ans: 0.1 % w/v dexamethasone sodium phosphate 4. If 100 mL of a pharmaceutical preparation contains 20 µL of a 50% w/v solution of benzalkonium chloride, what is the percentage strength of that agent in the solution? 75

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 20 microliter = 20 ×10-3 ml = 0.2 ml 100 ml of pharmaceutical preparation contain 50 % w/v of BKC solution 0.02 ml of pharmaceutical preparation contain = BKC solution

% w/v of

= 0.01 %w/v of BKC solution Ans: 0.01 % w/v benzalkonium chloride

5. A tissue plasminogen activator (TPA) ophthalmic solution is prepared to con tain 25 µg/100 µL. (a) Calculate the percentage concentration of TPA in the solution. (b) What volume of a solution containing TPA, 50 mg/50 mL, should be used to prepare each 100 µL of the opthalmic solution? W = 25 µg = 25 × 10-6 g = 2.5 × 10-5g V = 100 µL = 100 × 10-3 ml = 0.1 ml (a)

% w/v TPA 76

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION (b) Solution1 Solution2 So,

g 25 µg = 25 µL = 25 × 10-3 ml = 0.025 ml Ans: 0.025 ml 6. How many milligrams of methylparaben are needed to prepare 8 fluidounces of a solution containing 0.12% (w/v) of methylparaben?

o

v w

77

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

283.872 mg methylparaben 7. If a pharmacist dissolved the contents of eight capsules, each containing 300 mg of clindamycin phosphate, into a sufficient amount of an astringent liquid base to prepare 60 mL of topical solution, what would be the percentage strength (w/v) of clindamycin phosphate in the prescription? Total weight = 8 × 300 mg = 2400 × 10-3 g = 2.4 g V = 600 ml %=?

Ans: 4 %

08. ACULAR (ketorolac tromethamine) Ophthalmic solution 0.5 % Disp. 5 ml Sig: one drop q.i.d prn allergic conjunctivitis How many milligrams of the active ingredient would be present in each drop of the opthalmic solution if the dropper service delivers 20 drops per milliliter (a) 0.25 mg (b) 25 mg (c) 0.025 mg (d) 1.25 mg Amount of Active ingredient in 5 ml solution = 0.5 % × 5 = 0.025 g = 25 mg 78

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 ml of the solution present in 20 drop So 5 ml solution present in 20×5 = 100 drop So, active ingredient present in each drop = 25 /100 = 0.25 mg Ans: (a) each drop deliver 0.25 mg of active ingredients. 9. A formula for an antifungal shampoo contains 2% w/v ketoconazole. How many grams of ketoconazole would be needed to prepare 25 liters of the shampoo?

%=2 V = 25 L = 25 × 103 ml W=?

Ans: 500 g 10. The biotechnology drug interferon gamma-1b (ACTIMMUNE) contains 100 mcg/0.5 mL. Calculate the percentage strength of the solution V = 0.5 ml W = 100 µg = 100 × 10-6 g

0.02 Ans: 0.02 % 79

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 11. NEUPOGEN (filgrastim) prefilled syringes contain 480 mcg of active constituent in each 0.8 mL. The equivalent concentration is: (a) 0.6% (b) 0.384 mg/mL (c) 0.06% (d) 0.6 g/mL (a) 100 ml syringe contain

=0.6 g of active constituent.

1 ml

=

syringe contain

0.8 ml syringe contain

g of active constituent = 4.8 x 10-3 g = 4.8 × 10-3 × 106 mg = 4800 mg

(b) 1 ml of solution contains 0.384 mg of active constituent. 0.8 ml of solution contains 0.384 × 0.8 mg of active constituent. = 0.3072 mg of active constituent. (C) 0.06 % represents 100ml of solution contain

= 0.06 g of active constituent.

0.8 ml of solution contain

=

of active constituent. (d) 1 ml of solution contains 0.8 ml of solution contains

= 0.6 g of active constituents. = 0.6 × 0.8 g 80

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 0.48 g = 480 mg Ans: (c) 0.06 % 12. LEVAQUIN (levofloxacin) injection contains 5 mg/mL of levofloxacin and 5% of dextrose. How much of each would be delivered to a patient upon the administration of a 100mL injection? (a) 5 g levofloxacin and 5 g dextrose (b) 50 mg levofloxacin and 5 g dextrose (c) 500 mg levofloxacin and 500 mg dextrose (d) 0.5 g levofloxacin and 5 g dextrose 1 ml of injection contains 5 mg of levofloxacin. 100 ml of injection contains 5 ×100 mg of levofloxacin. = 500 mg of levofloxacin 100 ml of injection contain 5 g of dextrose Ans: (d) 0.5 g levofloxacin and 5 g dextrose. 13. An injection (ARANESF) contains in each milliliter, 60 mcg of darbepoetin alpha, 0.05 mg of polysorbate80, and 8.18 mg of sodium chloride. Calculate the percent of each in the injection. For Darbepoetin alpha: 60 microgram = 60×10-6 = 6×10-5 Percentage =

×100 = 0.006%

For Polysorbate80: 0.05 mg polysorbate80 = 0.00005 g polysorbate80 Percentage =

×100 = 0.005%

For Sodium chloride: 8.18 mg of sodium chloride = 0.00818 g of NaCl Percentage =

×100 = 0.818% 81

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

14. An injection of adalimumab (HUMIRA) contains 40 mg/0.8 mL. Calculate the percentage concentration of the injection. W = 40 mg = 40 × 10-3g V = 0.8 mL

=5 Ans: 5 % 15. Erythromycin Lactobionate 500 mg Dexamethasone Sodium Phosphate 100 mg Glycerin 2.5 mL Sterile Water for Injection ad 100 mL M. ft. Ophthalmic Solution (a) What is the percentage strength of erythromycin lactobionate in the prescription? (b) If glycerin has a specific gravity of 1.25, what is its concentration (w/v) in the prescription? (a) W = 500 mg = 500 × 10-3 g V = 100 ml

= 0.5 82

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans: 0.5 % (b) Glycerin 2.5 mL

= 3.125 V = 100 mL

= 3.12 Ans: 3.12 % 16. How many milliliters of a 0.9% (w/v) solution of sodium chloride can be pre- pared from 50 tablets, each containing 2.25 g of sodium chloride? Total w = 50 × 2.25 g = 112.5 g V=? % = 0.9 %

= 12,500 mL Ans: 12,500 mL 17. The antibacterial agent moxifloxacin hydrochloride is available in 250 ml bags for intravenous infusion containing 400 mg of drug and 0.8 % w/v sodium chloride. Calculate (a) the percent strength of moxifloxacin hydrochloride and (b) the quantity of sodium chloride in grams in the infusion. 83

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION (a) Percentage of moxifloxacin hydrochloride = ×100 = 0.16 % (ans) (b) Quantity of sodium chloride = ×250 =2g Ans: 2 g of sodium chloride. 18. A prefilled syringe contains 50 mg of lidocaine hydrochloride per 5 mL of injec- tion. Express the percentage concentration of lidocaine hydrochloride in the injection. V = 5 mL W = 50 mg = 50 × 10-3 g %=?

=1 Ans: 1 % 19. A blood volume expansion solution contains 6% (w/v) of hetastarch and 0.9% (w/v) of sodium chloride. How many grams of each agent would be present in 250 mL of the solution?

For hetastarch solution %=6 V = 250 mL W=?

84

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

= 15 g Ans: 15 g For NaCl solution % = 0.9 V = 250 mL W=?

= 2.25 g Ans: 2.25 g 20. A pharmacist adds 10 mL of a 20% (w/v) solution of a drug to 500 mL of D5W for parenteral infusion. What is the percentage strength of the drug in the infusion solution? (a) 2% v/v (b) 2% w/v (c) 1.96% w/v (d) 0.39% w/v 100 mL contain 20 g 1 mL contain 10 mL contain = =2 g 500 mL contain 2 g

85

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 mL contain 100 mL contain = 0.4 % Ans: 0.4 % 21. Calculate the percentage strength of an injection that contains 2 mg of hydromorphone hydrochloride in each milliliter of injection %=? w = 2 mg = 2 × 10-3 g,

v= 1 ml

= 0.2 % Ans: 0.2 % 22. VIRAMUNE Oral Suspension contains 1% w/v of nevirapine. Calculate the milligrams of nevirapine present in a 240 mL bottle of the suspension %=1 W=? V = 240 mL

= 2.4 g = 2.4 × 103 mg = 2400 mg (ANS) 86

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 23. Misoprostol 200-µ g tablets , Lidocaine Hydrochloride Glycerin qs ad

12 tablets 1g 100 mL

Calculate the strength of misoprostol in the prescription. (a) 2.4% w/v misoprostol (b) 0.0002% w/v misoprostol (c) 0.024 mg/mL misoprostol (d) 2.4 mcg/mL misoprostol 1 tablet contain 200 µg of misoprostol 12 tablets contain 200 × 12 µg of misoprostol = 2400 µg misoprostol 100 mL of solution contain = 2400 µg of misoprostol 1 mL of solution contain = 24 µg = 24 × 10-6 g of misoprostol = 24 × 10-6 × 103 mg = 0.024 mg Ans: (c) 0.024 mg/ mL misoprostol. 24. Fentanyl Citrate Bupivacaine Hydrochloride Sodium Chloride

20 µg/mL 0.125 % (0.9%) Injection ad 100 mL

Calculate the percentage concentration of fentanyl citrate in the prescription W = 20 µg = 20 × 10-6 g V = 1 mL

87

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

= 2 × 10-3 = 0.002 Ans: 0.002 % 25. Bepotastine besilate (BEPREVE) ophthalmic solution contains 1.5 % w/v of the therapeutic agent. Express this concentration in mg/ml. 1.5 % w/v solution represents, 1.5 g of bepotastine besilate in 100 ml of solution 1.5 g = 1500 mg, so 1500/100 = 15 mg/ml Ans: 15 mg/ml 26. If 100 mL of a solution for patient-controlled anesthesia contains 200 mg of morphine sulfate and 8 mg of droperidol, calculate the percentage strength of each of these ingredients in the solution. V = 100 mL Wms = 200 mg = 200 × 10-3 g W dr = 8 mg = 8 x 10-3 g % m.s =? % of dr = ?

Ans: 0.2 % morphin sulphate 88

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Again,

= 0.008 % Ans: 0.008 % droperidol 27. Oxycodone hydrochloride oral concentrate solution (OXYFAST) contains 20 mg/ 1 mL. If a dose of 0.75 mL is added to 30 mL of juice prior to administration, calculate (a) the milligrams of oxycodone hydrochloride administered, and (b) the percentage concentration (w/v) of oxycodone hydrochloride in the drink. (a) 1 ml solution contain 20 mg of oxycodone HCl So

ml …………………

mg of oxycodone HCl mg ……………

Ans: 15 mg of oxycodone HCl is administered (b) % of oxycodone HCl in the drink =

×100

= 0.050 % (ans) 28. A morphine sulfate extended-release liposome injection (DEPODUR) contains morphine sulfate 10 mg/mL of injection. Calculate the percentage strength of morphine sulfate in the injection. W = 10 mg = 10 × 10-3 g V = 1 mL %=?

89

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION =1% Ans: 1 % 29. A topical solution contains 3% w/v hydroquinone. How many liters of the solution can be prepared from 30 g of hydroquinone? % = 3, V= ? ,

W= 30 g

So,

= 1000 mL =1L Ans: 1 L

Volume-in-Volume Calculations 30. What is the percentage strength (v/v) if 225 g of a liquid having a specific gravity of 0.8 is added to enough water to make 1.5 liters of the solution? W = 225 g S.G = 0.8 Added volume =

= 281.25 Total volume = 1.5 L = 1500 mL

90

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 18.75 Ans: 18.75 31. How many liters of a mouthwash can be prepared from 100 mL of cinnamon flavour if its concentration is to be 0.5% (v/v)?

= 2000 mL = 20 L Ans: 20 L 32. A lotion vehicle contains 15% (v/v) of glycerin. How much glycerin should be used in preparing 5 gallons of the lotion? (a) 2271 g glycerin (b) 3339.7 mL glycerin (c) 2671.8 g glycerin (d) 3548.4 g glycerin 1 gallon = 3785 mL (USA) 1 gallon = 4545 mL (U.K) 5 gallon = 5 × 4545 mL = 22725 mL 100 mL of lotion contain 15 mL of glycerine 22752 mL of lotion contain

mL of glycerine

= 3408.75 mL of glycerine 3408.75 mL glycerine represent = 3408 g of glycerine. Ans: 3408 g 91

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 33. The formula for 1 litre of an elixir contains 0.25 mL of flavouring oil. What is the percentage (v/v) of the flavouring oil in the elixir? Total volume = 1 L = 1000 mL Added volume = 0.25 mL %=?

= 0.025 % Ans: 0.025% 34. A dermatologic lotion contains 1.25 mL of liquefied phenol in 500 mL. Calculate the percentage (v/v) of liquefied phenol in the lotion. Total volume = 500 mL Added volume = 1.25 mL %=?

= 0.25 Ans: 0.25 %

Weight-in-Weight Calculations 35. Each gram of LOTRISONE lotion contains 10 mg of clotrimazole and 0.643 mg of betamethasone dipropionate. Calculate the percent concentration of each of these two agents in the lotion. 92

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION In case of clotrimazole: 10 mg = 0.01 g Percent concentration =

×100 = 1 % (ans)

In case of betamethasone dipropionate: 0.643 mg = 0.643 /1000 = 0.000643 g Percent concentration =

× 100 = 0.0643 %

36. A hemorroidal ointment contains on a weight in weight basis, 46.6% mineral oil, 1% pramoxine HCl, and 12.5 % zinc oxide in an ointment base. Calculate the grams of each ingredients, including the ointment base, in each 30 g tube. Grams of mineral oil =

×30 = 13.98 g

Grams of pramoxine HCl = Grams of Zinc oxide =

×30 = 0.3 g

×30 = 3.75 g

Grams of ointment base = 30- (13.98+0.3+3.75) = 11.97 g

37. What is the percentage strength (w/w) of a solution made by dissolving 62.5 g of potassium chloride in 187.5 mL of water? Total volume = 62.5 + 187.5 = 250 g

= 25 Ans: 25 % 93

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 38. If 500 g of dextrose are dissolved in 600 mL of water with a resultant final volume of 1 liter, what is the percentage strength of dextrose in the solution on a w/w basis? Total volume = 1100

= 45.45 Ans: 45.45 % 39. Hydromorphone hydrochloride suppositories contain 3 mg of active ingredient and weigh approximately 2 grams each. What is the equivalent percentage strength? (a) 1.5% (b) 0.15% (c) 0.015% (d) none of the above 2 g of hydromorphone hydrochloride suppositories contain = 3 mg of active ingredient = 3 × 10 -3 g of active ingredient ∴ 1 g hydromorphone hydrochloride suppositories contain =

g

∴ 100 g hydromorphone hydrochloride suppositories contain= = 0.15 % Ans: 0.15 %

94

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 40. A metronidazole vaginal gel contains 0.75% of drug in 70-g tubes. An applicator will hold 5 g of gel for each administration. How much drug will be contained in each application? (a) 0.0375 mg metronidazole (b) 3.75 mg metronidazole (c) 37.5 mg metronidazole (d)

375 mg metronidazole

100 g metronidazole vaginal gel contain = 0.75 g of metronidazole 5 g of metronidazole vaginal gel contain =

g of metronidazole

= 0.0375 g of metronidazole = 37.5 mg of metronidazole Ans : (c) 4 1. ZOVIRAX (acyclovir) 5% Cream Lidocaine 4% Cream aa. 15g The percent of acyclovir and quantity of lidocaine in the filled prescription are: (a) 3.75% acyclovir, 0.3 g lidocaine (b) 5% acyclovir, 1.2 g lidocaine (c) 2.5% acyclovir, 0.6 g lidocaine (d) 2.5% acyclovir, 1.2 g lidocaine 100 g of cream contain = 4 g of lidocaine 15 g of cream contain = = 0.6 g of lidocaine Ans: 2.5 % aciclovir , 0.6 g lidocaine. 42. How many grams of hydrocortisone should be used in preparing 120 suppositories, each weighing 2 g and containing 1% of hydrocortisone? 100 g weight of suppositories contain 1 g hydrocortisone 95

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 2 g weight of suppositories contain

g hydrocortisone

= 0.02 g hydrocortisone 1 suppository contain 0.02 g of hydrocortisone 120 suppositories contain 0.02 × 120 g hydrocortisone = 2.4 g Ans: 2.4 g 43. If a topical cream contains 1.8% (w/w) of hydrocortisone, which of the following strengths is equivalent? (a) 2.7 mg hydrocortisone in 15 g of cream (b) 27 mg hydrocortisone in 15 g of cream (c) 0.54 g hydrocortisone in 30 g of cream (d) 54 mg hydrocortisone in 30 g of Cream 100 g of cream contain 1.8 g of hydrocortisone 1 g of cream contain = 0.018 g = 18 mg (a) 15 g cream contain 2.7 mg of hydrocortisone 1 g cream contain = 0.18 mg (b)15 g of cream contain 27 mg of hydrocortisone 1 g of cream contain = 1.8 mg (c) 96

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 30 g of cream contain 0.54 g of hydrocortisone 1 g of cream contain

of hydrocortisone

= 0.018 g = 0.18 X 103 mg = 18 mg (d) 30 g cream contain 54 mg og hydrocortisone 1 g of cream contain = 1.8 mg of hydrocortisone Ans: 0.54 g of hydrocortisone in 30 g cream 44.

Benzoin Tincture 18 mL Peru Balsam 10 g Cold Cream 70 g Sig: cold sore ointment If benzoin tincture has a specific gravity of 0.88, calculate its percentage strength (w/w) in the mixture. (a) 1.26% w/w (b) 25.7% w/w (c) 22.5% w/w (d) 16.5% w/w Weight of Benzoin tincture = 18 × 0.88 = 15.84 g 15.84 g 10 g 70 g Total =95. 84 g

97

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

Ans: 16.52 % 45. Alclometasone dipropionate (ACLO VATE) ointment contains 0.05% w/w of the drug in 15-g and 45-g tubes. Calculate the difference in the quantity of drug between the two tube sizes. Suppose X1 = 15 g tube X2 = 45 g tube

Again, =

∴(X1 – X2) = ( 0.0225 – 2.5× 10-3) = 0.015 g = 0.015 × 103 mg = 15 mg Ans: 15 mg 46. How many grams of azelaic acid (FINA CEA) are contained in 30-g tubes of the 15% w/w ointment?

98

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans: 4.5 g 47. Tretinoin gel (RETIN-A MICRO) is avail able in two strengths: 0.1% w/w and 0.04% w/w. Which of these represents equivalent concentrations of the two strengths? (a) 15 mg/15 g and 30 mg/30 g (b) 5 mg/5 g and 0.06 g/15 g (c) 15 mg/15 g and 60 mg/15 g (d) 30 mg/30 g and 6 mg/15 g 100 g of tretinoin gel contain 0.1 g of RETINA MICRO 1 g of tritinoin get contain = 1 × 10-3 g = 1mg of GETINA MICRO And 100 g 0f tretinoin gel contain o.o4 g of GETINA MICRO 1 g of tretinoin gel contain

g of GETINA MICRO

= 4 × 10-4× 103 mg of GETINA MICRO = 0.4 mg (a) 15 g gel contain = 15 mg of drug 1 g gel contain = = 1 mg And, 30 g gel contain 30 mg 1g gel contain = 1 mg 99

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION (b) 5 g gel contain contain 5 mg of drug 1 g gel contain = 1 mg And 15 g gel contain = 0.06 g 1 g gel contain = = 4 ×10 -3 g = 4 mg (c) 15 g gel contain 15 mg of drug 1 g gel contain = 1 mg And 15 g gel contain 60 mg 1 g gel contain 60 mg 1 g gel contain = 4 mg (d) 30 g of gel contain 30 mg of drugs 1 g of gel certain 30 mg = 1 mg 15 g gel contain 6 mg 1 g gel contain 100

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 0.4 mg of drug. Ans:

Mixed Percent Calculations 48.

Progesterone, micronized 4g Glycerin 5 mL Methylcellulose (1%) Solution 50 mL Cherry Syrup ad 100 mL

(a) What is the percentage concentration (w/v) of progesterone in the prescription? (b) What is the percentage concentration (w/v) of methylcellulose in the prescription? (c) What is the percentage concentration (v/v and w/v) of glycerin (sp gr1.25) in the prescription?

(a) 100 mL of syrup contain 4 g of progesterone 1 mL syrup contain

of progesterone of progesterone

100 mL syrup contain

of progesterone

= 4 g of progesterone 4 % w/v progesterone (ans) (b) Methylcellulose 1% solution represents. 100 mL of solution contain 1 g 0f methylcellulose 5 mL of solution contain

of methylcellulose of methylcellulose

100 mL of syrup contain 0.5 g of methylcellulose 101

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans: 0.5 % (w/v) methylcellulose. (c) 100 mL of syrup contain 5 mL of glycerine. Ans: 5% (v/v) glycerine. And S.G fo glycerine = 1.25 Weight of glycerine in the prescription = volume × S.G = 5 × 1.25 = 6.25 g 100 mL of syrup contain 6.25 g of glycerine ∴

w/v of glycerine an

49. Lactic Acid 4g Salicylic Acid 5g Trichloroacetic Acid 2g Flexible Collodion q.s. ad 100 g Sig: wart remover. Use as directed. (a) Flexible collodion contains 20% w/w camphor and 30% w/w castor oil. How many grams of each would be contained in 30 g of the mixture? (b) The specific gravity of castor oil is 0.955. How many milliliters of the oil are contained in 30 g of the mixture? (c) If the specific gravity of the mixture is 0.781, what are the w/v concentrations of lactic acid, salicylic acid, and trichloroacetic acid in the mixture? Other component present in the mixture = 4 g (Lactic acid) + 5 g (salicylic Acid) + 2 g ( trichloroacetic acid) = 11 g Flexible collidon present in the mixture = (100 – 11) 102

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 89 g 100 g of solution contain 89 g of flexible collidon 1 g of solution contain

of flexible collidon

30 g of solution contain

of flexible collidon

= 26.7 g of flexible collidon Gram of camphor present in the 30 g of the mixture = 20% × 26.7 = = 5.34 g Ans: 5.34 g Gram of castor oil present in the 30 g of the mixture = 30% × 26.7 g = 8.01 g Ans: 8.01 g (b) S.G of castor oil = 0.955 Weight of castor oil in 30 g of the mixture = 8.01 g ∴ Volume of ca tor oil in the

g of mixture =

Ans: 8.387 mL (c) Weight of the mixture = 100 g S.G of the mixture

= 0.781 103

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION ∴volume of mixture = 128.04 mL 128.04 mL mixture contain 4 g of lactic acid 100 mL mixture contain =

of lactic acid

= 3.124 g ∴

of lactic acid

128.04 mL of mixture contain 5 g of salicylic acid 100 mL of mixture contain = 3.90 g ∴

of alicylic acid

128.04 mL of mixture contain 2 g of trichloro acetic acid 100 mL of mixture contain = 1.56 g ∴

of trichloroaceticacid of trichloro acetic acid

of trichloro acetic acid

Ans: 3.124 % lactic acid 3.90 % salicylic acid 1.56 % trichloroaceticacid Ratio strength calculation: 50. Express each of the following as a percentage strength: a. 1:1500 b. 1:10000 c. 1:250 d. 1:400 e. 1:3300 f. 1:4000 (a) ∶ 104

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

An ∶ (b) ∶

An ∶ (c) ∶ = An ∶

%

(d) ∶

= 0.25 % An ∶ (e) ∶ =

= 0.03% (ans) 105

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 51. Express each of the following as a ratio strength: (a) 0.125 % (b) 2.5 % (c) 0.80 % (d) 0.6 % (e) 1/3 % (f) 1/20 % (a) 0.0125% 100 unit contain 0.124 1 unit contain

∴ ratio trength ∶ (b) 2.5 % 100 unit contain 2.5 1 unit contains

∴ ∶ An ∶ ∶ (c) 0.80 % 100 unit contain 0.80 1 unit contain = ∴ ∶ Ans: ∶ (d) 106

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 0.6 % 100 unit contain 0.6 1 unit contain

∴ ∶ ∴ ∶ ∶ An ∶ ∶ (e)

unit contain unit contain

∶ ∶ An ∶ ∶

107

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 52. Express each of the following concentrations as a ratio strength: (a) 2 mg of active ingredient in 2 mL of solution (b) 0.275 mg of active ingredient in 5 mL of solution (c) 2 g of active ingredient in 250 mL of solution (d) 1 mg of active ingredient in 0.5 mL of solution (a) 2 ml contain

= 2 ×10-3 g active ingredient

1 mg represent

=

100mL represent

= = 0.1 % = 1∶

An ∶ ∶ (b), (c), (d) same rules as (a) 53. A doxycycline calcium syrup is preserved with 0.08% (w/v) of methylparaben, 0.02% (w/v) of propylparaben, and 0.10% (w/v) of sodium metabisulfite. Express these concentrations as ratio strengths. 0.08 %(w/v) of methylparaben represent 0.08 g of methylparaben represent in 100 mL ∴ of methylparaben ∶ Ans: ∶

of methylparaben of methylparaben 108

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

0.02 (w/v) of propylparaben represent 0.02 g present in 100 mL ∴

g propyl paraben

=

g propyl paraben

= ∶

w/v propyl paraben

Ans: ∶

w/v of propylparaben

0.10 % (w/v) of sodium metabisulfite represent 0.10 g represent in 100 mL ∴

( ) Ans:

( )

54. An injection contains 0.50% (w/v) of lidocaine hydrochloride and 1:200,000 (w/v) of epinephrine. Express the concen-tration of lidocaine hydrochloride as a ratio strength and that of epinephrine as a percentage. 0.50 % (w/v) of lidocaine hydrochloride represent 0. 50 g of lidocain hydrochloride present in 100 mL ∴ = ∶ An ∶

∶

( ) Lidocaine hydrochloride

( ) Lidocaine hydrochloride. 109

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION And, 200000 mL of injection contain 1 g of epinephrine 1 mL of injection contain

=

of epinephrine

100 mL of injection contain

=

of epinephrine

= 0.0005 % (w/v) epinephrine An ∶ 0.0005 % (w/v) epinephrine 55. A sample of white petrolatum contains 10 mg of tocopherol per kilogram as a preservative. Express the amount of tocopherol as a ratio strength. 10 mg of tocopherol present in 1 kg of sample ∴

-3 g

of tocopherol present in 1000 g of sample

∴ g of tocopherol present in = = 100000 g of sample ∴ ∶ An ∶ ∶

w/v tocopherol w/v tocopherol

56. Potassium Permanganate Tablets 0.2 g Disp. #100 Sig: two tablets in 4 pt of water and use as directed. Express the concentration, as a ratio strength, of the solution prepared according to the directions given in the prescription. 1 pint = 16 fl.oz =16 × 29.57 mL 4 pint = 1892.48 mL 110

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 tab = 0.2 g 2 tab =0.4 ∴

∶ 1893.48 ∶

An ∶ ∶ 57. A skin test for fire ant allergy involves the intradermal skin prick of 0.05 mL of a 1 : 1,000,000 (w/v) dilution of fire ant extract. How many micrograms of extract would be administered in this manner? 1000000 mL of skin pricks contain 1 g of extract 1 mL

of skin pricks contain

0.05 mL of skin pricks contain

of extract of extract

= 5 × 10-8 g = 5 × 10-8 × 106 µg = 0.05 µg An ∶

µg

58. In acute hypersensitivity reactions, 0.5 mL of a 1: 1000 (w/v) solution of epinephrine may be administered subcutaneously or intramuscularly. Calculate the milligrams of epinephrine given 1000 mL of solution contain 1 g of epinephrine 0.5 mL of solution contain = 5 × 10−4 g = 5 × 10-4 × 103 mg = 0.5 mg An ∶ 0.5 mg 111

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

66.

Tetracaine Hydrochloride Epinephrine Hydrochloride Cocaine Hydrochloride Sodium Chloride, qs Sterile Water ad

0.75% 1 :4000 3% 30 mL

How many milligrams each of tetracaine hydrochloride, epinephrine hy- drochloride, and cocaine hydrochloride are needed to fill the prescription? Tetracaine Hydrochloride needed to fill the prescription = 0.75 % ×30 = = 0.0225 g = 225 mg An ∶

mg

Epinephrine Hydrochloride needed to fill the prescription = = 7.5 mg An ∶

mg

Cocaine Hydrochloride needed to fill the prescription = 3 % × 30 = = 0.9 g = 900 mg An ∶

mg

Parts per million calculations:

112

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 60. purified water contains not more than 10 ppm of total solids. Express this concentration as a percentage. 1 PPM represent that, 1 parts present in 1000000 parts So 10 PPM represent 10 parts present in 10×1000000 parts So, % = = 0.001 % (ans) 61. how many grams of sodium fluoride should be added to 100,000 liters of drinking water containing 0.6 ppm of sodium fluoride to provide a recommended concentration of 1.75 ppm? 0.6 ppm means, 10,00000 ml contain 0.6 g= 600 mg So, 100000 ml contain = 60 mg 1.75 ppm means, 10,00000 ml contain 1.75 g = 1750 mg So, 100000 ml contain = 175 mg So, grams of fluoride required = 175 mg – 60 mg = 115 mg Ans: 115 mg fluoride is required.

62. If a commercially available insulin preparation contains 1 ppm of proinsulin, how many micrograms of proinsulin would be contained in a 10-mL vial of insulin? 1 g present in 1000000 mL 1000000 mL present in 1 g ∴

m pre ent in = 1 × 10-5 g = 1 ×10-5 × 106 µg = 10 µg

An ∶

µg

CALCQUIZ 113

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 6.A. AURALGAN Otic drops contain: Antipyrine 5.4% Benzocaine 1.4% Acetic acid 0.01% U-polycosanol410 0.01% Glycerin ad 10 mL (a) What would be the content of antipyrine, in mg/mL? (b) If a patient used 5 drops of the Otic solution, equivalent to 0.25 mL, how many milligrams of benzocaine would have been administered? (c) How many µL of acetic acid would be used to prepare the 10 mL of drops? (d) What would be the equivalent ratio strength (v/v) if u-polycosanol 410? (a) Content of Antipyrine =

×10 = 0.54 g

Ans: 0.54 g (b)10 ml of otic solution contain =

×10 of Benzocaine = 0.14 g of Benzocaine

So, 0.25 ml of ……………………………………

=

×0.25 g of ….

= 0.0035 g of Benzocaine = 3.5 g of Benzocaine Ans: 3.5 g of Benzocaine (c) ml of Acetic acid =

×10 = 0.001 ml = 0.001×1000 = 1 µL

Ans: 1 µL (d)Ratio =

×10 =

= 1:1000

Ans: 1:1000 6.B. Among it’s other ingredients, VISINE-A eye drops contain the active ingredients: 0.025% naphazoline hydrochloride and 0.3% pheniramine maleate; and, 114

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1:10,000 benzalkonium chloride as a preservative. Calculate (a) the corresponding percent strength of benzalkonium chloride and (b) the quantities of each of the three ingredients in a 15 mL container.

(a)

×100 = 0.01%

(b) Naphazoline Hydrochloride = Pheniramine maleate = Benzalkonium Chloride =

×15 = 0.00375 g

×15 = 0.045 g ×15

= 0.0015 g

6.C. An intravenous solution of AVELOX contains 400 mg of moxifloxacin hydrochloride (1.6 mg/mL). Calculate (a) the percent concentration of moxiflixacin hydrochloride and (b) the volume of solution in the product. (a) 1.6×10-3 ×100 = 0.16% (ans) (b) 1.6 mg present in = 1 ml So, 400 mg ………… = 400/1.6 = 250 ml (ans) 6.D. ATROVENT Nasal spray contain 0.03% of ipratropium bromide in a 30-mL metered dose container. If the container is calibrated to deliver 345 sprays, calculate (a) the volume of each spray, in microliters, and (b) the number of milligrams of ipratromium bromide in each spray. (a) 30 ml = 30×1000 = 30,000 µL So, volume of each spray =

= 86.95 µL

Ans: 86.95µL (b) 30,000 µL of solution contain = 400 mg of drug So, 86.95 µL ……………… =

= 1.16 mg

Ans: 1.16 mg 115

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 6.E. A homeopathic teething gel states on it’s product label it contains 0.0000003% alkaloid. Express the alkaloid content in ppm. 0.000000% means: 100 unit present in = 0.0000003 unit of Alkaloid So, 10,00000 unit ….. =

×10,00000 unit of Alkaloid

= 0.003 ppm Ans: 0.003 ppm

116

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

CHAPTER 07: CALCULATION OF DOSES: GENERAL CONSIDERATION Basic concept: DOSE: A specified quantity of a therapeutic agent, such as a drug or medicine, prescribed to be taken at one time or at stated intervals. DOSE calculation: Number of dose= Dose measuremet: Household measure (abbreviation)

OUNCE

METRIC MEASURE

1 teaspoonful (tsp) 1 tablespoonful (tbsp)

1/6 fluidounce ½ fluidounce

5 ml 15 ml

SOLUTION OF PROBLEM:

Doses: Solid Dosage Forms 1. How many capsules, each containing a 150-mcg dose of a drug may be prepared from 0.12 g of the drug?

1 capsule contain = 150 mcg of drug Given drug = 0.12 g = 0.12 × 106 µg Number of capsule = = 800 capsules Ans∶ 800 capsule 2. The following regimen for oral prednisone is prescribed for a patient: 50 mg/ day ×10 days; 25 mg/day ×10 days; 12.5 mg/day ×10 days; 5 mg/day× 10 weeks. How many scored 25-mg tablets and how many 5-mg tablets should be dispensed to meet the dosing requirements?

In case of 50 mg drug: 116

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION For 1 day 50 mg drug is required For 10 days 50 × 10 is required = 500 mg In case of 25 mg drug: For 1 day 25 mg drug is required For 10 days = 250 mg drug is required Total drug (500 + 250) mg = 750 mg ∴

3

25 mg tablet

Ans∶ 3 25 mg tablets (ans) And In case of 12.5 mg drug: For 1 day require 12.5 mg of drug For 10 day require 12.5 × 10 mg drug = 125 mg drug In case of 5 mg drug: For 1 day require 5 mg of drug For 10 week = 70 day require 5 × 70 mg of drug = 350 mg ∴ Total drug = 350 + 125 = 675 mg of drug ∴

95 5

(ans)

3. A physician reduces a patient's once-daily dose of conjugated estrogen (PREMARIN) from tablets containing 0.625 mg to tablets containing 0.45 mg. What is the total reduction in conjugated estrogens taken, in milligrams, during a 30-day month? Reduction amount dose from 1 tablet = (0.625 – 0.45) mg 117

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 0.175 mg ∴ Total reduction from 30 day = 30 × 0.175 mg = 5.25 mg Ans∶ 5 25 mg 4. A fixed-dose combination product contains amlodipine besylate and atorvastatin calcium (CADUET) for the treatment of both hypertension and hypercholesterolemia. If a physician starts a patient on a 5- mg/10-mg dose for 14 days and then raises the dose to 10 mg /20 mg, how many milligrams of each drug will the patient take during the first 30 days? 5 mg of besylate taken 14 day So

= 14 × 5 = 70 mg

Atorvastatin 10 mg taken =14 day = 14 × 10 = 140 mg Then after raising the dose Besylate 10 mg taken 16 day ∴ (16

1 ) mg = 160 mg

Atorvastatin 20 mg taken 16 day = 16 × 20 = 320 mg Total Besylate taken in 30 days = 160 mg + 70 mg = 230 mg Ans∶ 230 mg of amlodipine besylate. Total Atorvastatin taken in 30 days = 320 mg + 140 mg 118

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 460 mg of atorvastatin calcium Ans∶ 460 mg of atorvastatin calcium. 5. A patient cuts 100-mg scored tablets to take his 50-mg prescribed daily dose. A prescription for thirty 100-mg tablets costs $45, and a prescription for thirty 50-mg tablets costs $40. The patient asked the pharmacist to weigh an uncut tablet on an electronic balance into two ''halves.'' The uncut ta blet was found to weigh 240 mg, and the cut ''halves'' weighed 125 mg and 115 mg, respectively. (a) How much money did the patient save on a monthly basis by dosing with half tablets? (b) What was the percentage error in the weight of the cut tablets compared with ''exact halves''? Uncut tablet was found to weight = 240 mg Cut halves weighted

= 125 mg and 115 mg

Thirty 100 mg tablet cost = $ 45 Thirty 50 mg tablet cost

= $ 40

(a) 30, 100 mg tablets cost = 45 USD 30, 50 mg tablet cost

= 40 USD

The patient required 15 tablet of 100 mg tablet So, 15,100 mg tablet

= 22.5 USD

Save the money = (40 – 22.5) USD = 17.5 USD Ans∶ 17 5 USD (b) %=

1

= 4.2 % Ans∶ 4 2 %

119

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 6. The recommended dose of memantine HCl (NAMENDA) is: Week 1, 5 mg/day week 2, 10 mg/day (5 mg , b.i.d), Week 3, 15 mg/day (10 mg a.m., 5 mg p.m.) Week 4, 20 mg/day (10 mg b.i.d.) How many 5-mg tablets must be dispensed for a 4-week supply of the medication? Week 1: 5mg/day, 5 × 7 = 35 mg Week 2: 10mg/day, 10 × 7 = 70 mg Week 3: 15 mg/day, 15 × 7 =105 mg Week 4: 20mg/day, 20 × 7 = 140 mg Total

= 350 mg

5mg of drug present in 1 tablet ∴ 35 mg present in

35 =

= 70 tablets Ans∶ 7 tablets

120

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 07. Prior to a colonoscopy, a patient is instructed to take OSMOPREP tablets each of which contains 1.102 g sodium phosphate monobasic monohydrate and 0.398 g sodium phosphate dibasic anhydrous . the dose is: Evening before the procedure 4 tablets with 8 ounces of clear liquids every 15 minutes for 5 cycle and Starting 3 to 5 hours before the procedure 4 tablets with 8 ounce of clear liquids every 15 minutes for 3 cycle. How many tablets , how much liquid , and how much total sodium phosphate are taken ? (a) 8 tablets, 15 ounce liquid, 2 g sodium phosphates (b) 16 tablets , 1000 ml liquid , 40 g of sodium phosphates (c) 32 tablets , 0.5 gallon liquids, 48 g sodium phosphate

Total cycle = 8, So, total tablet, 4×8 = 32, Total liquid= 8×8 ounce = 64 ounce = 0.5 gallon Total sodium phosphate = (1.102+0.398)×32 = 48 g

(1 gallon US =128 ounce)

Ans: (c) 8 tablets, 0.5 gallon liquids, 48 g sodium phosphate. 8. CHANTIX (varenicline tartrate) a smoking cessation , is available in two strength, 0.5 mg and 1 mg tablets. The dose is :  Days 1 to 3 : 0.5 mg once daily  Days 4 to 7 : 0.5 mg twice daily  Day 8 to rnd of the treatment :1 mg twice daily The treatment period is 12 weeks. How many 0.5 mg tablets and 1 mg tablets should be dispensed? a) 7, 0.5 mg and 11, 1 mg tablets b) 8, 0.5 mg and 84, 1 mg tablets c) 10, 0.5 mg and 84, 1 mg tablets d) 11, 0.5 mg and 154 , 1 mg tablets Available strength is 0.5 mg and 1 mg tablets Treatment period = 12 ×7 =84 days Day 1 to 3 = 0.5 mg once daily = 3, 0.5 mg tablets is needed Day 4 to 7 = 0.5 mg twice daily So day 4 to 7 = 8, 0.5 mg tablets is needed So day 1 to 7 total 8+3=11 , 0.5 mg tablets is needed Day 8 to end of the treatment, total day= 84- 7 = 77 121

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION So, for 77 day = 77×2= 154 , 1 mg tablet is needed. Answer: (d) 11, 0.5 mg and 154, 1 mg tablet is needed Doses: drops 9. A ciprofloxacin otic solution contains 0.5 mg of ciprofloxacin in a 0.25 ml single dose package. Based on 20 drops/ml. (a) How many drops would be administered and (b) How many micrograms of ciprofloxacin would be in each drop? (a) Drops administered : 0.25×20 = 5 drops Ans: 5 drops ciprofloxacin otic solution (b) 5 drops otic solution contain 0.5 mg of ciprofloxacin So, 1 drop otic solution contain = 0.5/5 = 0.1 mg of ciprofloxacin =100 mcg of ciprofloxacin Ans: 100 mcg ciprofloxacin. 10. Acetaminophen Drops Disp. 15 mL Sig. 0.5 mL t.i.d. (a) If acetaminophen drops contain 1.5 g of acetaminophen per 15-mL container, how many milligrams are there in each prescribed dose? (b) If the dropper is calibrated to deliver 22 drops/mL, how many drops should be administered per dose? (a) 15 mL container contain 1.5 g of acetaminophen ∴ 5 mL container contain =

5

acetaminophen

= 0.05 g = 0.05 × 103 mg = 50 mg An∶ 5 mg 122

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION (b) 1 mL of drop deliver 22 drop 0.5 mL of drop delivers 22 × 0.5 drop = 11 drops An∶ 11 drops 11. RESTASIS Ophthalmic Emulsion contains 0.05% w/v cyclosporin. If a dose of one drop measures 28 µL, how many micrograms of cyclosporin are present? 100 mL of Emulsion contain 0.05 g of cyclosporine 28 µL = 28 × 10-3 = 0.028 mL of emulsion contain= cyclosporine

28 g of

= 1.4 × 10-5g of cyclosporine = 1.4 × 10-5 × 106 µg of cyclosporine = 14 µg of cyclosporine Ans∶ 14 µg of cyclosporine 12.The oral dose of a drug is 2.5 mg. If a solution contains 0.5% w/v of the drug in a dropper bottle that delivers 12 drops/mL, how many drops would supply the dose? 100 mL of solution contain 0.5 g of drug 1 mL of solution contain =

of drug

=

1

of drug

= 5 mg of drug Dropper bottle deliver 12 drop/mL ∴ 5 mg of drug deliver 12 drops 2.5 mg of drug deliver

2 5 drops

= 6 drops 123

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans∶ 6 drops 13. Infants MYLICON anti-gas drops contain 2 g of simethicone in a 30-mL container. (a) How many milligrams of the simethicone are contained in each 0.3-mL dose and 12 doses per day are not to be exceeded, calculate the corresponding 12 dose (b) volume and (c) simethicone content (a) 30 mL container contain 2 g of simethicone 0.3 mL container contain = 3 2 = 2 1 2 of simethicone Ans∶ 20 mg of simethicone (b)

Doses: Oral Liquids 14. Rimantadine HCl syrup contains 2.4 g of rimantadine HCl in each 240 mL of syrup. How many milligrams of rimantadine HCl would there be in 2.5 mL delivered by oral dispenser? 240 mL of syrup contain 2.4 g of Rimantadine hydrochloride. 2.5 mL of syrup contain

of Rimantadine hydrochloride = 25 mg

Ans∶ 25 mg of Rimantadine hydrochloride 15. If a liquid medicine is to be taken three times daily, and if 180 mL are to be taken in 4 days, how many tablespoonfuls should be prescribed for each dose? Patient has to be taken three times daily and 4 days. ∴ dose

(

)

= 15 mL 124

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 table spoonful = 15 mL Ans∶ 1 tablespoonful 16. If a cough syrup contains 0.18 g of dextromethorphan HBr in 120 mL, how many milligrams of the drug are contained in each teaspoonful dose? 1 teaspoonful = 5 mL 120 mL of cough syrup contain 0.18 g of dextromethorphan HBr 5 mL of cough syrup contain =

5 75

1

of dextromethorphan HBr of dextromethorphan HBr

= 7.5 mg of dextromethorphan HBr Ans∶ 7 5 mg of dextromethorphan 17. A cough syrup contains 0.09 g of dextromethorphan HBr in each fluidounce. How many milligrams of this agent would be present in each teaspoonful dose? We know 1 Fluidounce = 29.57 mL And 1 tea spoonful = 5mL ∴ 29 57 mL of syrup contain 5 mL of syrup contain

9 g = 90 mg of dextromethorphan HBr =

5

of dextromethorphan HBr

= 15.21 mg………………………… Ans∶ 15 21 mg 18. A physician prescribes tetracycline HCl syrup for a patient who is to take 2 teaspoonfuls four times per day for 4 days, and then 1 teaspoonful four times per day for 2 days. How many milliliters of the syrup should be dispensed to provide the quantity for the prescribed dosage regimen? 2 Tea-spoonful four times per day for 4 days = 2×5(ml)×4×4 = 160 mL And 125

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 teaspoonful four times per day for 2 days = 1 × 5(ml) × 4 × 1 × 2 = 40 mL Total mili litters of the syrup = (160 + 40) mL = 200 mL Ans∶ 2

mL

19. Ipecac oral solution has the following formula: Powdered Ipecac 70 g Glycerin 100 mL Syrup ad 1000 mL Powdered ipecac contains 2 grams of the combined alkaloids emetine and cephaeline in each 100 grams of powder. Calculate the quantity of these alkaloids, in milligrams, in each 5-mL dose of ipecac oral solution. 1000 mL of syrup contain 70 g of powdered Ipecac 5 mL of syrup contain

5 = 0.35 g

100 g of powdered Ipecac contain 2 g of combined alkaloids 0.35 g of powdered Ipecac contain =

35

…………

= 7 × 10-3 g of combined alkaloids = 7 mg Ans∶ 7 mg 20. A dose of digoxin for rapid digitalization is a total of 1 mg, divided into two or more portions at intervals of 6 to 8 hours. How many milliliters of digoxin elixir containing 50 µg/mL would provide the 1 mg dose? 50 µg of drug present in 1 mL of digoxin elixir 5 × 10-3 mg = 0.05 mg of drug present in 1 ml of digoxin elixir 1 mg of drug present in =

of elixir

= 20 mL of elixir 126

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans∶ 2 mL of elixir 21. Ciprofloxacin (CIPRO) oral suspension contains 250 mg of ciprofloxacin per 5 mL. A physician prescribed 125 mg of ciprofloxacin q.i.d. ×10 days. (a) How many doses are needed? (b) How many milliliters should be given per dose? (c) How many milliliters of ciprofloxacin oral suspension containing 250 mg per 5 mL should be dispensed? (a) Dose = q.i.d × 10 days = 4 times a day × 10 day = 4 × 10 = 40 times Ans∶ 4 times (b) Per dose of 125 mg of ciprofloxacin is needed ∴ 25 mg

of ciprofloxacin present in 5 mL of suspension

125 mg of ciprofloxacin present in

125

of suspension

= 2.5 mL of suspension Ans∶ 2 5 mL of suspension (c) Dose = 40 Per dose 125 mg of ciprofloxacin is needed For 40 dose 40 × 125 mg = 5000 mg of ciprofloxacin is needed 250 mg of ciprofloxacin present in 5mL of suspension 5000 mg of ciprofloxacin present in

5

of suspension

= 100 mL of suspension Ans∶ 1

mL of suspension 127

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 22. A patient has been instructed to take 15 mL of alumina and magnesium oral sus- pension every other hour for four doses daily. How many days will two 12-fl.-oz bottles of the suspension last? 4 × 15 mL = 60 mL of oral suspension is required for 1 day 12 Fl.oz = 12 × 29.57 mL = 354 mL Two 12 Fl.oz bottle So, 354 × 2 = 708 mL ∴ 6 mL of oral suspension is required for 1 day 708 mL of oral suspension is required for

7 8 day

= 11.8 day Ans∶ 11 + day 23. dextromethorphan HBr 50 mg/ tsp Guaifenesin syrup ad 120 ml Sig: Ӡi q i d a c and h s How many grams of dextromethorphan HBr would be needed to fill the prescription? 5 mL of syrup contain 50 mg of dextromethorphan HBr 120 mL of syrup contain

12 mg of dextromethorphan HBr

= 1200 mg…………… = 1.2 g……………………………… Ans∶ 1 2 g…………………

Doses: Injections 24. The dose of AUGMENTIN oral suspension for a patient is 5 ml b.i.d. Each 5 ml of suspension contains 400 mg of amoxicillin and 57 mg of clavulanic acid. If the suspension is to be taken for 10 days and is available in 50 ml, 75 ml, and 100 ml containers, calculate (a) the last wasteful package size to dispense and (b) total quantity of amoxicillin taken during the treatment period.

128

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

(a) b.i.d means two times a day. So for 1 day 10 ml of suspension is required. For 10 days 100 ml of suspension is required. Ans∶ 1

mL of suspension

(b) Total quantity of amoxicillin were taken during the treatment period =

×100

= 800 mg Ans: 800 mg of amoxicillin. 25. A physician ordered 20 mg of MEPERGAN and 0.3 mg of atropine sulfate to be administered preoperatively to a patient. MEPERGAN is available in a syringe containing 25 mg/mL, and atropine sulfate is in an ampul containing 0.4 mg per 0.5 mL. How many milliliters of each should be used in filling the medication order? 25 mg MEPERGAN present in 1 mL of syringe 20 mg MEPERGAN present in

2 mL of syringe

= 0.8 mL of syringe 0.4 mg of atropine sulfate present on 0.5 mL of ampule 0.3 mg of atropine sulfate present on

3 mL of ampule

= 0.375 mL of ampule Ans∶ 0.8 mL MEPERGAN and 0.375 mL of atropine sulfate 26. How many milliliters of an injection containing 250 mg of aminophylline in each 10 mL should be used in filling a medication order calling for 15 mg of aminophylline? 250 mg of aminophylline present in 10mL of injection 15 mg of aminophylline present in

15 mL of injection

= 0.6 mL of injection 129

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans∶ 6 mL of injection 27. Pediatric LANOXIN injection contains digoxin, 100 mcg/mL. What volume must be administered to provide a dose of 0.04 mg? 100 µg of digoxin present in 1 mL of Lanoxin injection 0.04 mg = 0.04×103 = 40 µg of digoxin present in injection

4

of Lanoxin

= 0.4 mL of Lanoxin injection (ans)

Doses: Other Dosage Forms 28. The recommended maintenance dose of BECLOVENT (beclomethasone diproprionate), an aerosolized inhalant, is 100 mcg administered twice daily. The commercial inhaler delivers 50 mcg per metered inhalation and contains 200 inhalations. How many inhalers should be dispensed to a patient if a 60-day supply is prescribed? The recommended maintenance dose of BECLOVENT is 100 µg administered twice daily Dose = 100 µg × 2/day = 200 µg /day = 200 × 60 µg/60 days = 12000 µg /60 days Commercial inhaler delivers 50 µg per inhalation and contains 200 inhalations. ∴ a commercial inhaler contain = 50 µg × 200 = 10,000 µg of drug ∴ for 12000 µg of drug inhaler required = = 1.2 = 2 inhalers (Ans)

130

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 29. A 16-week regimen for a brand of a nicotine patch calls for a patient to wear a 21-mg patch each day for the first 6 weeks, followed by a 14-mg patch each day for the next 2 weeks, and then a 7-mg patch for the next 2 weeks to conclude the treatment regimen. In all how many milligrams of nicotine are administered? First 6 week = 21 × 7 × 6 mg = 882 mg Next 2 week = 14 × 7 × 2 mg = 196 mg Next 2 week = 7 × 7 × 2 mg = 98 mg Total = (882 + 196 + 98) mg = 1176 mg Ans∶ 1176 mg 30. A transdermal patch contains 5 mg of fentanyl and has a drug-release rate of 50 mcg/ hour. The patch is worn for 72 hours. Calculate (a) the milligrams of fentanyl deliv- ered daily, (b) the milligrams of fentanyl re- maining in the patch when it is removed, and (c) the percentage of drug remaining in the patch when it is removed. Transdermal patch contain 5 mg of fentanyl Release rate = 50 µg/hour (a) Milligram of fentanyl delivered daily = 24 × 50 µg = 1200 µg = 1200 × 10-6 × 103 mg = 1.2 mg Ans∶ 1 2 mg (b) 72 hours = 3 day = 3 × 1.2 mg 131

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 3.6 mg ∴ Milligram of fentanyl remaining in the path

(5 – 3.6) mg

= 1.4 mg Ans∶ 1 4 mg (c) % of drug remaining in the path =

1

= 28 % Ans∶ 28 % 31. If a VENTOLIN inhaler contains 20 mg of albuterol, how many inhalation-doses can be delivered if each inhalation-dose contains 90 mcg? 1 inhaler dose contain = 90 µg of Albuterol Inhaler contain 20 mg of albutero = 20 × 103 µg of Albuterol = 20,000 µg of Albuterol Number of inhalation dose = 222 Ans∶ 222 doses 32. FLONASE Nasal Spray contains 50 mcg of fluticasone propionate per actuation spray in each 100 mg of formulation. Each container provides 120 metered sprays. How many milligrams of fluticasone propionate are contained in each container? 1 actuation spray contain 50 µg of Fluticasone propionate 120 metered spray contain = 50 × 120µg pf Fluticose propionate = 6000 µg = 6000 × 10-3 mg = 6 mg Ans∶ 6 mg 132

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 33. The dose of VOLTAREN (diclofenac sodium) GEL, when applied to the hands in the treatment of arthritic pain, is 2 g four times a day. The gel contains diclofenac so- dium 1% and is available in 100-g tubes. How many grams of the drug diclofenac sodium would be administered per day and how many days of treatment would be available per tube of gel? (a) 8 g diclofenac sodium per day for 8 days (b) 8 g diclofenac sodium per day for 12.5 days (c) 80 mg diclofenac sodium per day for 8 days (d) 0.08 g diclofenac sodium per day for 12.5 days Dose of the VOITAREN gel is = 2g×4/day = 8 g per day 1 day require 8 g of diclofenacl sodium 8 g of diclofenacal sodium required for 1 day 100 g diclofenacal sodium required for

1

= =12.5 day Ans∶ (b) 8g diclofenac sodium per day for 12.5 day 34. SYMBICORT 80/4.5 is an oral inhalation product containing 80 mcg of budesonide and 4.5 mcg of formoterol fumarate per inhalation. The dose is stated as ''two inhalations twice daily.'' How much of each drug would be administered daily? (a) 160 mcg budesonide and 9 mcg formoterol fumarate (b) 0.32 mg budesonide and 0.18 mg formoterol fumarate (c) 320 mcg budesonide and 0.18 mg formoterol fumarate (d) 0.32 mg budesonide and 0.0l8 mg formoterol fumarate Dose = 2 inhalation × 2/day = 4 inhalation per-day. 1 inhalation contain 80 µg of budesonide 4 inhalation contain 4×80 = 320 µg of budesonide = 0.32 mg of of budesonide 1 inhalation contain = 4.5 µg of formoterol fumerate 133

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 4 inhalation contain 4.5 × 4 = 18 µg of formoterol fumerate = 0.018 mg Ans∶(d) 0.32 mg of budesonide and o.017 mg of formoterol fumerate.

CALCQUIZ 7.A. The ophthalmic solution ALPHAGAN P contains 0.15% brimonidine tartrate in 10 ml containers. The recommended dose is one drop in the affected eye (s) three times daily . IF A glaucoma patient doses each eye, and the dropper used delivers 20 drops/ ml , calculate the quantity , in milligrams, of brimonidine tartrate administered in each day. Patient need for one day = 3 drops 20 drops contain = 1 ml solution So, 3 drops contain = 3/20 = 0.15 ml solution 0.15 % represents : 100 ml solution contain=0.15 g So, 0.15 ml ……….. =

= 0.000225 g = 0.000225×103 mg = 0.225 mg

Ans: 0.225 mg 7.B. THE starting dose of sodium oxybate oral solution ( XYREM ) is 4.5 g/night divided into two equal doses and administered 2.5 to 4 hours apart . HOW many milliliters of the oral solution containing sodium oxybate, 500mg/ml , should be administered in each divided dose? 4.5 g/night divided into two dose So, each dose require = 4.5/2 = 2.25 g 500 mg = 0.5 g drug present in 1 ml of solution 134

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION So, 2.25 g ………………….. = 2.25/0.5 = 4.5 ml solution Ans: 4.5 ml solution 7.C. A pediatric stool softener contains 393.3 mg of docusate sodium in each four fluidounce(118ml) container .if the labeled dose is two tablespoonful for a 5 year old child how many milligrams of docusate sodium would be contained per dose ? Labeled dose = 2 tablespoonful = 2×15 = 30 ml solution 118 ml solution contain = 393.3 mg docusate sodium So, 30 ml ………………. =

= 99.99 mg

Ans: 99.99 mg 7.D. An oral inhalation (DULERA) to treat asthma, provides in each inhalation, 100 µg of mometasone furoate and 5 µg of formarate . The recommended dose is “two inhalations twice daily (morning and evening )” Calculate the quantity , in milligrams , of each drug inhaled daily. 1 inhalation contain 100 µg mometasone furoate and 5 µg formoterol fumerate So, 2 inhalation …. = 100×2 µg …….. and 2×5µg ……… = 200 µg mometasone furoate and 10 µg formoterol fumerate Ans: 200 µg mometasone furoate and 10 µg formoterol fumerate 7. E. In an experiment of tablet –splitting effectiveness, a pharmacist had a pharmacy student split a previously weighed lisinoprit tablet containing 20 mg of drug . on an electronic balance , the whole tablet weighed 111.62 mg After splitting , one “half tablet “ weighed 51.21 mg and the other “ half ,” 58.49mg .There was residue powder remaining . Calculate ( a ) the percent of lost tablet ( residue) ,(b) the percent accuracy in actual weight ( to ideal weight ) for each “ half-tablet ,” and (c ) the supposed quantity of drug , in milligrams ,(not assayed , of course ) in each “ half – tablet.” (a) Total Weight of two, half tablet = 51.21+58.41 = 109.70 mg 135

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 111.62 mg tablet contain = 20 mg lisinopril So, 109.70 mg tablet contain =

= 19.65 mg lisinopril

Ans: 19.65 mg Lisinopril (b) Percent accuracy for each half For 51.21 mg: Actual weight =111.62/2 = 55.81 mg So, accuracy =

= 91.75%

For 58.49 mg: % Accuracy =

= 104.80%

136

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

CHAPTER : 08 CALCULATION OF DOSES: PATIENT PARAMETERS Basic concept: DRUG DOSAGE BASED ON AGE: Young’s rule, based on age

× adult dose = dose for child (

Cowling’s rule (

Fried’s rule

)

(

Clark’s rule

)

= dose for child = dose for infant

)

(

)

= dose for child

DRUG DOSE BASED ON BODY WEIGHT: Patienrs dose = patient’s weight (kg)×

(

)

EXAMPLE CALCULATION OF DOSE BASED ON BODY WEIGHT: The usual initial dose of chlorambucil is 150 mcg/kg of body weight. How many milligrams should be administered to a person weighing 154 lb.? Solving by the equation: 150 mcg = 0.15 mg Patient’s dose(mg) = 154 (lb) ×

= 10.5 mg chlorambucil answer

DRUG DOSAGE BASED ON BODY SURFACE AREA: EXAMPLE CALCULATION DOSE BASED ON BODY SURFACE AREA: An useful equation for the calculation of dose based on BSA is: Patient’s dose =

( (

)

)

× drug dose (mg)

If the adult dose of a drug is 100 mg, calculate the approximate dose for a child with a BSA of 0.83 m2, using (a) the equation and (b) Table 8.3. 137

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

Child’s dose =

× 100 mg = 47.97 or 48 mg answer

DETERMINATION OF BODY SURFACE AREA: Patient’s BSA= √

(

)

(

)

EXAMPLE: If the patient weight is 40 kg and height 132 cm. what is the BSAof the patient? Patient’s BSA= √

= 1.21 m2 answer SOLUTION OF PROBLEM

Calculations Based on Body Weight 1. The dose of a drug is 500 mcg/kg of body weight. How many milligrams should be given to a child weighing 55 lb.? 1 lb = 0.4535 kg 55 lb = 24.94 kg Drug dose for 1 kg of body weight = 500 µg Drug dose for 24.94 kg of body weight = 500 × 24.94 µg = 12470 µg = 12.47 mg Ans∶ 12 47 mg 2. The dose of gentamicin for premature and full-term neonates is 2.5 mg/kg administered every 12 hours. What would be the daily dose for a new born weighing 5.6 lb.? 1 lb = 0.4535 kg 138

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 5.6 lb = 2.52 kg Patient dose for every 12 hours = patient weight (kg) × 25 2 52 1 63

1 day = 24 hours So daily dose = 6.3 × 2 = 12.6 mg Ans∶ 12 6 mg 3. The dose of gentamicin for patients with impaired renal function is adjusted to ensure therapeutically optimal dosage. If the normal daily dose of the drug for adults is 3 mg/kg/day, administered in three divided doses, what would be the single (8-hour) dose for a patient weighing 65 lb. and scheduled to receive only 40% of the usual dose, based on renal impairment?

1 lb = 0.4535 kg 65 lb represents = 29.25 kg Patient dose for 65 lb = patient’s weight (kg)×

(

)

= 29.25 × = 87.75 mg per day Single dose (8 hours) = 29.25 mg Ans∶ 29 25 mg /65 lb/ 8 hours 4. A patient weighing 120 lb. was administered 2.1 g of a drug supposed to be dosed at 30 mg/kg. Was the dose administered correct, or was it an overdose, or was it an underdose? 120 lb represents = 54.43 kg Original dose = 30 mg/kg

139

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = patient’s weight (kg)×

Administered dose

= 54.43 (kg) ×

(

(

)

)

= 113.4 g = 113400 mg Per kg = = 2100 mg/kg ∴

It is overdose

Ans∶ It is overdose 5. In a clinical trial of ciprofloxacin (CIPRO), paediatric patients were initiated on 6 to 10 mg/kg intravenously every 8 hours and converted to oral therapy, 10 to 20 mg/kg, and every 12 hours. Calculate the ranges of the total daily amounts of ciprofloxacin that would have been administered intravenously and orally to a 40-lb. child. 1 lb = 0.4535 kg 40 lb represent = 18.14 kg Dose of ciprofloxacin for 18.14 kg of the patient weight intravenously every 8 hours = patient’s weight (kg)×

(

)

= 18.14 kg × = 108.84 mg to 181.4 mg Daily dose of ciprofloxacin for 18.14 kg of the patient weight intravenously = 108.54 × 3 mg to 181.4 mg × 3 = 326.52 mg to 544.2 mg Ans∶ 326 52 mg to 544 2 mg intravenously. Dose of ciprofloxacin For 18.14 kg of patient weight orally every 12 hours = patient weight (kg) × 140

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 18 14 = 181.4 mg to 362.8 mg Daily dose of ciprofloxacin for 18.14 kg of the patient weight orally daily = 181.4 mg × 2 to 362.8 × 2 mg = 362.8 mg to 725.6 mg Ans∶ 362 8 mg to 725 6 mg orally 6.

Erythromycin 400 mg/5 mL Ethylsuccinate Disp. 100 mL Sig. …………. tsp. q.i.d. until all medication is taken.

If the dose of erythromycin ethyl succinate is given as 40 mg/kg per day, (a) What would be the proper dose of the medication in the Signa if the prescription is for a 44lb. child? (b) How many days will the medication last?

Dose of erythromycin ethylsuccinate for 44 lb (20 kg) of the patient weight per day : (

= patient’s weight (kg)×

)

=20× = 800 mg 400 mg of Erythromycin Ethylsuccinate present in = 5 mL of solution 800 mg of Erythromycin Ethylsuccinate present in =

8

= 10 mL Tsp = 5 mL Q.i.d = four times a day 141

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 10 mL of solution = 2 tsp So proper dose of the medication in the signa = = 0.5 tsp . q.i.d Ans∶ 5 tsp q i d (b) 5 mL contain 400 mg of Erythromycin 100 mL contain

1 = 8000 mg of Erythromycin

1 day require for 44 lb child = 800 mg of Erythromycin. Number of day will the medication last = = 10 days Ans∶ 1 days 7. If the pediatric dosage of chlorothiazide (DIURIL) is 10 to 20 mg/kg of body weight per day in a single dose or two divided doses, not to exceed 375 mg per day, calculate the daily dosage range of an oral suspension containing 250 mg chlorothiazide per 5 mL that should be administered to a 48-lb child 48 lb represent = 21.77 kg (

Patient daily dose = patient’s weight (kg)×

)

= 21.77 (kg) × = 217.7 mg to 435.4 mg of chlorothiazide 250 mL chlorothiazide present in

= 5 mL of oral suspension.

217.7 mg of chlorothiazide present in =

217 7

of oral suspension.

= 4.354 mL of oral suspension So, 250 mg chlorothiazide present in 5 mg of oral suspension ∴ 375 mg chlorothiazide present in

375 142

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 7.5 mL of oral suspension Ans∶ 4 4 - 7.5 mL chlorothiazide oral suspension 8. Cyclosporine is an immunosuppressive agent administered before and after organ transplantation at a single daily dose of 15 mg/kg. How many milliliters of a 50- mL bottle containing 100 mg of cyclosporine per milliliter would be administered to a 140-lb. kidney transplant patient? 140 lb represent = 63.5 kg Patient daily dose = 63.50 × = 945 mg 100 mg of cyclosporine present in 1 mL bottle 945 mg of cyclosporine present in

945

= 9.45 mL bottle Ans∶ 9 45 mL bottle 9. The adult dose of a liquid medication is 0.1 mL/kg of body weight to be administered as a single dose. How many teaspoonful’s should be administered to a person weighing 220 lb.? 220 lb represent = 99 kg 1 kg of the body weight require = 0.1 mL of liquid medication 99 kg of the body weight require = 0.1 × 99 = 9.9 mL of liquid medication 1 tsp = 5 mL ∴ 9 9 mL = 1.98 tsp = 2 tsp Ans∶ 2 tsp 10. A hospitalist prescribed dimenhydrinate to treat a 48-lb child. The labeled dose of the drug is 1.125 mg/ kg. Available oral solution contains dimenhydrinate, 12.5 mg/5ml, Prior to administering the solution, the floor nurse decides to check her calculated dose of 9.8 ml 143

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION with the hospital pharmacist. Were her calculations correct?

48-lb represents = 21.77 kg For 21.77 kg = 21.77×1.125 mg dimenhydrinate is required. = 24.49 mg 12.5 mg dimenhydrinate present in 5 ml solution So, 24.49 mg dimenhydrinate present in =

×24.49

=9.8 ml Ans: Yes, calculation was correct. 11. Fluconazole tabs 100 mg Disp. Tabs Sig: tab ii stat, then 3 mg/kg b.i.d. 7 d thereafter. Calculate the number of tablets to dispense to a patient weighing 147 lb. 147 lb represent = 66.67 kg Sig represent the following Tab = tablet ii = 2 Stat = immediately Bid = twice a day 7 d = 7 day So, sig tab ii stat then 3 mg/kg bid × 7d thereafter = 2 × 100mg × 3 mg × 2 × 7 × 66.67 = 3000.14 mg 100 mg of Fluconazole present in 1 tablet 3000 mg of Fluconazole present in

3 144

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 30 tablet Ans∶ 3 tablet 12. A physician desires a dose of 40 mcg/kg of digoxin for an 8-lb. new born child. How many milliliters of an injection containing 0.25 mg of digoxin per milliliter should be given? 8 lb represent = 3.63 kg Patient dose

= patient’s weight (kg)×

(

)

= 3.63 × = 145.2 µg = 0.145 mg 1 mL of injection contain 0.25 mg of digoxin 0.25 mg of digoxin present in 1 mL of injection 0.145 mg digoxin present in

145

= 0.58 mL of injection Ans∶ 58 mL of injection 13. Intravenous digitalizing doses of digoxin in children are 80% of oral digitalizing doses. Calculate the intravenous dose for a 5-year-old child weighing 40 lb. if the oral dose is determined to be 20 mcg/kg.

1 kg of the child weight require 20 µg of drug 40 lb = 18.14 kg child weight require = 18.14 × 20 µg = 362.873 µg Intravenous dose = 80 % × 362.873 µg of digoxin = 290.299 µg = 290 µg or 291 µg of digoxin Ans∶ 29 µg or 291 of digoxin 145

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 14. An intratracheal suspension for breathing enhancement in premature infants is dosed at 2.5 mL/kg of birth weight. How many milliliters of the suspension should be administered to a neonate weighing 3 lb.? 3 lb represent = 1.360 kg 1 kg of the neonate weight should be administered 2.5 mL of intratracheal suspension 1.360 kg of the neonate weight should be administered 2.5 × 1.360 mL of intratracheal suspension = 3.401 mL of intratracheal suspension Ans∶ 3 4 1 mL of intratracheal suspension 15. A 142-lb. patient was receiving filgrastim (NEUPOGEN) in doses of 10 mcg/kg/day when, as a result of successful blood tests, the dose was lowered to 6 mcg/kg/day. Using an injection containing 0.3 mg filgrastim per 0.5 mL, calculate the previous and new dose to be administered. (a) 17.7 mL and 64.6 mL (b) 5.23 mL and 3.14 mL (c) 1.08 mL and 0.65 mL (d) 3.87 mL and 2.3 mL 142 lb represent = 64.41 kg Before blood test dose of patient = patient’s weight (kg)×

(

)

= 64.41 × = 644.1 µg of patient = 0.6441 mg filgrastim per day 0.3 mg of fil grastim present in 0.5 mL of injection 0.6441 mg of filgrastim present in

6441 = 1.0735 mL of injection 146

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION After blood test daily dose of the patient = patient’s weight (kg)×

(

)

= 64.41 × = 386.46 µg of Filgrastim 0.3 mg of filgrastim present in 0.5 mL of injection 386.46 µg = 0.386 mg filgrastim present in

386

= 0.643 mL of injection Ans∶ 643 mL of injection 16. A 25-lb. child is to receive 4 mg of phenytoin per kilogram of body weight daily as an anticonvulsant. How many milliliters of pediatric phenytoin suspension containing 30 mg per 5 mL should the child receive? 25 lb represent = 11.34 kg Patient daily dose = patient weight (kg) × = 11.34 ×

(

)

= 45.36 mg of phenytoin 30 mg of phenytoin present in 5 mL of suspension 45.36 mg of phenytoin present in

45 36

= 7.56 mL of suspension Ans∶ 7 56 mL of suspension

17. The loading dose of digoxin in premature infants with a birth weight of less than 1.5 kg is 20 mcg/kg administered in three unequally divided doses (1⁄2, 1⁄4, 1⁄4) at 8- hour intervals. What would be the initial dose for an infant weighing 1.2 kg? For 1.5 kg Patient dose = 1.5 × 20 µg of digoxin = 30 µg of digoxin 147

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Three unequally divided dose 1 3 15 2 1 3 75 4 1 3 75 4 For 1.5 kg of the weight initial dose = 15 µg of digoxin For 1.2 kg of the weight initial dose =

12

= 12 µg of digoxin Ans∶ 12 µg of digoxin 18. The pediatric dose of cefadroxil is 30 mg/ kg/day. If a child was given a daily dose of 2 teaspoonful’s of a pediatric suspension containing 125 mg of cefadroxil per 5 mL, what was the weight, in pounds, of the child? 2 teaspoonful = 5 × 2 = 10 mL 5 mL of suspension contain 125 mg of cefadroxil 10 mL of suspension contain = = 250 mg of cefadroxil Patient weight = = 8.33 kg 1 kg = 2.20 lb ∴ 8 33 kg

8 33

2 2 lb

= 18.36 lb Ans∶ 18 36 lb 19. How many milliliters of an injection containing 1 mg of drug per milliliter of injection should be administered to a 6-month-old child weighing 16 lb. to achieve a subcutaneous dose of 0.01 mg / kg?

148

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 16 lb represent = 7.26 kg For 7.26 kg of the child weight dose of the child = 7.26 (kg) ×

of drug

= 0.0726 mg of drug 1 mg of drug present in 1 mL of injection 0.0726 kg of drug present in 1 × 0.0726 mL of injection = 0.0723 mL of injection Ans∶

73 mL of injection

20. Prior to hip replacement surgery, a patient receives an injection of an anticoagulant- drug at a dose of 30 mg. Following the patient's surgery, the drug is injected at 1 mg/kg. For a 140-lb. patient, calculate the total of the pre- and postsurgical doses. Prior to hip replacement surgery a patient receive an injection of an anticoagulant drug at a dose of 30 mg 140 lb = 63.50 kg ∴ post-surgical dose for 63.50 kg of the patient weight = 63.50 (kg) × = 63.50 mg of injection Total of the pre and post surgical dose = 30 mg + 63.50 mg = 93.50 mg = 94 mg Ans∶ 94 mg 21. Using Table 8.2 and a daily dose of 2 mg/ kg, how many 20-mg capsules would a 176-lb. patient be instructed to take per dose if the daily dose is to be taken in divided doses, q.i.d.?

176 lb represent = 79.83 kg Daily dose for 79.83 kg patient= patient’s weight (kg)×

(

)

= 79.83 (kg) × = 159.66 mg 149

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION q.i.d means= four times a day ∴ per dose drug needed = 39.916 mg Number of 20 mg capsule needed per dose = = 2 capsule Ans∶ 2 capsule 22. For a 22-lb pediatric patient, the dose of cefdinir (OMNICEF ) was determined to be 7 mg/kg. What quantity of an oral suspension containing 125 mg of cefdinir in each 5 mL should be administered? (a) 2.8 mL (b) 5.6 mL (c) 8.9 mL (d) 13.6 mL 22 lb represent = 9.979 kg Dose of cefdinir for 9.979 kg patient = patient weight × = 9.979 × 7 mg = 69.85 mg 125 mg of cefdinir present 5 mL of oral suspension 69.85 mg of cefdinir present

69 85

= 2.794 mL of oral suspension = 2.8 mL of oral suspension Ans∶ 2.8 mL of oral suspension 23. How many capsules, each containing 250 mg of clarithromycin, are needed to provide 50 mg/kg/day for 10 days for a person weighing 176 lb.? 176 lb represent = 79.83 kg Patient dose = patient’s weight (kg)×

(

)

150

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 79.83(kg) × = 3991.61 mg of clarithromycin per day = 3991.61 × 10 mg of clarithromycin per 10 days = 39916.1 mg of clarithromycin per 10 days 250 mg of clarithromycin present in 1 capsule 39916.1 mg of clarithromycin present in

39916 1

= 159.66 capsules = 160 capsules Ans∶ 16 capsules 24. If the pediatric dose of dactinomycin is 15 mcg/kg/day for 5 days, how many micrograms should be administered to a 40-lb. child over the course of treatment? 40 lb represent = 18.24 kg Patient dose

= 18.24 kg × = 272.15 µg of dactinomycin per day = 272.15 × 5 µg of dactinomycine per 5 days = 1360.77 µg of dactinomycine per 5 days

Ans∶ 136 77 µg of dactinomycine per 5 days 25. If the administration of gentamycin at a dose of 1.75 mg/kg is determined to result in pick blood serum levels of 4 mcg/ml . calculate the dose , in milligrams for a 120 lb. patient that may be expected to result in a blood serum gentamycin level of 4.5 mcg/ml.

120-lb = 54.43 kg Administered gentamycin = 1.75 mg×54.43 = 95.25 mg To reach 4mcg/ml pick blood serum levels 95.43 mg gentamycin should administered. 151

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION To reach 4.5 mcg/ml pick blood serum levels = ×4.5 =107.16 mg Ans: 107.16 mg gentamycin should be administered.

26. A medication order calls for tobramycin sulfate, 1 mg/kg of body weight, to be administered by IM injection to a patient weighing 220 lb. Tobramycin sulfate is available in a vial containing 80 mg per 2 mL. How many milliliters of the injection should the patient receive?

220 lb represent = 99.79 kg (

Patient dose = patient’s weight (kg)× = 99.79 kg ×

)

tobramycin sulfate

= 99.79mg of tobramycin sulfate 80 mg of tobramycin sulfate present in 2 mL vial 99.79 mg of tobramycin sulfate present in

99 79 = 2.5 mL of vial

Ans∶ 2 5 mL of vial 27. The usual pediatric dose of acyclovir is 20 mg/kg administered by infusion and repeated every 8 hours. What would be the single dose, in milligrams, for a child weighing 33 lb.? 33 lb represent =14.968 kg Patient dose

= patient’s weight (kg)×

(

)

= 14.968 (kg) × = 299.370 mg of acyclovir = 300 mg of acyclovir 152

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans∶ 33 mg of acyclovir 28. If the recommended dose of tobramycin for a premature infant is 4 mg/kg/day, di- vided into two equal doses administered every 12 hours, how many milligrams of the drug should be given every 12 hours to a 2.2-lb. infant? 2.2lb represent = 0.9979 kg 1 kg of the infant weight require 4 mg of tobramycin per day 0.9979 kg of the infant weight require 4 × 0.9979 mg per day = 3.99 mg of tobramycin per day ∴ Dose is divided into two equal dose ∴ = 2 mg of tobramycin every 12 hours Ans∶ 2 mg of tobramycin every 12 hours 29. If a 3-year-old child weighing 35 lb. accidentally ingested twenty 81-mg aspirin tablets, how much aspirin did the child ingest on a milligram per kilogram basis? 35lb represent = 15.87 kg 15.87 kg child weighing accidentally in quested twenty 81 mg aspirin tablet = 20 × 81 mg aspirin = 1620 mg aspirin ∴ mg/kg basis 162 15 87 102.079 mg/kg Ans∶ 1 2 79 mg/kg 30. The recommended pediatric dose of epinephrine for allergic emergencies is 0.01 mg/kg. If a physician, utilizing this dose, administered 0.15 mg, what was the weight of the patient in pounds? 0.01 mg of epinephirine should be administered for 1kg patient 153

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 0.15 mg of epinephirine should be administered for

15

= 15 kg of patient 1 kg =2.20lb ∴ 15 kg

15

2 2 lb

= 33.069 lb Ans∶ 33 69 lb 31. The initial maintenance dose of vancomycin for infants less than 1 week old is 15 mg/kg every 18 hours. (a) What would be the dose, in milligrams, for an infant weighing 2500 g? (b) How many milliliters of an injection containing 500 mg per 25 mL should be administered to obtain this dose? (a) 1 kg of the infant weight require 15 mg of vancomycin every 18 hours 2500 g = 2.5 kg of the infant weight require 2.5 × 15 mg = 37.2 mg of vancomycin (ans) (b) 500 mg of vancomycin present in 25 mL of injection 37.2 mg of vancomycin present in

37 2

= 1.86 mL of injection Ans∶ 1 86 mL of injection 32. The loading dose of indomethacin in neonates is 0.2 mg/kg of body weight by intravenous infusion. (a) What would be the dose for a neonate weighing 6 lb., 4 oz.? (b) How many milliliters of an injection containing 1 mg of indomethacin per 0.5 mL should be administered to obtain this dose? (a) 6 lb represent = 2.72 kg 4 oz = 4× 28.35 g = 113.4 × 10-3 154

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 0.1134 kg ∴ weight

2 72 kg + 1134 kg = 2.8334 Kg

∴ Neonate dose

(

= patient’s weight (kg)×

)

= 2.8334 kg × = 0.57 mg of indomethacin Ans∶ 57 mg of indomethacin (b) 1 mg of indomethacin present in 0.5 mL of injection 0.57 mg of indomethacin present in

57

= 0.28334 mL of injection (ans)

33. Jimmy Jones Age: 8 years Wt: 88 pounds Metronidazole Suspension 7.5 mg/kg/day M.ft. dose 5 mL Sig: 5 mL bid × 10 days (a) How many milligrams of metronidazole will the patient receive per dose? (b) How many milliliters of the prescription should be prepared and dispensed? (c) If metronidazole is available in 250mg tablets, how many tablets will be needed to fill the prescription? 88 pounds represent = 39.916 kg 1 kg of the patient weight require = 7.5 mg of metronidazole per day 155

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 39.916 kg of the patient weight require= 7.5 ×39.916 mg of metronidazole per day = 299.37 mg of metronidazole per day “Sig” represent that 5 mL bid that means 5 mL twice a day ∴ Milligram of metronidazole will the patient receive per day = = 149.685 mg = 150 mg of metronidazole Ans∶ 15 mg of metronidazole (b) Millilitres of the prescription should be prepared = 5 mL bid × 10 days = 5 mL × twice a day × 10 = 100 mL Ans∶ 1

mL

(c) 5 mL of suspension contain 150 mg of metronidazole 100 mL of suspension contain

1

= 3000 mg of metronidazole 250 mg of metronidazole present in 1 tablet 3000 mg of metronidazole present in

3

= 12 tablets Ans∶ 12 tablets

156

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 34. Betty Smith Age: 4 years Weight: 52.8 pounds Erythromycin Ethyl Succinate (EES) 200 mg/5 mL Disp.300 ml Sig:…………ml qid until gone (a) If the dose of EES is 50 mg/kg/day, how many milliliters would provide each dose? (b) How many days would the prescription last the patient? 52.8 pound represent = 23.95 kg (a) 1 kg of the patient weight require = 50 mg of EES per day 23.95 kg of the patient weight require 50 × 23.95 mg of EES per day = 1197.48 mg of EES per day 200 mg of present in 5 mL 1197.48 mg of EES present in

1197 48

= 30 mL per day Sig: represent that q.i.d means four times a day Each dose =

7 5 mL

Ans∶ 7 5 mL (b) 30 mL needed for 1 day 300 mL needed for

3

= 10 days

157

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

Calculations Based on Body Surface Area: 35. If the daily dose of a drug is given in the literature as 8 mg/kg of body weight or 350 mg/m2, calculate the dose on each basis for a patient weighing 150 lb. and measuring 5 ft. 8 in. in height. 1 kg of the patient weight require 8 mg of the drug 150 lb = 68.035 kg of the weight require 8 × 68.038 mg of the drug = 544.31 mg = 545 mg of the drug Ans∶ 545 mg of the drug Again,

5 ft = 5730.48 cm = 152.4 cm

And

1 inch = 2.54 cm 8 inch = 8 × 2.54 cm = 20.32

Total height = 152.4 cm + 20.32 cm = 172.72 cm Weight = 68.038 kg ∴ BSA

(

√

) (

)

=√ = 1.8067 m2 = 1.8 m2 For 1 m2 BSA 350 mg of drug is needed For 1.8 m2 BSA 350×1.8 mg of drug is needed = 630 mg of drug is needed (ans)

158

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 36. If the dose of a drug is 10 mg/m2 per day, what would be the daily dose, in milligrams, for a child weighing 30 lb. and measuring 26 in. in height?

Weight of the child = 30 lb = 13.607 kg Height of the child = 26 inch = 66.04 cm ∴ BSA √ = 0.5 m2 Patient daily dose = 0.5×10 = 5 mg Ans∶ 5 mg 37. The dose of mitomycin injection is 20 mg/ m2 per day. Determine the daily dose for a patient who weighs 144 lb. and measures 68 in. in height. Weight = 144 lb = 65.317 kg Height = 68 inch = 172.72 cm ∴ BSA

√

= 1.77 m2 ∴ patient daily dose

1 77 m2 ×

= 35.40 mg Ans: 35.40 mg

159

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 38. The paediatric starting dose of ritonavir (NORVIR) is 250 mg/m2 by mouth twice daily. The available oral solution contains 600 mg of ritonavir in each 7.5 mL of solution. The correct volume and corresponding quantity of ritonavir to be administered to a child with a body surface area of 0.75 m2 per dose is: (a) 5.6 mL (450.4 mg) (b) 2.8 mL (450.4 mg) (c) 2.8 mL (225.2 mg) (d) 2.3 mL (187.5 mg) Patient daily dose=BSA× = 0.75 m2 × = 187.5 mg of ritonavir 600 mg of ritonavir present in 7.5 mL of solution 187.5 mg of ritonavir present in

187 5

= 2.3 mL of solution Ans∶ (d) 2.3 mL of solution 39. Calculate the dose for a child 4 years of age, 39 in. in height, and weighing 32 lb. for a drug with an adult dose of 100 mg, using the following: (a) Young's rule, (b) Cowling's rule, (c) Clark's rule, and (d) BSA (use the BSA equation). (a) Young’s rule Dose for child = =

1

= 25 mg Ans∶ 25 mg (b) Cowling’s rule Dose for child =

(

(

)

)

= 20.83 mg 160

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans∶ 2 83 mg (c) Clark’s rule: ( )

Dose for child =

(

)

21 33 Ans∶ 21 33 mg (d)

Weight = 32 lb = 14.51 kg Height = 39 inch = 99.06 cm ∴ BSA √ = 0.63 m2 ∴ Dose of the patient

1

= 36.42 mg Ans∶ 36 42 mg 40. The daily dose of diphenhydramine HCl for a child may be determined on the basis of 5 mg/kg of body weight or on the basis of 150 mg/m2. Calculate the dose on each basis for a child weighing 55 lb. and measuring 40 in. in height. 55 lb represent = 24.94 kg ∴ Dose of the child on the basis of 5 mg/kg = 24.94 kg = 124.73 mg of diphenhydramine HCl Ans∶ 124 73 mg of diphenhydramine HCl Or,,,, Weight = 55lb = 24.97 kg Height = 40 inch = 101.6 cm 161

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION ∴ BSA √ = 0.84 m2 ∴ Dose of child on the basis of 15 mg/m2 = 0.84 m2 × = 125 mg of diphenhydramine HCl Ans∶ 125 mg of diphenhydramine HCl

44. The drug carboplatin for ovarin carcinoma is administered intravenously at a dose of 360 mg/m2 except in patients with impaired kidney function, in which case the dose is reduced by 30 % . how many milligrams of the drug should be administered to a renally impaired patient measuring 5 ft. 2 in. and weing 110 lb? 5 ft = 152.4 cm and 2 inch = 5.08 cm (by using scientific calculator) so , height = 152.4+5.08 cm = 157.48 cm Weight = 110 lb = 49.89 kg BSA = √

(

)

(

)

BSA= √ = 1.477 m2 After 30% reduced

= 360 mg - 360×30% = 252 mg

Milligram of the drug should be administered to a renally impaired patients = 252×1.477 =372.204 mg Ans: 252.204 mg 162

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 45. A high dose treatment of osteocarcoma includes the use of methothexate at a

starting dose of 12 g/m2 as a four hour intravenous infusion. For a patient having a BSA of 1.7 m2 and weighing 162 lb. calculate the dose on the basis mg/kg/min.

For BSA 1.7 m2 the dose of patient = 20.4 g 162 lb represents = 73.48 kg On the basis of mg/kg = 20.4/73.48 = 0.2776 g = 277.61 mg On the basis of mg/kg/min = 277.61/ (4×60) = 1.15 mg Ans: 1.15 mg/kg/min.

163

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 46. A two agent dosage regimen terned MP, for the treatment of multiple myeloma is as follows: Melphalan

0.25 mg/kg, PO D1-4/week×6 weeks

Prednisone 2 mg/kg,PO D1-4/week×6 weeks (a) Calculate the total milligrams each of Melphalan and Prednisone taken per week by a patient who weigh 165 lb. (b) If Melphalan is available in 2 mg tablets. How many tablets are required to dose this patient for the entire treatment cycle? (c) If the patient prefers prednisone oral solution to prednisone tablets. How many millilitres of the solution (5mg/ml) should be dispensed weekly?

(a) For Melphalan: 165 lb represents = 74.84 kg (1 lb = 0.45 kg) Total melphalan required per week = 0.25 mg ×74.84 ×4 = 74.84 mg = 75 mg For prednisone: Total Melphalan required per week = 2×74.84×4 = 598.72 mg = 600 mg Ans: 75 mg of Melphalan and 600 mg Prednisone. (b) Total mg of Melphalan is required for 6 weeks = 75 mg×6 = 450 mg 164

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Total tablet required for the entire cycle treatment = 450/2 = 225 tablets Ans: 225 tablets.

(c) 5 mg of prednisone presents in = 1 ml of oral solution 600 mg of prednisone presents in = 600/5 = 120 ml Ans: 120 ml Prednisone oral solution.

47. A three agent dosage regimen, termed VAD, for the treatment of multiple Myolema includes the following drugs taken over a 28 days cycle. Vincristine: 0.4 mg/d, CIVI Day 1-4 Doxyrubicin: 9 mg/m2/d, CIVI Day 1-4 Dexamethasone: 40 mg/d, PO, D Day 1-4,9-12,17-20 Calculate the total quantity of each drug administered over the course of the treatment cycle for a patient with a BSA of 1.65 m2.

Vincristine: 0.4 ×4 = 1.6 mg Doxyrubicin:

9 mg× 1.65 ×4 = 59.04 mg 165

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Dexamethasone: 40 mg×4×4×4 = 480 mg Ans: Vincristine 1.6 mg, Doxyrubicin 59.04 mg, Dexamethasone 480 mg 48. A four agent dosage regimen, termed MOPP, for the treatment of Hodgkin lymphoma includes the following drugs taken over a 28-day cycle. Mechlorethamine 6 mg/m2 , I.V., D 1,8 Vincristine

1.4 mg/m2 , I.V., D1,8

Procarbazine

100 mg/m2 /d, P.O., D 1-14

Prednisone

40 mg/m2/d, P.O., D 1-14.

Calculate the total number of 20 mg tablets of prednisone and 50 mg tablets of Procarbazine to dispense to treat a patient with BSA of 1.5 m2 during the course of one treatment cycle.

Prednisone: Total mg of prednisone required for one cycle = 40 mg×1.5 ×14 = 840 mg Total number of tablets required = 840/20 = 42 tablets. Procarbazine: 166

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Total mg of Procarbazine required for one cycle = 100 mg×1.5 ×14 = 2100 mg Total number of tablets required = 2100/50 = 42 tablets. Ans: 42 tablets both of prednisone and Procarbazine. 49. The oncolytic agent laptinib (TYKERB) is administered in the treatment of breast cancer in daily doses of 1250 mg for 21 consecutive days in combination with the drug capecitabine (XELODA), which is administered in doses of 1000 mg/m2/day during days 1 to 14 of the 21 days treatment cycle. Calculate the total quantity of each drug to be administered during the treatment cycle to a 5 ft 2 inch woman weighing 110 pounds.

Lapatinib: Daily dose = 1250 mg So, for 21 days = 1250 ×21 = 26250 mg = 26.25 g

Capecitabine: Height: 5 ft = 152.4 cm and 2 inch =5.08 cm

(1 ft = 30.48 cm and 1 inch =2.54 cm)

So height: 152.4 cm + 5.08 cm = 157.48 cm Weight: 110 pound = 49.895 kg BSA = √

(

)

(

)

=√ = 1.477 m2 Total Capecitabine required for entire cycle = 1000 mg×1.477 ×14 167

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION =20678 mg = 20.72 g Ans: 26.25 g Lapatinib and 20.72 g Capecitabine 50. Among the single chemotherapeutic agents for breast cancer is docetaxel (TAXOTERE), which is administered 60 mg/m2 IV every 3 weeks. Calculate the dose for a 5 ft 4 inch patient who weighs 160 lb. Height : 5 ft = 152.4 cm and 4 inch = 10.16 cm So, total height = 152.4 cm+ 10.16 cm = 162.56 cm Weight: 160 lb= 72.57 kg BSA = √

(

)

(

)

=√ = 1.81 m2 Dose = 60×1.81 = 108.6 mg Ans: 108.6 mg 51. Based on the dose calculated in the above problem, how many millilitres of an injection containing 80 mg/2 ml docetaxel would be administered per dose?

80 mg present in 2 ml injection So, 108.6 mg present in =

×108.6

= 2.715 ml 168

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans: 2.71 ml injection 52. The chemotherapy regimen “CAF” during a 21 day cycle is: Cyclophosphamide Doxyrubicin 5-Fluorouracil

500 mg/m2 , D-1 50 mg/m2 , D-1 500 mg/m2 , D-1,8

Calculate the dose of each drug/cycle for a patient with a BSA of 1.9 m2. Cyclophosphamide: =500 mg×1.9×1 = 950 mg Doxyrubicin: =50 mg ×1.9×1 = 95 mg 5-Fluorouracil: = 500×1.9×2 = 1900 mg

Ans: 950 mg cyclophosphamide, 95 mg doxyrubicin and 1900 mg 5Fluorouracil.

CALCQUIZ 8.A. The drug eribulin mesylate is used in late-stage metastatic breast cancer at an intravenous dose of 1.4 mg/m2. It is administered on days 1 and 8 of a 21 days cycle . The dose is reduced by 20 percentage for patient with moderate renal impairment. Calculate the reduced dose, in (a) mg/m2, (b) mg/kg, and (c) the treatment day dose, in milligrams, for a 110-lb patient measuring 5 ft 2 in. in height. 169

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

(a) Reduced dose = = 0.28 mg/ml (b) 0.28/49.94 = 0.0056 mg/kg Ans: 0.0056 mg/kg (c) Patient’s weight = 110×0.454 = 49.94 kg Patient’s height = 5 ft, 2 in = (5×12)+2 = 62 inch = 62×2.54 cm = 157.48 cm So, Body Surface Area (BSA) = √

(

)

(

)

=√ = 1.478 m2 So, dose = 1.4×1.478 = 2.06 mg Ans: 2.06 mg 8.B. A parent takes her 5 and 7 year old boys to the pediatrician, both with pharyngitis. The boys weigh 40 and 50 lb, respectively. The doctor prescribes an oral suspension of cefuroxime axetil (CEFTIN) at a dose of 20 mg/kg/day divided b.i.d×10 days. The suspension has a cefuroxime axetil concentration of 125 mg/mL. How many milliliters of suspension will be needed during the course of treatment?

We know that b.i.d means two times a day So, total dose = 2×10 = 20 for 10 days 40 lb = 40×0.454 = 18.16 kg And 50 lb = 50×0.454 = 22.7 kg 40 lb: mg of Cefuroxime axetil needed for 40 lb patient = 18.16×20 = 363.2 mg

170

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 125 mg cefuroxime present in = 1 mlsuspension So, 363.2 mg of cefuroxime present in =

= 2.9 ml

50 lb: mg of Cefuroxime present in 50 lb patient = 454 mg

125 mg of cefuroxime present in 1 ml suspension So, 454 mg of ……… = 454/125 = 3.63 ml Ans: 3.63 ml 8.C. The first day loading dose of a drug is 70 mg/m2 followed by a dose of 50 mg/m2 daily thereafter. Irrespectively of the pateint’s BSA, a dose is not to exceed 70 mg. For a 5-ft 8 in. 150-lb patient, Calculate the (a) BSA using the mosteller formula. (b) loading dose, (c) maintenance dose, and indicate whether each dose is within the safe limit.

(a) Patient’s weight = 5 ft 8 in = (5×12)+8 in = 68 in = 68×2.54 cm = 172.72 cm Height = 150 lb = 150×0.454 = 68.1 kg So, BSA= √ =√

(

)

(

)

= 1.807

(b) Loading dose = 70 mg×1.81 = 126.7 mg (c) Maintenance dose = 50×1.81 = 90.5 mg So, not safe

171

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 8.D. The pediatric oral dose of ciprofloxacin is given as 10 to 20 mg/kg every 8 hours, not to exceed a single dose of 400 mg irrrespectively of body weight. If a child weighing 55 ld is prescribed a once teaspoonful dose of a 5 % ciprofloxacin oral suspension every 8 hours, calculate whether or not the dose prescribed is within the therapeutic range.

55 lb = 55×0.454 = 24.97 kg Pediatric dose of ciprofloxacin = 10×24.97 to 20×24.97 = 249.7 to 499.4 mg Not exceed the dose 400 mg So, range = (200-400) mg Prescription represents, =

×5 = 0.25 g = 0.25×1000 = 250 mg

So, prescribed dose is within therapeutic range 8.E. The drug peginterferon alpha-2b is sometimes administered according to a stepdown protocol from a starting dose of 1.5 mcg/kg/wk, to 1 mcg/kg/wk, to 0.5 mcg/kg/wk. Calculate the three doses for a 5 ft 5 in, 132 lb patient (a) in milligrams and (b) on a mcg/m2 basis.

Weight = 132 lb = 132×0.454 = 59.92 kg Height = 5ft 5 in = 165.1 cm BSA = √ =√

(

)

(

)

= 1.726 m2 172

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION (a) First dose: 1.5×65 = 97.5 mcg, 2nd dose = 1× = 65 mcg 3rd dose = 0.5×65 = 32.5 mcg

173

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

CHAPTER : 09 SOME CALCULATIONS INVOLVING MEASURES OF POTENCY Basic concept: Units of Activity: The potency of many pharmaceutical products derived from biological sources is based on units of activity. Units of activity are determined against specific biologic standards and vary between products. Generally, there is an established relationship between a product's units of activity and a measurable quantity (e.g., units per milligram; units per milliliter). This relationship may be used in a ratio and proportion to determine either the number of units of activity or the weight or volume containing a specified number of units:

= Example calculation of units of activity: How many milliliters of U-100 insulin should be used to obtain 40 units of insulin

X= 0.4 ml (answer)

SOLUTION OF PROBLEM: Units of Activity Calculations 1. How many milliliters of U-100 insulin zinc suspension should be used to obtain 18 units of insulin? U-100 insulin contain 100 units/ mL 8

8

8 Ans∶

8 mL 174

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Or 100 units of insulin present in 1 mL of insulin zinc suspension 18 units of insulin present in=

8

= 0.18 mL of U100 insulin zinc suspension Ans∶

8 mL

2. If a diabetic patient injects 20 Units of insulin twice daily, how many days will a 10mL vial of the U-100 product last the patient? U-100 represent 100 units /mL

X = 1000 units 20 unit twice daily = 20 × 2 = 40 unit 40 unit insulin needed per day 1000 unit insulin needed per = 25 day Ans∶ 25 days

3. The biotechnology-derived product interferon beta-1b contains 32 million international units per milligram. Calculate the number of international units present in a vial containing 0.3 mg of interferon beta-1b. 2 X = 9.6 million unit Ans∶ 9 6 million units

4. ALFERON N injection contains 5 million IU of interferon alpha-n3 per milliliter. How many units will an injection of 0.05 mL deliver? 5 5 X = 0. 25 million units Ans∶ 25 million units 175

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 5. Insulin glargine (LANTUS) injection is available in 10-mL vials containing 100 units/mL. How many milliliters would a patient administer for (a) a starting dose of 10 units and (b) a maintenance dose of 4 units? (a)

= 0.1 mL insulin glargine Ans∶

mL insulin glargine

(b)

∴X = 0.04 mL insulin glargine Ans∶

mL insulin glargine

6. The content of a vial of penicillin G potassium weighs 600 mg and represents 1 million units. How many milligrams are needed to prepare 15 g of an ointment that is to contain 15,000 units of penicillin G potassium per gram? 1 g of the ointment contain = 15000 unit of penicillin G potassium 15g of ointment contain= 15 ×15000 units of penicillin G potassium = 225000 units of penicillin G potassium 10,00000 units of penicillin G potassium weighs = 600 mg 225000 units of penicillin G potassium weighs =

225

= 135 mg of penicillin G potassium Ans∶

5 mg of penicillin G potassium

7. HUMALOG contains 100 units of insulin lispro (rDNA origin) per milliliter. How many complete days will a 3-mL HUMALOG PEN last a patient whose dose is 35 units b.i.d?

176

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION ∴ Patient dose = 35 units bid that represent = 35 × 2 per day = 70 units per day ∴ mL of HUMALOG PEN will complete in = 4.28 day Ans∶ 28 day

8. A physician prescribes 2.5 million units of penicillin G potassium daily for 1 week. If 1 unit of penicillin G potassium equals 0.6 µg, how many tablets, each containing 250 mg, will provide the prescribed dosage regimen? Total units required for 7 day/ 1 week = 2.5 million × 7 units = 2.5 × 1000000 × 7 units = 17500000 units 1 units of penicillin G protein = 0.6 µg of penicillin G potassium 17500000 units of penicillin G potassium = 0.6 ×17500000 µg of penicillin G potassium = 10500000 µg of penicillin G potassium = 10500 mg of penicillin G potassium 250 mg of penicillin G potassium present in 1 tablet 10500 mg of penicillin G potassium present

5

= 42 tablets Ans∶ 2 penicillin G potassium tablet

9. Penicillin G Potassium

5000 units per mL

Isotonic Sodium Chloride Solution ad

15 mL

Sig. Nose drops. Using soluble penicillin tablets, each containing 200,000 units of crystalline penicillin G potassium, explain how you would obtain the penicillin G potassium needed in compounding the prescription. 177

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 mL of solution contain 5000 units of penicillin G potassium 15 mL of solution contain = 15 × 5000 units = 75000 units We need 75000 units of penicillin G potassium but 1 tablet supply 200000 units of crystalline penicillin G potassium. ∴ tablet dissolve in 8 mL of isotonic sodium chloride solution 200000 unit of penicillin G potassium present in 8 mL of solution ∴ 75

unit of penicillin G potassium present in

75

= 3 mL of solution Answer: So after dissolution to 8 mL of isotonic solution 3 mL of solution we have to take.

10. FOSAMAX PLUS D contains 70 mg alendronate and 140 mcg of vitamin D3, the latter equivalent to 5600 international units of vitamin D. At a once-a-week dose, calculate the daily intake of vitamin D3 in milligrams and units. FOAMAX PLUS contain 140 microgram of vitamin D = 0.14 mg of vitamin D 1 tab once a week ∴ Daily intake of vitamin D3 =

.

= 6.02 mg of vitamin D Ans∶ 6 2 mg of vitamin D Again, 0.14 mg of vitamin D3 contain 5600 units of vitamin D 0.02 mg of vitamin D3 contain

2

= 800 unit of vitamin D

(answer)

178

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 11. A vial for preparation of 100 mL of injection of the drug alteplase (ACTIVASE) contains 100 mg of drug equivalent to 58 million international units to be administered by intravenous infusion. Calculate (a) the units administered to a 176-lb. patient at a dose of 0.9 mg/kg and (b) the milliliters of injection to use. (a) 176 lb represent = 176 × 454 g = 79904 g = 79.90 kg 1 kg of the patient weight require = 0.9 mg of drug 79.90 kg of the patient required

= 79.90 × 0.9 mg = 71.91 mg of drug

100 mg of drug = 58000000 units 71.91 mg of drug contain =

7 9

= 41707800 units = 41.7 million units Ans∶

7 million units

(b) 58 million unit of drug present in 100 mL of injection 41.7 million unit of drug present in

7

= 71.89 mL of injection = 72 mL of injection (answer)

12. Calcitonin is available as an injection containing 200 international units per milliliter. Adult doses of up to 32 units per kilogram have produced no adverse effects.On this basis, if a 120-lb. patient were administered 0.75 mL of injection, would adverse effects be anticipated? 176 lb represents = 79.83 kg 1 kg of body weight needs 32 units 79.83 kg of body weight need 32 × 79.83 unit = 2554.56 units 179

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION If patient take 2554.56 units no adverse effect will produce Patient were administered 0.75 mL of injection 1 mL of injection contain 200 unit 0.75 mL of injection contain 200 × 0.75 unit = 150 units Ans∶ No

13. A physician's hospital medication order calls for a patient to receive 1 unit of insulin injection subcutaneously for every 10 mg/dL of blood sugar over 175 mg/dL, with blood sugar levels and injections performed twice daily in the morning and evening. The patient's blood sugar was 200 mg/dL in the morning and 320 mg/ dL in the evening. How many total units of insulin injection were administered? Patient over blood sugar in the morning = ( 200 mg/dl – 175 mg/dl) = 25 mg/dl Patient over blood sugar in the evening

2 mg/dl − 75 mg/dl

= 145 mg/dl In case of morning : For 10 mg/dl of blood sugar over 175 mg/dl patient needed 1 unit of insulin injection For 25 mg/dl of blood sugar over 175mg/dl patient needed =

25 Unit

= 2.5 unit of insulin injection In case of evening : For 10mg/dl of blood sugar over 175 mg/dl patient needed 1 unit of insulin injection For 145 mg/dl of blood sugar over 175 mg/dl patient needed =

5

Unit

= 14.5 unit of insulin injection ∴ Total

5 + 2 5 unit = 17 units (answer)

14. A physician's hospital medication order calls for isophane insulin suspension to be administered to a 136-lb. patient on the basis of 1 unit/kg per 24 hours. How many units of insulin suspension should be administered daily? 180

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 136 lb represents = 61.688 kg 1 kg of the patient weight should be administered 1 unit of isophane insulin suspension per day 61.688 kg of the patient weight should be administered = 61.688 × 1 unit of isophane insulin suspension per day = 61.688 unit per day Ans∶ 6 688 unit per day

15. Somatropin (NUTROPIN) contains 5 mg of drug equivalent to approximately 15 international units of drug in a vial to prepare 10 mL of injection. If the starting adult dose is 0.006 mg/kg, calculate the dose (a) in units and (b) in milliliters for a 132-lb. patient. (a) 132 lb represent = 59.87 kg Starting adult dose for 1 kg of the patient weight = 0.006 mg of drug Starting adult dose for 59.87 kg of the patient weight 0.006 × 59.87 mg = 0.34 mg of drug 5 mg of Somatropin = 15 unit of drug in vial 0.34 mg of drug = = 1.02 unit of somatropin Ans∶

2 unit of somatropin

(b) 15 unit of somatropin is used to prepare 10 mL of injection 1.02 unit of somatropin

2

= 0.68 mL of injection Ans∶ 68 mL of injection

181

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 16. Cod liver oil is available in capsules containing 0.6 mLper capsule. Using Table 9.1, calculate the amounts, in units, each of vitamins A and D in each capsule. The specific gravity of cod liver oil is 0.9. Volume of cod liver oil = 0.6 mL /capsule S.G of cod liver oil = 0.92 ∴ weight of cod liver oil

SG

volume

= 0.6 × 0.92 = 0.552 g /capsule From table 9.1: 1 g of cod liver oil contain 600 to 2500 units of vitamin A and 60 to 250 unit of vitamin D ∴ 552 g of cod liver oil contain (600×0.552) to (2500 × 0.552) units of vitamin A and (60×0.552) to (250 × 0.552) units of vitamin D = 331.2 to 1380 units of vitamin A and 33.12 to 138 units of vitamin D Ans∶

8 unit of vitamin A and

8 unit of vitamin D

17. A hepatitis B immune globulin contains 312 international units per milliliter. If the dose is 0.06 mL/kg for certain at-risk persons, calculate the dose (a) in units and (b) in milliliters for a 132-lb. person. (a) 132 lb represent = 59.87 kg 1 kg of the patient weight required 0.06 mL of hepatitis B immune globulin 59.87 kg of the patient weight required 59.87 × 0.06 mL of hepatitis B immune globulin = 3.59 mL of hepatitis B immune globulin 1 mL contain 312 unit of hepatitis B immunoglobulin 3.59 mL contain 3.59 × 312 unit of hepatitis B immunoglobulin = 1120 unit of hepatitis B immunoglobulin Ans∶

2 unit of hepatitis B immunoglobulin

(b) 182

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 312 unit of hepatitis B immunoglobulin present in 1 mL 1120 unit of hepatitis B immunoglobulin present in

2

= 3.6 mL Ans∶ 6 mL

18. If a 5-mL vial of HUMATROPE, a biosynthetic somatotropin of rDNA origin, contains 5 mg of somatotropin equivalent to 13 international units, how many milligrams of somatotropin and how many international units would be administered in a 0.6-mL dose? 5 mL vial contain 5 mg of somatotropin 0.6 mL vial contain

6

= 0.6 mg of somatotropin Ans∶ 6 mg of somatotropin 5 mL of vial contain 13 unit of somatotropin 0.6 mL of vial contain

6

= 1.56 unit of somatotropin Ans∶ 56 unit of somatotropin

19. EPOGEN injection is available containing in each milliliter, 2000, 3000, 4000, or 10,000 units of epoetin alfa. If the staring dose for a 160-lb. patient is prescribed at 50 units/kg, which of the following would provide that dose? (a) 4 mL of 2000 units/mL (b) 1 mL of 3000 units/mL (c) 0.9 mL of 4000 units/mL (d) 0.8 mL of 10,000 units/mL 160 lb represent = 72.57 kg 1 kg of the patient weight require 50 units of epoetinalfa 72.57 kg of the patient weight require 50 × 72.57 units of epoetinalfa = 3628.7 unit of epoitin alfa 2000 units of epoetin alfa present in 1 mL of EPOGEN injection 3628.7 units of epoetin alfa present in 183

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 1.8 mL 3000 units of epoetin alfa present in 1 mL of EPOGEN injection 3628.7 units of epoetin alfa present in = 1.21 mL 4000 units of epoetin alfa present in 1 mL of EPOGEN injection 3628.7 units of epoetin alfa present in

628 7 = 0.90 mL of injection

Ans∶ c

9 mL of

units /mL

20. The prophylactic dose of tetanus antitoxin is 1500 units for persons weighing less than 65 lb. and 3000 to 5000 units for persons weighing more than 65 lb. The antitoxin is available in dose vials of 1500 units, 3000 units, 5000 units, and 20,000 units. Which vial should a pharmacist provide for administration to a patient weighing 25 kg? 25 kg represent = 25 × 2.20 lb = 55.11 lb So , 1500 units vial Ans∶ 5

units vial

Additional Calculations of Potency 21. Using Table 9.1, calculate the clindamycin potency equivalence, in milligrams per milliliter, of a solution containing 1 g of clindamycin hydrochloride in 10 mL of solution Clindamycin hydrochloride

solution

= 0.1 × 103 mg/mL solution = 100 mg/mL solution From 9.1 : NLT 800 mcg of clindamycin hydrochloride present per mg

184

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 mg contain 800 µg of clindamycin hydrochloride 100 mg contain 800 × 100 µg of clindamycin hydrochloride = 80,000µg of clindamycin hydrochloride = 80,000 ×10-3 mg of clindamycin hydrochloride = 80 mg/mL of clindamycin hydrochloride Ans∶ 8 mg/mL clindamycin hydrochloride

22. Each 1-mL adult dose of hepatitis A vaccine contains 1440 EL.U. of viral antigen. What would be the pediatric dose of this vaccine if 360 EL.U. of viral antigen are to be administered? (a) 0.8 mL (b) 0.25 mL (c) 4 mL (d) 0.4 mL

1440 ELU of viral antigen present in 1 mL of hepatitis A vaccine 360 ELU of viral antigen present in

6

of hepatitis A vaccine

= 0.25 mL of hepatitis A vaccine Ans∶ 25 mL

23. Each 0.01 mL of a mumps vaccine contains 400 TCID50 of the mumps virus. If the usual dose contains 20,000 TCID50, how many milliliters of vaccine should be administered? 400 TCID 50 of mumps virus present in 0.01 mL of mumps vaccine 20,000 TCID 50 of mumps virus present in

2

= 0.5 mL of mumps vaccine Ans∶ 5 mL of mumps vaccine

24. If a biologic product contains 7.5 Lf Units of diphtheria toxoid per 0.5 mL, how many flocculating units would be present in a 7.5-mL multiple dose vial? 0.5 mL of product contain 7.5 Lf unit of diphtheria toxoid 7.5 mL of product contain

75 185

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 112.5 Lf unit of diphtheria toxoid Ans∶

2 5 Lf of diphtheria toxoid

25. Zoster Vaccine Live (ZOSTAVAX) contains about 29,850 plaque-forming units (PFU) of attenuated virus per 0.1 cL. Approximately how many PFUs would be contained in each 0.65-mL dose? (a) 45,900 PFU (b) 4590 PFU (c) 1940 PFU (d) 19,400 PFU 0.1 cL =0.1 × 10-2 L = 0.1 × 10-2 × 103 mL = 1 mL 1 mL of zoster live vaccine contain 29850 plague forming units (PFU) 0.65 mL of zoster live vaccine contain 0.65 × 29850 PFU = 19402.5 PFU Ans∶ d

9

PFU

CALCQUIZ 9.A. If a 5-ml quantity of a nystatin oral suspension is prepared to contain 500,000 USP Nymstatin units, using table 9.1, calculate (a) the concentration of Nystatin in the suspension in mg/mL. If a child’s dose is 2 mL four times a day, how many (b) nystatin units and (c) milligrams of nystatin would be administered daily?

(a) Table 9.1 stated that, 186

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 4400 Nystatin USP unit present in 1 mg So, 500,000 Nystatin USP unit in = = 113.63 mg So, mg/ml = 113.63/5 = 22.72 mg/ml Ans: 22.72 mg/ml (b) 2 ml four times a day So, 4×2 =8 ml needed 5 ml contain = 500,000 unit of Nystatin USP So, 8 ml contain = = 800,000 unit of Nystatin USP Ans: 800,000 units of Nystatin (c) 5 ml contain = 113.63 mg of Nystatin So, 8 ml contain =

×8

= 181.80 mg of Nystatin Ans: 110 mg of Nystatin

9.B. The drug dalteparin sodium (FRAGMIN) is administered by subcutenous injection in patients with unstable angina or myocardial infraction at doses of 120 units/kg but not to exceed 10,000 units. Prefilled calibrated syringes are available with the following strengths (unit/ml): 2500/0.2ml, 5000/0.3 mL, 10,000/0.4 mL, 12500/0.5 mL, and 15,000/0.6 mL. Calculate (a) the most efficient product strength to use to dose a patient weighing 148 lb, (b) the volume of that injection to administer, and (c) the weight of a hypothetical patient, in pounds, to reach the maximum dose of 10,000 units. 187

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

(a) 148 lb = 148×0.454 = 67.19 kg So, dose = 120×67.19 unit = 8062 unit So, 10,000/0.4 ml strength product is efficient (b) 10,000 unit present in = 0.4 ml inj So, 8062.6 unit present in = ×8062.6 = 0.32 ml injection Ans: 0.32 ml injection (c) 120 units need for 1 kg patient weight So, 10,000 units need for = = 83.33 kg Ans: 83.33 kg 9.C. An injection contains 5 million international unit (MIU) of interferon alpha n3 (ALFERON N) proteins per milliliter. The recommended dose is 0.05 mL. The literature states that the ativity of interferon alpha-n3 is approximately equal to 2.8 ×108 international units/mg of protein. Calculate; (a) the number of international units and (b) the micrograms of interferon alfa-n3 proteins administered per dose.

(a) Recommended dose = 5 million ×0.05 = 0.25 million = 0.25×10,00000 = 250,000 units Ans: 250,000 units (b) 2.6×108 units present in 1 mg So, 250,000 units present in = = 9.61×10-4 mg = 9.61×10-4×103 µg 188

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION = 0.96 mcg Ans: 0.96 mcg 9.D. One general guideline for the maintenance dosing of heparin in pediatric patients is 100 units/kg every 4 hours, or, 20,000 units/m2/24 h administered continuously. The available injection for use by intravenous infusion contains 100 USP heparin units/mL. For a 44-lb child, measuring 42 in. in height, calculate the difference between the quantities of heparin administered over a 24 hour period in (a) heparin units, (b) milligrams of heparin (sodium) , and (c) in milliliters of heparin injection. Try yourself, If you need any help then email to – [email protected]

189

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION

CHAPTER: 10 SELECTED CLINICAL CALCULATIONS Basic concept: Dosage calculation based on creatinine clearance: Dosage may be defined as , Administration of a therapeutic agent in prescribed amounts. There are two mechanism by which drugs can be eliminated from the body 01. Hepatic metabolism 02. Renal excretion. The ideal body weight gives an excellent estimation of the volume of distribution, particularly for some polar drug that are not well distributed in adipose tissue. IBW can be calculated by following equation: For male : IBW = 50 kg +2.3 kg for each of patients height over 5 feet Or in pound, 110 lb. + 5 lb. for each inch over 5 feet. For females: IBW= 45.5 kg + 2.3 kg for each inch of patient height over 5 feet Or in pound, 100 lb. + 5 lb. for each inch over 5 feet Example calculation of IBW: Calculate the ideal body weight for a male patient weighing 164 lb. and measuring 5 ft.8 inch in height. IBW= 110 lb + (8×5 lb.) = 110 lb. + 40 lb. = 150 lb, answer Equation for calculating creatinine clearance: By the jelliffe equation: For males: CrCl = For females: 189

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION CrCl = 0.9 × CrCl determined using formula for males

By the cockcroff-gault equation: For males: CrCl

=

For females: CrCl = 0.85× CrCl determined using formula for males. Loading dose and maintenance dose: LD = IBW in kg or lb × drug dose per kg per dosing interval For the normal patient Maintenance dose: MD = IBW × dos per kg dosing interval For renally impaired patient: MD =

× dose for normal patient

Adjusting CrCl for body surface area: × CrCl = adjusted CrCl

SOLUTION OF PROBLEMS: 1.. A hospital pharmacy order calls for 5000 units of heparin to be administered to a patient, twice daily, subcutaneously, for the prevention of thrombi. The pharmacist has on hand a vial containing 10,000 Heparin Units/mL. How many milliliters of the injection should be administered for each dose?

190

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION 1 mL of vial contain 10,000 units of heparin 10000 units of heparin present in 1 mL of vial 5000 units of heparin present in = 5 = 0.5 mL of vial Ans∶ 0.5 mL of vial

02. A physician orders 1500 units of heparin to be administered by intravenous infusion per hour. The pharmacy provides a heparin intravenous bag containing 25,000 units of heparin in 250 mL of D5W. How many milliliters should be administered per minute? Per 1 hour = 60 minutes physician ordered 1500 unit of heparin Per 1 min physician ordered = unit of heparin = 25 unit of heparin 25000 unit of heparin present in 250 mL of D5W 25 units of heparin present in 5 = 0.25 mL Ans∶ 0.25 mL /min 3. A male patient weighing 76 kg is placed on heparin therapy for the prevention of deep vein thrombosis after surgery. (a) How many milliliters of a heparin injection containing 5000 units/mL should be administered for a loading dose of 80 units/kg? (b) What should be the infusion rate, in mL/hr, using a solution that contains heparin 25,000 units/500 mL, to administer 18 units/kg/hr? (c) Six hours after heparin therapy is initiated, the patient's PTT is found to be 60 seconds. Adjust the infusion rate, in mL/hr, according to the highdose heparin protocol (Fig. 10.1). (a) 1 kg of the patient weight required 80 unit of heparin 76 kg of the patient weight required 80 × 76 = 6080 unit of heparin 5000 units of heparin present in 1 mL of injection 6080 units of heparin present in 6 8 = 1.216 mL of injection 191

TROUBLESHOOT OF PHARMACEUTICAL CALCULATION Ans∶ 1 216 mL of injection (b) Per hour 1 kg of the patient required 18 units of heparin Per hour 76 kg of the patient required 76 × 18 units of heparin = 1368 units of heparin 25000 units of heparin present in 500 mL of solution 1368 units of heparin present in 1368 L of solution = 27.36 mL of solution Ans∶ 27 36 mL per hour 04. A blood sample taken from a 113 lb patient 6 hours after heparin therapy is initiated shows a PTT of 24 seconds . calculate (a) thebolus dose rate and (b) infusion rate , in ml /hr, according to the high dose heparin protocol (fig 10.1) (a) We know that for the PTT