the solubility and activity coefficient of silver acetate in mixed solvents

THE SOLUBILITY AND ACTIVITY COEFFICIENT OF SILVER ACETATE I N MIXED SOLVENTS‘

F. H. MAcDOUGALL AND CHARLES EDWARD BARTSCH School of Chemistry, University of Minnasota, Minneapolis, Minnesota

Received January 86, 1096

INTRODUCTION

The experimental work described in this paper was undertaken in order to furnish an additional test of the applicability of the theory of Debye and Huckel (2) to strong electrolytes dissolved in mixed solvents. With this purpose in mind, we measured the solubility of silver acetate in various mixtures of water and ethyl alcohol in the presence of various amounts of a soluble nitrate. The nitrates used were those of lithium, sodium, potassium, calcium, strontium, and barium.

The solubility of silver acetate in water a t 25°C. has been determined by a number of investigators. We give herewith the results obtained in moles per liter: Raupenstrauch (lo), 0.0671; Goldschmidt (3), 0.0669; Jaques (5 ) , 0.0663; Hill and Simmons (4), 0.0667; Knox and Will (6), 0.0667; MacDougall (7), 0.0664; MacDougall and Rehner (8), 0.0663. The value obtained in the present research was 0.06634.

MATERIALS USED

The silver acetate, obtained from Mallinckrodt, was 64.62 per cent silver (theoretical, 64.64 per cent) and was used without further purification. It was kept in black lacquered bottles and stored in the dark. The nitrate salts were recrystallized from “conductivity” water and dried at 150OC. The water was “conductivity” water, nrepared by distillation of distilled water in a tin-lined vessel in the presence of sodium hydroxide and potassium permanganate. The ethyl alcohol used was approximately 95 per cent by volume and was tested according to Murray (9). It was found to be free from acetone, aldehyde, other organic impurities, and heavy metals. It was used without further purification.

EXPERIMENTAL PROCEDURE

The mixed solvent was prepared by mixing weighed amounts of 95 per cent alcohol and conductivity water, but the exact alcoholic content of

This paper gives the essential portions of the dissertation presented by Charles E. Bartsch to the Graduate Faculty of the University of Minnesota in partial fulfill- ment of the requirements for the degree of Doctor of Philosophy, June, 1935.

649

650 F. H. MACDOUGALL AND CHARLES E D F A R D BARTSCH

the mixture was calculated from its density. Mixtures containing approximately 10, 20, and 30 per cent by weight of alcohol were used as solvents.

Weighed amounts of the solvent and of the nitrate salt were brought together in a glass-stoppered flask. When the nitrate had dissolved, equal portions of the solution were transferred to two amber-colored glass-stoppered bottles containing an excess of silver acetate. The bottles were sealed immediately with a heavy layer of paraffin. They were then rotated end over end in a water bath a t 25.00 & 0.05’C. for a t least forty-eight hours. For the purpose of sampling, the bottles were removed from the rotator and clamped upright and almost completely immersed in the bath. After half an hour, the paraffin was removed from the stopper, a siphon (containing a small cotton wad in the “bottle” end) was inserted in the liquid, and about 125 cc. of the liquid was blown by compressed air into a 250-cc. Erlenmeyer flask, immersed as completely as was permissible in the water bath. The Erlenmeyer flask was fitted with a rubber stopper to minimize evaporation. From this flask two samples of 50 cc. each were withdrawn by means of an accurately calibrated pipet and weighed in glass-stoppered weighing bottles. Results for density and for analysis were accordingly obtained in quadruplicate for each concentration of added nitrate.

The solutions containing 10 or 20 per cent alcohol were analyzed gravi- metrically for silver; all other solutions were analyzed volumetrically. The volumetric analysis was carried out by the Volhard method for silver as suggested by Professor I. M. Kolthoff. The samples were transferred to 250-cc. Erlenmeyer flasks, acidified with 5 cc. of concentrated nitric acid, and diluted to 100 cc. Then 5 cc. of ferric nitrate indicator solution was added. The solutions were titrated immediately with 0.04 N potassium thiocyanate to a reddish-brown coloration. The solutions were then shaken until the color disappeared. The titration with potassium thiocyanate was continued until a faint rose coloration remained after vigorous shaking. The thiocyanate solution was standardized with a solution containing a known amount of silver acetate. The standardiza- tion was checked with a solution containing a known weight of silver nitrate.

METHODS O F EXPRESSINQ COMPOSITION OF THE SOLUTIONS

If p is the fraction of alcohol in the mixed solvent, the number of moles of water, No,, and of ethyl alcohol, No,, in 1000 g. of solvent can be found from the equations

1000 (1 - p ) 18.015 No, =

lO0Op No, = 46.045

SOLUBILITY AND ACTIVITY COEFFICIENT OF SILVER ACETATE 651

The molar concentration, c, of a solute salt is the number of moles of the salt in a liter of the solution. The molal concentration, m, is the number of moles in 1000 g. of mixed solvent. In calculating the mole fraction of a component of the solution we have assumed that $he dissolved silver acetate and added nitrate salt are conipletely ionized. If z is the mole fraction of Ag+ or of C2Ha0i in a solution in which the molalities of silver acetate and added nitrate are m and m, respectively, then

where v is the number of ions obtainable on complete ionization of one molecule of added nitrate salt.

The density of the solvent (alcohol-water mixture) is represented by do, that of the solution saturated with silver acetate and containing various amounts of nitrate salt by d.

ACTIVITY COEFFICIENTS

If f, y, and yo bre the mole-fraction, molality, and molarity activity coefficients respectively of any solute then

f Y = 2m + vma + No,+No,

do (1 + m~ + m.Ma),, 1000 ye = - d

(3)

(4)

M and M , are the molecular weights of silver acetate and added nitrate salt, respectively.

According to Debye and Hiickel (2), the activity coefficient of a univalent ion (or of a uni-univalent salt) a t 25'C. is given by the equations

B S log,,f = log1020 - log102 = - ~

1 + A S $

352.61 Dt B = -

2.914 X lo8 a Dt A =

(5 )

(7)

where D is the dielectric constant of the solvent and a is a suitable mean ionic diameter. In equation 5, z is the mole fraction of silver ion in a given saturated solution and z0 is the extrapolated value of z for an ionic strength equal to zero; in other words, $0 is the activity of silver ion in any solution saturated with silver acetate.

652 F. H. IdACDOUGALL AND CHARLES EDWARD BARTSCH

SATURATED TRATIOX O F

1 ,0048 0.0663 0,9955 0,0577 0.9898 0.0523

The dielectric constant of an alcohol-wate: mixture was calculated by linear interpolation from the values given by Akerlof (1).

EXPERIMENTAL DATA

In table 1 we give the solubility a t 25°C. of silver acetate in alcohol- water mixtures containing from 0 to 50 per cent ethyl alcohol. In tables

TABLE 1 Solubili ty at 25°C. of silver acetate in mixtures of ethyl alcohol and water

SATURATED

25,06 0,9616 29.82 0.9530 30,05 0.9526

PER CENT ALCOHOL

0.00 5.00 7.62 9.00

15.03 19,96

0.9882 0.9784 0.9696

0.0506 40.27 0,9323 0.0413 11 50.14 0.9102 0.03

MOLAR CONCEN- TRATION OF

SILVER ACETATE

0,0294 0,0251 0.0249 0.0180 0.0124

TABLE 2

Solubili ty at 25°C. of silver acetate in mixtures of ethyl alcohol and water containing

9.41 PER CENT ALCOHOL D = 73.14

i<ko,

0.0 0.05131 0.09865 0 , 2 0 4 0.3006 0.4057 0.5012 0.6013 0.8046 1.0049 1 ,2957 1 ,6227

d Satd. soln

0 9875 0 9909 0 9939 1 0010 1 0075 1 0153 1 0174 1 0271 1 0381 1 0495 1 0655 1.0828

103 X Ag+

0.9649 1.0311 1.0710 1.1333 1.1751 1.2190 1,2462 1.2662 1.3114 1 ,3517 1.3868 1.4313

.~ potassium nitrate

20.37 PER CENT ALCOHOL D = GG.78

ni ICNOI

0.0 0.05006 0.03945 0.1998 0,2982 0,3958 0.4959 0.5994 0,7923 0.9898 1 ,2539 1.4916

d iatd. sol1

0 9709 0 9742 0 9776 0 9838 0 9897 0 9952 1 0009 1 0070 1 0180 1 0281 1 0422 1 0540

___ 108 X Ag.

0.7449 0.8196 0.8612 0.9191 0.9623 0.9892 1.0271 I ,0507 1 ,0925 1,1285 1.1686 1.1964

30.02 PER CENT lLCOHOL D = 61.09

KEOs

0 0 0 04949 0 09996 0.2004 0 3007 0 3990 0 4984 0.6265 0 8813 1 0365

d Jatd s o h

0.9520 0,9581 0.9615 0.9669 0.9728 0,9774 0.9838 0.9906 1 0028 1.0103

103 x .4g+

0.5811 0.6488 0.6910 0,7506 0.7974 0 8298 0.8591 0 8931 0.9452 0,9705

2 to 7 we give the solubility in the presence of added nitrates in solvents containing approximately 10, 20, and 30 per cent ethyl alcohol. The data are also represented graphically in figures 1, 2, and 3. An examination of the tables and of the figures will show that the solubility of silver acetate increases with the concentration of added nitrate, and that for a solution


of a given ionic strength the effect of a given nitrate is given in general by the order KNOs < NaN03 < Ba(N08)2 < Sr(NO& < LiN03 < Ca(NO3)p.

TABLE 3 Solubili ty at 25°C. of silver acetate in mixtures of ethyl alcohol and water containing

ln Ba(NOdz

0.0 0.01036 0.02463 0.05384 0.1241

--

sodium nitrate

20.37 PER CENT ALCOHOL D 2 66.78

d Satd. solc

0.9722 0.9749 0.9780 0.9842 0.9986



~ 0 3 X Ag+

- oa x Ag+ d

latd. s o h

0.9520 0.9558 0.9590 0,9652 0.9704 0.9745 0.9800 0.98% 0.9948 1.0048 1.0192 1.0343 1.0508

103 x &+ m NaNOs

- d

atd. aoln m

NaNOa

0.0 0,05054 0.1002 0.2011 0.3012 0.3996 0.5001 0.6014 0,8003 0.9983 1.3025 1.6015 2.0047

m NaNOi

0.0 0.04711 0 ,09579 0.1911 0.2864 0.3859 0.4702 0.5822 0.7735 0.9579 1.1903 1.4411 1 ,9095 2.3876 2,8732

d 3atd. soh.

0.9879 0,9910 0.9948 1 .ooo1 1.0047 1.0102 1.0147 1.0206 1 ,0309 1 ,0405 1.0522 1.0644 1 ,0861 1.1077 1.1284

0.9815 1.0485 1.0892 1.1548 1.2009 1 ,2395 1.2660 1.3042 1.3464 1.3826 1.4123 1 ,4466 1.4934 1 ,5292 1.5555

0.0 0.04819 0,09547 0.1937 0.2880 0.3821 0.4776 0.5738 0.7626 0.9571 1.1894 1.4258 1,8935 2.3764 2.8061

0.9709 0.9735 0.9762 0.9823 0.9859 0.9921 0.9971 1.0022 1.0116 1.0214 1 ,0336 1.0437 1 ,0646 1.0861 1.1047

0.7449 0.8141 0.8591 0.9251 0.9652 1 .W23 1.0355 1.0637 1,1103 1.1557 1.1923 1 ,2327 1,2920 1 ,3353 1.3659

0.5811 0.6452 0.6931 0.7565 0.8066 0.8375 0.8757 0.9060 0.9573 0.9990 1.0594 1.1034 1.1583

TABLE 4

Solubili ty at 85'C. oj silver acetate in mixtures of ethyl alcohol and water containing barium nitrate


19.39 PBR CENT ALCOHOL D = 67.35

30.02 PER CENT ALCOHOL D - 61.09

101 X Ag+

0.9815 1 ,0877 1.1412 1 ,2326 1.2824 1 ,3462 1 ,3798 1.4187

- loa x &+

0.7456 0.8013 0.8506 0.9226 1 ,0235

__ 103 X Ag+

0.5811 0.6328 0.6684 0.7229 0,7643 0.7979 0.8274

m Ba(N0ah

0.0 0.02541 0.05050 0.1012 0,1454 0,2021 0.2343 0.2978

d h t d . s o h

0.9520 0.9568 0.9589 0.9628 0.9669 0.9711 0.9748

d Satd. eoln

0.9879 0.9941 0.9994 1.0107 1.0198 1.0314 1.0381 1 ,0456

m Ba(N0s)i

0.0 0.01028 0.01978 0.04002 0.06038 0,08023 0.09930

APPLICATION OF THE DEBYE-HUCKEL THEORY

Values of A and xo of equation 5 were obtained for each series of solutions by substituting in the equation the observed values of x and X+ for two

654 F. H. MACDOUCIALL AND CHARLES EDWARD BARTSCH

TABLE 5

Solubili ty at 86°C. of silver acetate in mixtures of ethyl alcohol and watercontaining strontium nitrate



30.45 PER CENT ALOOHOL D = 60.83 __

d Iatd. so11

m Sr (NO$) 2

d atd. soh

d 3atd. s o h

0.9866 0.9912 0.9964 1.0045 1.0206 1 ,0370 1.0530 1.0685 1.0832 1.1135 1.1425 1.1764 1 ,2088 1.2746

sr(G00i)r

0.0 0.02672 0.05250 0.09925 0,1991 0.2986 0.4018 0.4995 0.5978 0.8013 1.0021 1.2463 1 ,4855 2 . W 5

m Sr (NO*) 2

0.0 0.01236 0.02495 0.04085 0.07072 0.09976 0.2019 0.2998 0.4018 0.6033 0.7999 0.9954 1.4888

-. 108 X Ag+

0.9565 1.0664 1.1258 1.2116 1.3441 1.4381 1.5189 1.6898 1.6486 1.7717 1.8844 2.0015 2.0959 2.3012

10s x A& l oa x Age

0.5781 0.6428 0.6872 0.7305 0.7918 0.8403 0.9685 1.0711 1.1591 1.3073 1 .4536 1,5780 1.8837

__ 0 .'9712 0.9768 0,9808 0.9893 1.0041 1 ,0210 1.0362 1.0514 1.0658 1.0950 1,1214 1,1561 1.1950 1.2497 I_

0.9534 0.9557 0.9581 0.9604 0.9858 0.9706 0.9865 1.0007 1.0163 1 ,0453 1 ,0722 1.0994 1.1651

0.0742 0,8505 0.9202 1.0074 1.1348 1.2345 1 ,3162 1 ,3913 1 ,4620 1.5890 1 ,6968 1.8414 1 ,9961 2.1990

0.0 0.02730 0.05039 0.09969 0.1988 0.2997 0.3973 0.4986 0.5965 0.7974 0.9896 1 ,2403 1.5377 1 ,9768

TABLE 6 Solubility at 8'5°C. of d o e r acetate in mixtures of ethyl alcohol and water containing

l i th ium nitrate

9 . 4 1 PER CENT ALCOEOL D = 73.14



__ d

atd. Y O ~ I

0.9722 0.9746 0.9767 0.9813 0.9855 0.9894 0.9936 0.9969 1.0042 1.0117 1.0213 1.0328 1.0462 1.0640 1.0809

___

-

d atd. Yoln

0.9520 0.9550 0.9572 0.9606 0,9650 0.9685 0.9728 0.9764 0,9836 0.9912 1.0031 1.0119 1.0257

__

__

d iatd. aoln

m LiNOg

0.0 0.05177 0.1018 0.2017 0.2991 0.4082 0.5092 Q.6191 0.8042 1.0214 1 .3229 1.6556 2.1024 2,5195 3.0930

m LiNOj 108 X Ag+

0.9647 1.0412 1 ,0877 1.1625 1.2192 1.2718 1.3103 1.3507 1.4178 1 ,4781 1 .5552 1 ,6310 1 ,7288 1.8260 1.9543

108 X Ag+ 0' X Ag+

0.0 0.05225 0.09767 0.2030 0.2973 0.4053 0.5114 0.5981

0.9913 1 ,2529 1 I5749 1.9670 2.5001 3.0096

0.7966

0.9883 0,9909 0.9931 0.9977 1 .m19 1.0062 1.0103 1.0145 1.0219 1 ,0303 1.0415 1 ,0536 1.0693 1 ,0836 1.1027

0,7456 0.8232 0.8692 0.9479 0.9961 1.0433 1.0861 1.1191 1.1830 1 .2422 1.3111 1.3915 1.4911 1 ,6226 1 ,7457

0 . 0 0.04890 0.10622 0.19890 0.2979 0.3881 0.4969 0.5977 0,7969 0.9974 1.3072 1 I5735 1 ,9970

0.5811 0.6557 0.7097 0.7712 0,8217 0.8621 0.9047 0.9417 1.0085 1 ,0721 1.1552 1.2284 1 ,3294


lo* x As+

0.9565 1.0758 1.1466 1.2510 1.4229 1.5420 1.6396 1.7366 1.8219 1 .9879 2.1386 2.3090 2.5202 2.8394

, TABLE 7 Solubility at db°C. of silver acetate i n mixtures of ethyl alcohol and water containing

calcium nitrate

-- Ca(G0a)z -- 0.0 0.02404 0.04888 0.09900 0.2022 0.3008 0.3938 0.4932 0.5919 0,7914 0.9958 1.2466 1.4687 1 .9823

g.w PER CENT ALCOHOL I 19.85 PER CENT ALCOHOL D - 72.86 D - 67.03

m Ca(NOa)r

0.0 0.01338 0.02549 0.04072 0.07269 0.10118 0.1997 0.2974 0.4010 0.5994 0.7996 0.9991 1.4869

-- m

Ca(N0a)z

0.0 0.02581 0.04913 0,09891 0.1966 0,3028 0.3987 0.4956 0.6006 0.8013 0.9916 1 .2375 1.5338 2.0224

d b t d . soh

0.9534 0.9554 0.9575 0.9592 0.9826 0.9664 0.9775 0.9883 0.9997 1.0203 1.0409 1.0606 1.1056

d htd. soln.

0.9857 0.9908 0.9935 1.00004 1.0118 1.0245 1.0354 1.0469 1.0586 1 .W98 1.1002 1.1252 1.1544 1.1994

- d

htd. soh

0.9712 0.9754 0.9789 0,9848 0.9971 1.0085 1.0190 1.0313 1.0407 1.0615 1 .0828 1.1074 1.1285 1.1759

0.7420 0.8643 0.9394 1.0411 1.2199 1,3342 1.4418 1.5361 1.6241 1.8033 1.9712 2.1742 2,3428 2.7582

a0.41 PER CENT ALCOHOL D - w.83

10' X Ag+

0.5781 0.6548 0.7046 0.7524 0 I 8328 0.89% 1.0601 1.1749 1.2905 1.4818 1.6677 1.8486 2.860

t I I 1 05 LO 15 2.0 25

Si FIQ. 1. Solubility of silver acetate in about 10 per cent alcohol in the presence of

various nitrates. I. KNOa; solvent, 9.41 per cent alcohol. 11. NaNOs; solvent, 9.17 per cent alcohol. 111. Brt(N0s)a; solvent, 9.17 per cent alcohol. IV. Sr(NO&; solvent, 9.90 per cent alcohol. V. LiNOa; solvent, 9.41 per cent alcohol. VI, Ca(N0s)a; solvent, 9.90 per cent alcohol.

solutions, one of which was always the solution that contained no added nitrate salt. From the two simultaneous equations so obtained, a value of A and a value of 20 were calculated. We have summarized in table 8

656 F. H. hfACDOUGALL AND CHARLES EDWARD BARTSCH

the results of these calculations. One might infer from this table that the Debye-Huckel equation is in general valid up to approximately the same

LO 15 25 20 Sf

05

FIG. 2. Solubility of silver acetate in about 20 per cent alcohol in the presence of various nitrates. I . KSOs; solvent, 20.37 per cent alcohol. 11. SaSOs; solvent, 20.37 per cent alcohol. Is’. Sr(S03)*; solvent, 19.95 per cent alcohol. V. LiSOa; solveut, 19.39 per cent alcohol. VI. Ca(S03)1; solvent, 19.95 per cent alcohol.

111. B B ( S O ~ ) ~ ; solvent, 19.39 per cent alcohol.

FIG. 3. Solubility of silver acetate in about 30 per cent alcohol in the presence of various nitrates. I. KN08; solvent, 30.02 per cent alcohol. 11. SaNOa; solvent, 30.02 per cent alcohol. IV. Sr(KOa)z; solvent, 30.45 per cent alcohol. V. LiSOa; solvent, 30.02 per cent alcohol. VI. Ca(SOa),; solvent, 30.45 per cent alcohol.

111. Ba(XO,),; solvent, 30.02 per cent alcohol.

ionic strength, irrespective of the nature of the added nitrate. For higher ionic strengths, there are marked differences in the effects of different


10'20

0.466 0.466 0.464 0.459 0.464 0.455

nitrates. In the case of the less soluble barium nitrate, the validity of the Debye-Huckel equation extends up to solutions saturated with this salt. For all other nitrates investigated (except sodium nitrate in 9.17 per cent alcohol) there is a falling off in the calculated values of A when we go to solutions of higher ionic strengths than those given in table 8, but whereas this decrease in A is relatively slow when sodium nitrate and potassium nitrate are the added salts, it is more rapid in the case of strontium nitrate and lithium nitrate and still more so for calcium nitrate. It would there- fore be more correct to say that the range of approximate validity of equation 5 is greatest for sodium nitrate and potassium nitrate, less for strontium nitrate and lithium nitrate, and least for calcium nitrate.

As will be pointed out in a later publication from this laboratory, the great increase in solubility of silver acetate in the presence of calcium nitrate is probably due to the formation of the intermediate ion CaOAc+.

$2.9 $3

%'& g e m

0.6 0.8 0.75 0.75 0.75 0.75

__-

TABLE 8 Calculated values of A and xo

KNOs. . . . . . . . . . . . . . . . . NaNOs.. . . . . . . . . . . . . . Ba(N0s)Z.. . . . . . . . . . . . . Sr(NOs)t . . . . . . . . . . . . . Li(NO&. . . . . . . . . . . . . . Ca(NO8)a.. . . . . . . . . . . . .

ADDED NITRATB I-

1.43 1.28 1 .I4 1.08 1 .I4 0.86

I A 0.775 0.783 0.778 0.758 0.766 0.750

0 . 5 1.37 0.597 1.0 2.65 1.31 0.596 0.9 0.9 1.08 0.593 0.8 0.9 1.02 0.588 0.88 0.8 1.10 0.593 0.85 0.9 0.75 0.582 0.98

CB. 30 PER CENT ClH5OH

__

A

1.39 1.34 1.20 1.08 1.23 0.80 -

Since the solvents referred to as approximately 10 per cent alcohol varied appreciably in composition (e.g., 9.17, 9.41, and 9.90 per cent alcohol) the calculated values of 1O3xO in table 8 for these solvents are not expected to be identical. Moreover the extrapolated value of zo depends somewhat on the value of A used in equation 5. If we assume that the value of zo and the value of the solubility, 2, of silver acetate in a mixed solvent vary relatively in the same way with the per cent of alcohol, and if we take as most reliable the values of 20 obtained in the presence of sodium nitrate, potassium nitrate, and barium nitrate, we readily find the following relation for the value of $0 as a function of the per cent, p , of alcohol when p is in the neighborhood of 10 per cent; viz.,

103x0 = 0.760 + 0.026 (10 - p )

658 F. H. MACDOUGALL AND CHARLES EDWARD BARTSCH

Water.. ..................................... 10 per cent alcohol.. ....................... 20 per cent alcohol.. ....................... 30 per cent alcohol.. ........................

This relation gives

103z, = 0.783, for p = 9.17 (NaN03, Ba(N03)2) 103z0 = 0.776, for p = 9.41 (KNOs, LiN03) 103z0 = 0.767, for p = 9.90 (Sr(NOs)z, Ca(NOs)z)

The solvents richer in alcohol differ relatively so little from exactly 20 per cent and 30 per cent, respectively, that we may infer from table 8 (giving greatest weight to the results with sodium nitrate and potassium nitrate) that

103za = 0.596, for p = 20 per cent alcohol 103z0 = 0.466, for p = 30 per cent alcohol

TABLE 9 Values of a i n A . U .

0.960 0.760 0.596 0.466

VALUES OF a PER CENT CiRsOH 1 KNOi I NaNOa

0.0531 0.0388 0.0281 0.0201

0 .0 10.0 20.0 30 .O

0.800 0.797 0.803 0.802

4.35 4.21 3.85 3.91

3.69 3.86 3.67 3.62

TABLE 10 Activity coefiient of silver acetate i n saturated solutions at W C .

I

mo

0.0533 0.0396 0.0291 0.0211

CP 1 f

IONIC DIAMETERS

The values of A obtained by application of equation 5 can be interpreted in terms of average ionic diameters, a, by means of equation 7. In table 9 we give the values of a so obtained for solutions containing potassium nitrate and sodium nitrate, respectively. The values of a for 0 per cent alcohol are taken from the papers by MacDougall (7) and MacDougall and Rehner (8).

ACTIVITY COEFFICIENTS

The mean activity coefficient, f, of silver acetate is given by the ratio

5. The activity coefficients, y and yo, may be calculated by means of

equations 3 or 4 or from the equations 2


mo y = - m

co yc = -

C

where mo = (Nol - N B ) x o (see equation 11) and co = dome; do is the density of the solvent. It will be observed that we have assigned a value of unity to the activity coefficient of an ion in any of our solvents (water, 10 per cent, 20 per cent, or 30 per cent alcohol) when the ionic strength approaches zero. We give in table 10 values of the mean activity coefficients of silver acetate in saturated solutions of that salt when the solvent is water, 10 per cent, 20 per cent, and 30 per cent alcohol, respectively. For the data in aqueous solutions containing no alcohol, see the papers by MacDougall (7) and MacDougall and Rehner (8). For the solutions listed in table 10 the values of y and of yo do not differ appreciably from the corresponding values off.

SUMMARY

This paper gives the solubility of silver acetate at 25OC. in 10, 20, and 30 per cent ethyl alcohol in the presence of the nitrates of potassium, sodium, lithium, calcium, strontium, and barium.

The Debye-Huckel equation seems to be valid for the solutions investigated up to values of the ionic strength listed in table 8.

Values of the mean ionic diameter are calculated for the solutions containing potassium nitrate or sodium nitrate.

Data are presented which will enable one to determine the activity coefficient of silver acetate in any of the solutions investigated.

The activity coefficient of silver acetate in solvents saturated with that salt but not containing any nitrate is given in table 10.

REFERENCES (1) A K E R L ~ F , G.: J. Am. Chem. SOC. 64, 4125 (1932). (2) DEBYE AND HUCKEL: Physik. 2. 24, 185 (1923). (3) GOLDSCHMIDT, H.: Z. physik. Chem. 26,91 (1898). (4) HILL, A., AND SIMMONS, J.: J. Am. Chem. SOC. 31,821 (1909). (5) JAQUES, A. : Trans. Faraday SOC. 6, 225 (1909). (6) KNOX, J., AND WILL, H.: J. Chem. SOC. 116, &53 (1919). (7) MACDOUGALL, F. H.: J. Am. Chem. SOC. 62, 1390 (1930). (8) MACDOUGALL, F. H., AND REHNER, JOHN, JR.: J. Am. Chem. SOC. 66,368 (1934). (9) MURRAY: Standards and Tests for Reagent Chemicals. D. Van Nostrand Co.,

New York (1920). (10) RAUPENSTRAUCH, G. A.: Monatsh. 6, 563 (1885).

TEE JOURNAL OF PHYSICAL CHEMI~TRY, VOL. 40, NO. 5

the solubility and activity coefficient of silver acetate in mixed solvents

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