1096
JOHN E. RICCI AND ANTHONY R. LEO
tive the valence of the added ion, the greater is its effect on the migration velocity. The obvious explanation suggests that adsorption of the anions increases as the charge is increased, and the adsorption of negative ions then results in enlarging the double layer and consequently increasing the electrokinetic potential. Thus the recharging effect of ferrocyanide ion is higher than that of the bivalent anions. The curves for the bivalent ions sulfate, chromate, and biphosphate lie close together and occupy an intermediate position between those for the chloride and ferrocyanide ions. SUMMARY!
The effect of cations and anions of different valences on the migration velocity of colloidal carbon has been studied. It was found that the cations of higher valence cause the greater decrease in the velocity. Anions, on the other hand, exert a recharging effect on the particle, the effect being greater the higher the valence. REFERENCES (1) BRIOQS,D.R.:J. Phys. Chem. 34, 1326 (1930). (2) FREUNDLICH, H., AND ZEH,H. P.: 2. physik. Chem. 114,65 (1925). (3) HAUSER,E . A,, AND HIRSHON,S.: J. Phys. Chem. 43, 1015 (1929). (4) HAZEL,F.,AND MCQUEEN, D. M.: J . Phys. Chem. 37, 553 (1933). (5) KRUYT,H.R., AND WILLINOEN, P. C. V A N : 2. physik. Chem. 130,170 (1927). (6) MATTSON,S.:J. Phys. Chem. 32, 1532 (1928). (7) MUKHERJEE, J. N. AND ROYCHOUDHURY, S. P.: Nature 122, 960 (1928). (8) TWORILA, P.: Kolloidchem. Beihefte 27, 44 (1928).
THE ACTIVITY COEFFICIENT OF SILVER ACETATE IN SOME DIOXANE-WATER MIXTURES, IN THE PRESENCE OF ADDED ELECTROLYTES' JOHN E. RICCI
AND
ANTHONY R. LEO
Deparlment of Chemietry, New York University, New York, New York Received February 6, 19.41
In connection with certain work (2) on the solubilities of electrolytes in media of varying dielectric constant, an approximate but useful constancy has been observed (7) for the activity coefficient of a slightly soluble electrolyte in its pure saturated solution, independent of the dielectric constant 1 The experimental part of this paper is taken from a thesis submitted by A. R. Leo to the Graduate School of New York University in partial fulfillment of the requirements for the degree of Master of Science, June, 1940.
ACTIVITY COEFFICIENT O F SILVER ACETATE
1097
of the solvent. On the basis of this constancy, the solubilities, SI and Se, of such an electrolyte in two media of dielectric constant D1 and Da, respectively, are related by the simple formula
s1 = s&wD~)~
(1)
Examination of all the easily available data showed that this empirical rule was considerably better than the theoretical Born equation for predicting a t least the correct order of magnitude of the solubilities of slightly soluble electrolytes in media covering a wide range of dielectric constant. Professor Wolfgang Ostwald has since pointed out ( 5 ) an interesting analogy between this observed constancy of the activity coefficient of saturating electrolytes in pure solvents and the behavior of certain colloids, which he had previously noted and had in fact discussed in this Journal (6), in respect to coagulation by electrolytes. The coagulation of a lyophobic sol such as arsenic trisulfide, for example, caused by the addition of various salts, occurs a t concentrations of these salts corresponding always to the same value of the mean activity coefficient of the added electrolyte, this value being again independent of the dielectric constant of the medium, of the temperature, and of the valence type of the added electrolyte. Professor Ostwald remarks ( 5 ) , on the basis of this similarity between the coagulation of lyophobic sols and the condition of saturation for electrolyte solutions,-in which the activity coefficient of the electrolyte in solution is characteristic of the solid phase and independent of the dielectric constant of the solvent,-that the rble of the activity coefficient itself would seem then to be not merely that of a numerical factor but rather that of a function with real, physical meaning, indicating the conditions, in respect to the intensity of the interionic attractive forces, required for the phenomena of coagulation and saturation. This analogy suggested by Professor Ostwald is being reported here, with his approval, in the belief that it may be of general interest. The theoretical significance of the similarity is not yet apparent. That the coincidence should be purely accidental is possible, but does not seem probable. In any case it seems worth while to examine each regularity further and more carefully or quantitatively, in order t o determine more precisely its range and degree of validity, with the hope of discovering, if possible, the connection between the two regularities. The present report consequently presents some further measurements on the solubility of silver acetate in dioxane-water mixtures at 25'C., in the presence of added uni-univalent electrolytes, from which the activity coefficient of the silver acetate at saturation can be calculated. The materials and experimental methods were similar to those used in previous work (2). Equilibrium for the solubility of silver acetate was checked in respect to both time and direction of approach. The results, listed in
1098
JOHN E. RICCI AND ANTHONY R. LEO
TABLE 1 Solubility of silver ucetate i n dioxane-water miztures, in the presence of uni-univalent salts m
8
- log 8
0.004984 0. 04996 0.1024 0.1999 0.2884 0.4998 0.9529
0.03631 0.03671 0.03996 0.04238 0.04545 0.04751 0.05119 0.05368
1.4400 1.4352 1.3984 1.3728 1.3425 1,3232 1.2908 1.2702
0,1906 0.2042 0.2998 0.3805 0.4953 0.5791 0.7423 1.004
(6.22) * 4.32 4.30 4.21 4.19 4.09 4.46
0.01oO0 0.05002 0.09991 0,1999 0.4997 1.050
0.03727 0.04055 0.04322 0.04711 0.05438 0.06268
1,4286 1.3920 1.3643 1.3269 1.2646 1.2029
0.2174 0.3009 0.3773 0.4970 0.7444 1.055
(4.49) 3.36 3.39 3.39 3.42 3.10
0. 01oO0 0.04994 0.09992 0.2000 0.4998 1.OOO
0.02426 0.02483 0,02756 0.03033 0.03303 0.03786 0.04317
1.6151 1.6050 1* 5597 1.5181 1.4811 1.4218 1.3648
0.1558 0.1866 0.3609 0.4827 0.7333 1.021
10.4) (5.08) 4.14 4.22 4.16 3.92
NaClOt
0.009953 0.05002 0.09952 0.1999 0.5003 0.9980
0.2553 0.02878 0.03097 0.03450 0.04189 0.04932
1.5930 1.5409 1.m1 1.4622 1.3779 1.3070
0.1884 0.2807 0.3612 0.4841 0.7363 1.0233
(2.65) 3.00 3.52 3.52 3.00 3.12
NaNOa
0. 0.005011 0,04999 0.09988 0.4998 0.9995
0.008572 0.009223 0.01192 0.01351 0.01569 0.02005 0.02453
2.0669 2.0351 1.9237 1.8693 1.8044 1.6979 1.6103
0.09259 0.1194 0.2488 0.3369 0.4644 0.7210 1.012
(3.50) 4.66 4.70 4.56 4.20 3.96
0.009952 0.04992 0.1000 0.1998 0.4996 0.9980
0.009663 0.01223 0.01414 0.01703 0.02264 0.02736
2.0139 1.9126 1.8597 1.7688 1.6451 1.5629
0.1401 0.2493 0.3364 0.4657 0.7227 1.013
(4.64) 4.06 3.98 3.82 3.50 3.50
P E E CBNT DlOXMl
ItELECTEIC CONSTANT
ADDED 8ALT
20
60.81
NaNOs
NaClOt
30
50
51.91
34.28
NaNOs
0.2000
XaClOa
* Values in parentheses were
omitted in calculating averages.
a
0.n84
1099
ACTIVITY COEFFICIENT OF SILVER ACETATE
table 1,are the averages of values agreeing within 1 or 2 parts per thousand, determined by Volhard’s method; this table shows the molarity of added electrolyte, m (column l), the mean molar solubility of silver acetate, S (column 2),-log S (column 3), and the square root of the ionic strength (column 4). The last column of table 1 gives the values of the mean ionic diameter, a, in ihgstrom units, calculated in the usual manner by the solution of successive sets of simultaneous equations describing the effect a t 25OC. of the ionic strength and the ionic diameter on the activity co-
X) 7. DIOXANE
30% DIOXANE 2OI.DIOXANE 1
FIG.1 . Activity coefficient of silver acetate in dioxane-water mixtures: (a) with sodium nitrate as added electrolyte; (21) with sodium chlorate
BB
added electrolyte.
effirient of a uni-univalent electrolyte, according to the theory of Debye and Hiickel: namely,
--”;: log so
- log Scc
=
1
1/;
+ 2.914 -4
The results are shown graphically in the usual way, in figure 1, in which -log S is plotted against
1100
JOHN E. RICCI AND ANTHONY R. LEO
It is seen that the Debye-Huckel equation, both in its extended form, equation 2, and in ita limiting form, equation 3, logf, =
--352.6 4
(3)
D8/2
holds fairly well for the data up to the 50 per cent dioxane mixtures, in which D = 34.28. The limiting slopes of the curves of figure 1 are in agreement with the theoretical values of the slopes (shown by dashed lines on the diagram) calculated a t each dielectric constant,-namely, 0.744 in 20 per cent, 0.943 in 30 per cent, and 1.757 in 50 per cent dioxane. Furthermore, the average ionic diameter in the presence of a given added electrolyte such as sodium nitrate is fairly constant, as required by eyuation 2, for any given medium over the range of concentrationstudied. The greatest deviation from constancy is observed in 50 per cent dioxane, where the value of a appears to drop more or less steadily with increasing
TABLE 2 Average ionic diameters jrom salt efects
I
PER CENT DIOXANE
O*
lot
20 30 50
78.55 69.71 60.81 51.91 34.28
I I I
(1
With NaNOa
3.69 4.03 4.26 4.11 4.41
IN
I
A. With NaCIO:
3.35 3.23 3.77
concentration. The average value of a for a given salt, such as sodium nitrate, moreover, is fairly independent of D itself, up to 50 per cent dioxane. Some values of a derived from the effect of such added salts on the solubility of silver acetate in water-dioxane solvents are summarized in table 2. The solubility of silver acetate in zero ionic strength in each medium, which might be estimated by extrapolation of the curves of figure 1, was calculated from the data by means of equation 2, using the values of a just discussed. These SOvalues, including corresponding values in water and in 10 per cent dioxane taken from the literature, are given in table 3; the last column of this table lists the activity coefficient, f , for the salt a t saturation in the pure solvent (with no added salt), calculated as SO/S. The approximate constancy of the activity coefficient of silver acetate in its pure saturated solution, here observed for the range of dielectric
1101
ACTIVITY COEFFICIENT O F SILVER ACETATE
constant from 78 to 34, corroborates the assumption which was stated as implied in the empirical rule noted by Ricci and Davis (7) for the relation between the solubility of slightly soluble electrolytes and the dielectric constant of the medium (equation 1); it explains again why the solubility of this salt can be calculated a t least to the correct order of magnitude over a wide range of dielectric constant by means of this simple equation. Further indirect evidence of this constancy of the activity coefficient of an electrolyte a t saturation, independent of the dielectric constant, may be mentioned at this point from the measurements of the solubility of lead chloride in solvents containing up to 80 per cent dioxane (3), in which the plot of log S against log D gave a slope of 2.5, as compared with a slope of 3 expected according to equation 1 in the form log S1= log SZ 3(log Di - log 0 2 ) . Finally, with SOvalues actually available for a considerable range of dielectric constant, a better test of the Born equation should be possible than the usual application through actual solubilities. The Born equation
+
TABLE 3 Activity coeficient of silver acetate at saturation in pure solvent PER CENT DIOXANE
0 10 20 30 50
D
78.55 69.71 60.81 51.91 34.28
1 0.0531 0.0396 0.0277 0.0184 0.00626
S
f
0.800 0.786 0.764 0.757 0,729
(l), relating the solubilities of an electrolyte of ionic diameter a in two media of different dielectric constants, is
or
in which C is a factor having the value 242 a t 25'C. and depending on N , the Avogadro number, e, the charge of the electron, R , the gas constant, and T, the temperature; z+ and z- &re the valences of the ions involved. This is an ideal relation, taking no account of interionic effects, and should therefore apply, theoretically, for solubilities in zero ionic strength. Such solubilities are, of course, hypothetical and can be calculated only through effects such as that of added salts on the actual solubility under consideration. The Born equation should be applied then to the & values listed
1102
JOHN E. RICCI AND ANTHONY R. LEO
in table 3. For this purpose a value of a for silver acetate averaged from all the observed values given in table 2 v a s chosen,-namely, 3.87 A. (this value agrees closely with the average value of a for silver acetate, 3.83 A., in previous work (2)). The solubility in esch medium, at p =0, or SO, was then calculated from the limiting solubility in water by the formula
Table 4 compares the SOvalues derived directly from the data with those so calculated according to the Born equation. The agreement i s seen to be fair through the 30 per cent dioxane value, as had already been noted (2) when the calculation was made through the actual solubilities corrected theor&ically for interionic effects, with no significant difference between the results of the two methods of calculation. In 50 per cent dioxane, with D = 34.28, the agreement between calculated and observed values is poor, and of course will become increasingly worse as the effects of ionic TABLE 4 Test of the Born equation at zero ionic strength D
78.55 69.71 60.81 51.91 34.28
SO
%Born
(OBSERVED)
0.0531
0,0396 0.0277 0.0184 0.00626
RATIO
(CALCULATED)
1
s'Oobed. o.-
BAT*O
sfoslsd. S0b.d.
~
0.0113 0.0270
0.0206 0.00189
' ~
i
1
1.04 0.97 1.12 0.30
0.92 0.84
0.78 0.65
ACTIVITY COEFFICIENT OF SILVER ACETATE
1103
2. The limiting slopes for the variation of log S with fi show the Debye-Huckel limiting lam to hold through the range of dielectric constant covered (78 to 34). 3. The Debye-Huckel equation, modified for the effect of ionic size, is also seen to hold approximately for the solubilities over the range studied, on the basis of the approximate constancy of the parameter a, the effective ionic diameter, calculated from the data. 4. Using values of the average ionic diameter and of So, the solubility in zero ionic strength, derived from the data, the Born equatiop was tested directly on the limiting solubilities, So; the agreement, however, is the same as that obtained on the observed solubilities, corrected theoretically for interionic effects. 5. The activity coefficient of silver acetate in its pure saturated solution is approximately constant (0.80 to 0.73) over the range of D studied. This is further evidence of the regularity previously noted, of the constancy of the activity coefficient of slightly soluble electrolytes at saturation in pure solvents, irrespective of dielectric constant, on the basis of which the solubility of the electrolyte can be related to the dielectric constant of the solvent by the simple but useful equation, SI/& = (D1/D2)3. 6. An analogy is reported, pointed out by Professor Ostwald, between the rule of constant activity coefficient for electrolytes a t saturation, independent of dielectric constant, and a similar rule for the constancy of the activity coefficient of electrolytes required for the coagulation of a given lyophobic sol, likewise independent of the dielectric constant. REFEREKCES (1) BORN,M . : Z. Physik 1, 45 (1920). (2) DAVIS,T.W . , AND RICCI,J. E . , WITH SAUTER,C . G . : J . Am. Chem. SOC.61,3274 (1939). (3) GARRETT, A . B . , AND NOBLE,M. V.: Paper read a t the Ninety-ninth Meeting of the American Chemical Society, held in Cincinnati, Ohio, April, 1940. (4) MACDOWALL, F.H., AND REHNER, J.: J . Am. Chem. SOC. 66,368 (1934). (5) OSTWALD, W . : Private communication t o J. E.Ricci, March, 1940. See HOFFYANN,K . : Kolloid-Z. 91, 196 (1940); also OSTWALD, W.:Kolloid-2. 94, 169 (1941). (6) OSTWALD, W . : J . Phys. Chem. 42,981 (1938). See also OSTWALD, W.: Kolloid-2. 88,l (1939); OSTWALD, W.,KOKKOROS, H., AND HOFFMANN, K . : Kolloid-2. 79, 287 (1937); 81, 48 (1937). (7) RICCI,J. E.,AND DAVIS,T. W . : J. Am. Chem. SOC. 62, 407 (1940).
