1074
HERBERT N. MCCOY.
THE RELATION BETWEEN THE IONIZING POWER AND THE DIELECTRIC CONSTANTS OF SOLVENTS. BY H E R I I B R T N. I I C C O Y .
Received A p r i l 17, :go\.
I n a recent paper, Walden' gives an account of his newer studies on the conductivities of solutions of salts in numerous organic solvents. Among other conclusions, Walden has pointed out a very simple quantitative relationship between the ionizing power of a solvent and its dielectric constant. Sernst? had observed earlier, that liquids with high dielectric constants are good ionizing solvents, and gives a theoretical explanation. Walden finds t h a t in case solutions of one and the same electrolyte in various solvents have the same degree of ionization, then the product of the dielectric constant and the cube-root of the dilution for all such solutions, lias practically a constant value. _ ~ Thus if a = al, then ;4V -- . :,qb.,; where a == the degree of ionization, E = the dielectric constant, and I/ = the dilution. The nature of Walden's results is illustrated by the figures in Table I , for thc salt tetraethyl ammonium iodide, dissolved it1 various solvents.
r.
,
I1
_,l(
;S
-, -I
This relation, involving 3'7 suggests that found by Kohlrausch" between the equivalent conductivity of an aqueous salt solution and its concentration, viz: A = A - k C C ; where - 1 is tlie eyui\-alent conductivity a t the concentration C, .Im is the conductivity a t infinite dilution, and k is a constant. Instead of following the procedure ol Kohlrausch, by testing the applicability of this equation graphically, in the case of any specific electrolyte, one may by a simple algebraic expedient proceed arithmetically and obtain a t the same time the value of A m . In practice, the values of C are usually multiples, by a power of 2 , of the smallest concentration. Suppose C,= SC,; then it, = 2 W , : -1, = ilm --k 4Tl and A, = Am --k2?,. 'l'herefore, ilz = z112--If A m , as calculated for several pairs of concentrations, is constant, then the Kohlrausch equation applies t o the case. Thus, for an aqueous solution of common salt, at z s 0 , 214;,0-:132 = 130 6 ; 2.2512 ---.I,,, = 131.5; 24,,, -A,,, = 131.4. Therefore, the Kohlrausch law holds for tlie case, and A= = 1 3 1 . 2 . ~
-8
*
Z . physik. Chetn., 54, 133 (1906). Zhid.,3, j 3 1 (1894). !Vied. Aptn., 26, 2 0 0 (188j).
IONIZING POWER .4ND DIELECTRIC CONSTANTS.
1075
The Kohlrausch equation may be written A / A m = I - k / A m 4'7;or a = I-K 4'F1( I ) where the degree of ionization, a =A / Am and k / Am = K, a constant. Transformation of equation ( I ) gives K = ( I - a ) 4V. (2) Table I1 gives complete data and results for sodium chloride. The values of a , column 5 , are calculated by equation (I). Column 6 contains the differences between the observed and calculated values of a ; these differences are of the same order as the probable experimental errors. TABLE
V. 32 64
A,
a.
114.6 117.9 120.4
0.874
256
122.6
0.899 0.918 ("935
jI2
124.;
0.950
1024
I2j.C)
0,960
00
131.2
I28
Mean,
11. K. 0.400 0.404 0.413 0.413 0.400 0.403
---
0.405
a
Calc.
Aa .
0.872 0.899
0.002
0.920
0.002
0.936 0.949 o ,960
0.001
Mean,
0.000
0.001 0.000
__
0.001
In order to find how well equations (I) and (2) represent the behavior of common electrolytes, I have made calculations like those of Table I1 for about 30 salts. The data are from measurements by Ostwald, Walden, Bredig and Francke.' As Table I11 shows, the mean difference, Aa, between a as calculated and as observed is 0.2 per cent., which diference may easily be ascribed to experimental error. Calculation shows that equation ( I ) applies also, with fair accuracy, t o many solutions in non-aqueous solvents. Suppose the same salt dissolves in two different solvents; then ccl = I -K,i'C, and a, = I - K,Q?, will represent the existing relationships in the two cases. Now, suppose a1= (Y, ; then K , Vel =K,S?, or K,@, = K,Qv,. (3) But Walden has shown, as already stated, that if a1= a,, E ~ = We231V2. ~ Therefore, K , E= ~ Kle2= a constant. (4). But since both K and E are independent of a, equation (4) should hold for all values of a. Table IV gives the values of K = (I - a ) i;V, e and KE for the salt (C,H,),NI in various solvents, as calculated from Walden's data. While the mean deviation from the mean value of KE is & I O per cent., nevertheless, it seems certain that a fundamental connection exists between K and E ; but that i t is modified by unknown causes. Landolt, Bornstein, Meyerhoffer, Tabellen (190 j).
1076
HERBERT N. M C C O S .
LiI . . . . . . . . . . . . . . . . . . . . . .
LiC10,. . . . . . . . . . . . . . . . . . . I,i >In0, ................. I.iNOJ. . . . . . . . . . . . . . . . . . XaF. . . . . . . . . . . . . . . . N:1CI. . . . . . . . . . . . . . . . . . f:tHr. . . . . . . . . . . . . . . . . . . .
SaI.. . . . . . . . . . . . . . . . . . . SaC10, . . . . . . . . . . . . . . . . SaC10,. . . . . . . . . . . . . . . . SdO,, . . . . . . . . . . . . . . . .
Nn SC)$ . . . . . . . . . . . . . . . .
s :1L111 0 . . . I;I: . . . . . . KC1 . . . . . . Kl%r . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . KI. . . . . . . . . . . . KCIO,. . . . . . . . . . . . . . . . . .
RCIO, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
RNO,. . . . . . . . . . . . . . . . KllnO,, . . . . . . . . . . . . l
