The densities of aqueous solutions of certain electrolytes at 25°C

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NAME AND ADDRESS

DATE

NORTHWESTERN UNIVERSITY

THE DENSITIES OP AQUEOUS SOLUTIONS OF CERTAIN ELECTROLYTES AT 25°C

A DISSERTATION SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS for the degree DOCTOR OF PHILOSOPHY

DEPARTMENT OF CHEMISTRY

BY CHARLES FRANKLIN ECKERT

EVANSTON, ILLINOIS JUNE, 1942

P ro Q u e st N u m b e r: 10101352

All rights re s e rv e d IN FO RM A TIO N TO ALL USERS The q u a lity o f this re p ro d u c tio n is d e p e n d e n t u p o n th e q u a lity o f th e c o p y s u b m itte d . In th e unlikely e v e n t th a t th e a u th o r d id n o t sen d a c o m p le te m a n u sc rip t a n d th e r e a re missing p a g e s , th e s e will b e n o te d . Also, if m a te ria l h a d to b e re m o v e d , a n o te will in d ic a te th e d e le tio n .

uest. P ro Q u es t 10101352 P ublished b y P ro Q u e s t LLC (2016). C o p y rig h t o f th e Dissertation is h e ld b y th e A uthor. All rights re se rv ed . This w ork is p r o te c te d a g a in s t u n a u th o rize d c o p y in g u n d e r Title 17, U n ite d States C o d e M icro fo rm Edition © P ro Q u est LLC. P ro Q u e s t LLC. 789 East E ise n h o w er P arkw ay P.O . Box 1346 A nn Arbor, Ml 48106 - 1346

AC KN 0WLED GMENTS

The author wishes to express his sincere appreciation to Dr. Frank T. Gucker, Jr., under whose direction this research was carried out. He is also indebted to Dr. I. M. Klotz for his aid in interpreting the experimental results for sulfuric acid.

f

j o i't

TABLE OF CONTENTS page Introduction................ . ................

1

Statement of the Problem

• • • • ............

8

Experimental Method and Apparatus ............ Floats...................... Thermostat................................ Balance and W e i g h t s ......................

11 11 12 13

Materials and Solutions...................... 15 Ammonium Dichrornate...........................15 15 Thorium Nitrate............................ Urany1 Nitrate ............................ 15 Magnesium Chloride ........................ 16 17 Magnesium Sulfate.......................... Sodium Chloride............................ 17 Sulfuric Acid.............................- . 17 17 Water............ Experimental Procedure........................

18

Experimental Results and Discussion Definition of symbols...................... Ammonium Dichr ornate........................ Thorium Nitrate. ........................ Uranyl Nitrate ............................ Magnesium Chloride ........................ Magnesium S u l f a t e ........................ Solutions Containing TwoSolutes ............ Magnesium Sulfate andSodiumChloride. . . . Sulfuric Acid..............

21 22 24 28 30 31 35 40 45

Summary.

50

...............................

^ '2^”

INTRODUCTION The thermodynamic properties of solutions have interested many investigators who have desired to learn more about the nature and structure of solutions*

Among these thermodynamic

properties are the apparent molal quantities involving volume, expansibility, heat capacity, and compressibility* An apparent molal property of a solute may be defined by the equation

q

- mGj.0

m

where G is any extensive property of a solution, G* the corresponding molal property of the solvent, and ni and n2 the 1

number of moles of solvent and solute.

Thus, the apparent

molal volume of the solute may be defined by the equation

(2 ) where V is the volume of solution containing n2 moles of solute and n* mdes of solvent, and V*0 is the molar volume of the pure solvent.

The other apparent molal quantities may be defined

by a similar treatment of equation (1).

The apparent molal

volume may also be defined by either of the following equations 1Q00 - 1000

4>vs or

c _ 1000

CpVs 2 “

c

(3)

mdi 1 di

1000

(1) Gucker, J.Phys.Chem*, 38, 307 (1934)

c

d

M2

(4 )

2. where c and m represent molarity and molality, respectively. The apparent molal quantities are used as intermediate steps in the calculation of the partial molal properties of solute, Gs, and solvent, Gi, defined by the equations:

- (anJnijT and

(B G ) Gi = U n J n2)T

(6)

A perfect solution may be defined as one for which the apparent molal properties of the solute in solution are identical with the corresponding molal properties of the pure solute.

In general, it has been found that the deviations of

non-electrolytes from perfect solute behavior are linear functions of the first power of the concentration. According 2 to the theoretical work of Fuoss these deviations may be ascribed to the mutual interaction of dipolar solute molecules, and they should increase with increasing dipole moment* A systematic study of the heat capacities and densities of aqueous solutions of some amino acids and their uncharged isomers has been carried out in this laboratory in recent years. It has been found that the apparent molal heat capacities of solutions of glycine, glycolamide,©2.25)

F

= -47.896 + 2.069/a £ , Wirth15a

(C)

For

KBr,

F

= -85.141 + 1.842//-, Wirth

(D)

For

K2S04 ,

F

= -142.068 + 6.987/1^, Wirth

(E)

For

HC1,

F

= - 18.445 + 0.952/*'*'- 0.033/*, Wirth

Js

15 V,

u (F)

}

For

MgS04 ,

F

= -124.24 + 1 0 . 6 3 ^ % this research

(G)

The following table shows how well the above equations reproduce the observed density data. TABLE 10 lation

Upper Limit Ionic Strength

A B C D E F G

1.0 1.0 1.0 1.0 0.7 1.0 1.0 2.2 (1 .0)

£d = obs.-calcd. p. p.m. Max. Ave • +2.5 +2.0 +3.7 +5.2 +2.0 +9.0 +2.1 +3.0 +9.0

6 6 +7 -9 5 +36 +3 16 -27

(In the case of magnesium sulfate the upper limit of concen­ tration is about one mole per liter, which cannot be expressed in terms of ionic strength because the degree of dissociation is not known exactly.)

The results of the comparisons of calculated values with the observed values of the density are shown in Tables 11, 12, 13, 14 and 15, where A d = observed-calculated is given in p*p«m* in the last column,

eg refers to the concentration of

sodium chloride in moles per liter and C3 is the molar concen­ tration of the other solute.

The following observations can be

made. For the solutions of potassium chloride and sodium chloride in varying proportions the average deviation between the observed and calculated values is +6 p.p.m. up to an ionic strength of 0.98.

At higher concentrations the calculated

values are larger and the deviations tend to get larger with increasing concentration. For mixtures of potassium bromide and sodium chloride the average deviation between the observed and calculated values is ±7 p.p.m. up to an ionic strength of 0.98.

As in the previous

case the calculated values are larger and the deviations are about the same. For solutions containing hydrochloric acid and sodium chloride in varying proportions the average value of A d is +4.5 p.p.m. up to an ionic strength of 0.98.

At higher con­

centrations the calculated values are generally too low and the magnitude of the deviations increases with increasing con­ centration. For solutions of potassium sulfate in sodium chloride solutions of varying concentrations the average deviation between the observed and calculated values is -6 p.p.m. up to

TABLE 11 Densities of Aqueous Solutions of Potassium Chloride and Sodium Chloride at 25°C. i5a Data of Wirth KCl,

F = -47.896 + 2.069/h-

HaCl, F = -41.894 + 1.873/A C3

c3

0.03845 .1547 .03832 .1541 .3465 .03810 .3453 .1533 .6189 .03779 •3433 .6167 .1520 .6131 .3404 .9708 .9673 .9614

0.03967 .03937 .15904 .15870 .03958 .36704 .16003 .35562 .03956 .63849 .35840 .15980 .64044 .35790 .63804 .03972 .15906 .35906

JA 0.07812 .19407 .19736 .31280 .38608 .39884 .50533 .50892 .65846 .67628 .70170 .77650 .79244 .97100 .97844 1.01052 1.12636 1.32046

an ionic strength of 0.4.

s-x 0.27949 •44048 .44425 .55931 .62136 .63154 .71087 .71335 .81744 .82236 .83768 .88119 .89018 .98537 .98918 1.00522 1.06128 1.14911

lOOOCd-di ) observed 3.465 8.199 9.043 13.714 15.958 18.357 21.437 22.729 26.808 30.991 30.389 32.170 35.614 40.947 42.872 40.644 45.837 54.491

1000(d-d±) calcd.

Ad p.p.m

3.467 8 .203 9.044 13.712 15.958 18.357 21.438 22.725 26.816 31.020 30.389 32.180 35.609 40.964 42.884 40.663 45.872 54.551

-2 -4 -1 2 0 0 -1 4 -8 -29 0 -10 5 -17 -12 -19 -35 -60

Almost all of the calculated values

are too large and the deviations increase rapidly as the con­ centration increases. Eight solutions containing magnesium sulfate and sodium chloride in constant proportion and ranging in concentration from 0.04 M to 0.74 M were investigated.

The ratio of the

molarity of sodium chloride to the molarity of magnesium sulfate was 16.431 as in the work reported by Bremner, Thompson and fttterback16a on sea water.

The solutions were prepared

TABLE 12 Densities of Aqueous Solutions of Potassium Bromide and Sodium Chloride at 25°C. i5a Data of Wirth KBr, ’F = -85.141 + 1.842/1^ NaCl, F = -41.894 + 1.873/*^ c3

Cg 0.03902 .1571 .03885 .1564 .3497 .03857 .3482 .1553 *6161 .03819 .3457 .6134 .1537 .6089 .3421 .9702 .9658 .6026 .9585 .9484

0*03998 .03997 .15982 .15946 .03971 .36075 .15940 .36000 .03950 .63524 .35949 .15915 .63956 .35969 .63693 .03939 .15936 .63854 .36027 .63474

Hu 0.07900 .19707 .19867 .31586 .38941 .39932 .50760 .51530 .65560 .67343 .70519 .77255 .79326 .96859 .97903 1.00959 1.12516 1.24114 1.31877 1.58314

0.28106 .44393 .44572 .56205 .62403 .63192 .71247 .71785 .80970 .82063 .83974 .87897 ..89066 .98418 .98948 1.00476 1.06070 1.11405 1.14837 1.25823

1000(d-dj.) observed 4.996 9.822 15.077 19.806 17.581 31.876 27.504 36.481 28.174 54.673 44.017 37.969 59.589 54.355 66.770 42.059 51.673 77.030 67.802 89.717

1000(d-di) calcd.

Ad p.p.m.

4.997 9. 821 15.071 19.799 17.577 31.865 27.485 36.471 28.180 54.666 43.990 37.979 59.586 54.358 66.766 42.100 51.800 77.043 68.006 90.070

-1 1 6 7 4 11 19 10 -6 7 27 -10 3 -3 4 -41 -127 -13 -204 -353

in the following manner: A dilute solution of magnesium sulfate of known concentration was prepared and its density was determined.

To a weighed portion of this solution sufficient

solid sodium chloride was weighed in so that the salts were present in the desired ratio.

Then more water-was added, and

the weight of the whole solution and its density were deter­ mined.

From the weights of materials and the densities, the

final concentration was calculated. A plot of F vs yU^is given in Figure 7> the straight line is

equation of

TABLE 13 Densities of Aqueous Solutions of Hydrochloric Acid and Sodium Chloride at 25°C.

NaCl

c2 0.03982 .04996 .11539 .03977 .08916 .15884 .03964 .19720 .15849 .31397 .35587 .12945 .47057 .35406 .27714 .03941 .15763 .63098 .82688 .35239 .62650 .15653 .97546 .97088 1.0476 .34941 .42686 .96104 .92398 .29725 2.2375 .63318 2.2231 1.3308 2.1907 2.1592 .39819 .82676

.445 + 0. 952 jx

•833 + 1. 609 JA- + 0.213/* (yU2. 25)

c3 0.05052 .04151 .04146 .12175 .15557 .08781 .29836 .15527 .19603 .04131 .12580 .35880 .15448 *.27855 .35782 .59643 .48263 .04107 .15343 .62819 .35544 .84330 .19075 .42460 .35248 1.0539 .98102 .92486 .97125 2.1659 0.29181 2.1510 .59933 2.1190 1.2864 1.9514 4.1980 4.1590

- 0.033yU

II 1 ^ H

H C1,

li I H 00

Data of Wirth

0.09034 .09147 .15685 •16152 .24473 .24665 .33800 .35247 .35452 .35528 .48167 .48825 .62505 .63261 .63496 .63584 .64026 .67205 .98031 .98058 .98194 •99983 1.16621 1.39548 1.4001 1.4033 1.40788 1.88590 1.89523 2.4632 2.5293 2.6842 2.8224 3.4498 3.4771 4.1106 4.5962 4.9858

0.30056 .30244 .39604 .40190 .49470 .49664 .58138 .59369 .59541 .59606 .69402 .69875 .79060 .79537 .79684 .79740 .80016 .81979 .99011 .99024 .99093 .99991 1.0799 1.1813 1.1832 1.1846 1.1865 1.3733 1.3766 1.5694 1.5904 1.6686 1.6800 1.8574 1.8647 2.0275 2.1439 2.2329

1000(d-d i) observed

1000(d-di) calcd.

Ad p.p.m

2.562 2.816 5.496 3.839 6.446 8.089 6 .960 10.817 9.976 13.547 16.694 11.647 21.760 19.284 17.551 12.154 14.924 26.206 35.806 25.151 31.341 21.039 42.219 45.899 47.682 32.197 34.003 53.708 53.048 48.506 91.696 61.043 95.961 86.658 105.416 114.509 84.581 99.774

2.564 2.819 5.499 3.837 6.452 8.089 6.960 10.824 9.973 13.549 16.691 11.641 21.760 19.243 17.537 12.154 14.913 26.201 35.792 25.121 31.345 21.043 42.196 45.856 47.672 32 .157 33.981 53.602 52.971 48.771 91.666 61.229 95.859 86.721 105.350 114.092 84.798 99.769

-2 -3 -3 2 -6 0 0 -7 3 -2 3 6 0 41 14 0 11 5 14 30 -4 —4 23 43 10 40 22 106 77 -265 30 -186 102 -63 66 417 -217 5

43.

TABLE 14 Densities of Aqueous Solutions of Potassium Sulfate and Sodium Chloride at 25°C. 15 a Data of Wirth KsS04 ,

F = -142.068 + 6.987/ixA

NaCl,

F = -41.894 + 1.873yu.‘ ‘ik

c3 0.03893 .1540 .03887 .1538 .3509 .03876 .3502 .1533 .6187 .03860 .3492 .6176 .1527 .6156 .9731 .3477 .9712 .6128 .9680 •9634

0.014625 .014783 .059978 .060003 .014838 .13312 .060203 .13400 .015082 .23522 .13311 .058837 .23482 .13363 .014963 .23764 .058857 .23711 .13183 .23612

0.08281 .1983 .2188 .3381 .3954 .4381 .5308 .5553 •6639 .7443 .7485 .7941 .8572 1.0165 1.0180 1.0606 1.1478 1.3241 1.3635 1.6718

0.28776 .44542 .46777 .57775 .62882 .66191 .72858 .74521 .81484 .86271 .86519 .89112 .92744 1.00822 1.00894 1.02985 1.07134 1.15070 1.16770 1.29296

1000(d-di) observed 3.657 8.378 9.917 14.545 16.322 19.865 22.412 24.518 27.016 33.526 32.101 32.785 38.052 42.560 40.914 45.828 46.572 55.924 55.914 69.132

lOOO(d-di) Ai calcd. p.p 3.658 8.377 9.919 14.559 16.330 19.872 22.440 24.548 27.033 33.554 33.540 32.774 37.970 42.670 40.948 48.327 46.661 56.131 56.090 69.441

-1 1 -2 “14 -8 -7 -28 -30 -17 -28 -1439 11 82 —110 -34 -2499 -89 -207 -176 -309

F = -46.795 + 2.240JJThis shows that the apparent molal volume of the mixed salt is a linear function of the square root of the ionic strength as predicted by the Debye-IitLckel theory.

However, the equation is

hot quite the same as the one obtained by combining the equation for sodium chloride with the equation for magnesium sulfate. This may be due to the fact that the magnesium sulfate is not dissociated to the same extent in both cases.

This lack

of agreement is shown in Table 15 where 1000(d-di) calculated

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46

□

THOM PSON

0.5 ¥

FIGURE 7

from equations A, G and (22) are tabulated for comparison with the observed values*

The average value for A d in this

comparison is about +9 p*p*m* up to an ionic strength of 0*4* When the equation for the lower portion of the magnesium sulfate curve is used, the deviations are even larger*

The

densities observed in this research are about 0.00015$ higher than Thompson reported for the same mixture.

The difference

seems to be constant as is evident in Figure 7 where Thompson*s values are included for comparison. These calculations indicate that for strong electrolytes the apparent molal volumes of the ions are additive in solu­ tions of very low concentrations*

A useful application of

this fact is that the densities of dilute solutions containing mixtures of electrolytes can be calculated if data for the single solutes are available* Sulfuric Acid.

The apparent molal volume of sulfuric

acid has an unusual dependence on the concentration, increas­ ing very rapidly with increasing concentration in dilute solutions.

Figure 8 shows this unusual behavior which has 34

been explained qualitatively by Geffcken and Price the ionization of bisulfate ion.

as due to

The classical dissociation

constant for bisulfate ion in dilute solutions as a function of the ionic strength has been recently determined by a precise 18 spectrophotometric method. The densities of twelve solutions

(34) Geffcken and Price, Z •physik.Chem., B26_,. 81 (1934)

46.

of sulfuric acid ranging in concentration from 0.014 molar to 3.2 molar were determined in order to get precise data with, which it is possible to give a quantitative explanation of the observed change in the apparent molal volume. It was assumed that the sulfuric acid solutions could be treated as mixtures of two solutes in water, (H+ )2(S04=) and (H+ )(HS04~)•

Thus, if C3 moles of sulfuric acid are added to

water to make a liter of solution, it has the following comp­ osition:

(H+)2 (S04~) , cj. molar, and (H+)(HS04“), c2 molar

(where c2 = c3 - Ci).

ci is determined by c3 and K c , the

classical dissociation constant which may be written as Kc = (c3 + c1)(c1)/(c2).

Assuming that the apparent molal

volumes of the solutes are additive, we arrived at the follow­ ing equations: 4 >,

=

< “

*>

where 4>3 is the observed apparent molal volume, Cj)i is the apparent molal volume of (H+ )2(S04=), and 0.5) is reached the proportion of sulfate ions becomes progressively smaller and the observed volumes approach those calculated for (H+ )(HS04“).

Thus the

unusual behavior of the apparent molal volumes of sulfuric acid from 0 to 3 molar can be interpreted quantitatively in terms of the contributions of the constituent ions. The equation for the apparent molal volume of bisulfate ion is ‘t s = 35.15 + 2 . 0 3 / A Combining the values for

'A and

(f>2 5 we find the volume change

upon ionization of bisulfate ion at infinite dilution to be -20.2 ml/mole.

Our extrapolated values of

and 4>z are

certainly not in agreement with Fajans1 table of apparent ionic volumes by which (p± is equal to 15.8 ml. and