1642
VICTORK. LA MERAM,
JAMES
P. CHITTUM
Vol. 58
The rate of interdiffusion of the same acid sharper because of the neutralization within the and base in sodium chloride solution has been disk. studied. It is shown that the diffusion coeffiSome limitations of the porous disk diffusion cients are unchanged if sufficient sodium chlo- cell are demonstrated. Adequate mixing must ride is present initially; in the porous disk cell, be maintained in the cell solutions either by natuthe diffusion rates are, however, greatly increased ral convection or by auxiliary stirring. since the concentration gradients become much NEWYCRK, N. Y. RECEIVED FEBRUARY 12,1936
[ CONTRIRUTION FROM THE DEPARTMENT OF CHEMISTRY, COLUMBIA UNIVERSITY]
The Conductance of Salts (Potassium Acetate) and the Dissociation Constant of Acetic Acid in Deuterium Oxide BY VICTOR K. LA MERAND JAMES P. CHITTUM The accurate calculation of the dissociation constant of a weak acid, like acetic acid, in deuterium oxide requires values of comparable accuracy of the limiting conductances lo,of deuterochloric acid, potassium chloride and potassium acetate. In ordinary water the problem is solved by measuring a series of conductance values a t increasing dilutions and controlling the extrapolation to infinite dilution by the Onsager' equation. The limited quantities of heavy water available do not permit execution of this tedious and experimentally difficult problem at this time. We are accordingly interested in establishing the validity of two approximate rules, which will permit the calculation of A. for the deuteronium ion and for the anion of the weak acid with sufficient precision for present purposes from a single measurement at an experimentally convenient concentration (C = 0.01) in heavy water which is not necessarily 100% D2O. These rules are [ A , / A O ~ H ~E O [A,/Aol
D ~ O
(1)
valid for acids and salts in pure DzO, but presumably accurate only for salts in intermediate mixtures of D20-Hz0, owing to the complication of the exchange reactions which acids suffer in the mixed waters2 Aq = Constant; q = Viscosity,
(2)
valid for interpolation and for extrapolation to pure DzO of the data obtained for the salts in HzO-DzO mixtures. (1) Onsager, Phrsik Z.,27, 288-292 (1926); 28, 27F.298 (1927). (2) Baker and La Mer, J , Chem. Phys., P, 406 (1835).
The justification of (1) follows from the Onsager equationa A, = Ao
-
[ d o
-!- 2Pl
.\Tc
(3)
where 8.173 X 106 a =
41.7
(DT)8/2 and 6 = (DT)'/x
1
11
(4)
Let p' = 2077, then a and 8' differ in H2O and D2O only by the ratio of the dielectric constants of HzO and DzO which ratio appears to be almost unity. 4 ~ 5 AC/Ao = 1
- [ a f 6'/Aoql .\Tc
(5)
and
The experimental data on potassium chloride and on potassium acetate presented below show that differs from (Aoq)D20 by only 1.93%. Hence equation (6) reduces without appreciable error to equation (1).6 The error in Ao(DzO) calculated through equations (1) and (6) is thus less than 0.1% and less than our present experimental errors. The A, os. dc curves in DzO are, therefore, sensibly parallel to those in HzO, and the DzO curve can be constructed from a measurement of A a t a single low concentration. Since the only difference in the limiting conductance of non-acid ions in DzO and in H2O appears to be resident in the change in p, the electrophoretic part of the Onsager equation, we expect (3) MacInnes, Shedlovsky and Longsworth, Chem. Rev., 13, 28 (1933), eq. (7). (4) Horst Muller, Physik. Z.,86, 1009-1011 (1935). (5) P. Abadie and G. Champetier, Compt. rend., 200, 1387 (1935). (6) does not change significantly on passing from C 0.01 to
c
-
0.
-
Sept., 1936
o
AS
m
-
CONDUCTANCES I N DEUTERIUM OXIDE
1G43
TABLE I 0.0
NDzo
106 K’ acetic AOKAO (hop) KAc
A4°*9’a KAc
(HAC-DAc) A (Eq. 8) A0
1.84 114.4 114.4 114.4 390.6 148.6
27.4
77.0
93.0
97.0
100.0
1.352 108.1 115.0 114.4 345.6 134.8
0.741 98.2 115.8 114.1 297.5 117.2
0.608 96.0 116.4 114.5 285.9 114.2
0.575 95.5 116.5 114.5 285.2 113.7
( 0.555) ( 94.7) (116.6)
that ilO(HzO)/dO(D~O) is practically constant for all completely dissociated salts of the same Valence type and equal to approximately qL)io/gH20 Experimental.-The measurements on potassium acetate have been made a t 2 5 O , using a Jones bridge and the semi-micro method described previously,2 a t approximately 0.015 N a t different mixtures of H~O-DZO. A0 obtained by linear extrapolation from 93 and 97% D 2 0 is 94.8 Kohlrausch units (K. U.), a decrease of 1’7.1%from the H2O 1.9 value. The corresponding decrease for potassium chloride is 17.2%. Table I shows that the empirical equation A070.913 =
Constant
(7)
agreement with the value of 0.55 X obtained by Korman and La Mers from the e. m. f. of quinhydrone-silver chloride, Ag cells without transference and a formula defined by them for extrapolating K to 100% D20. As was found previously for potassium chlo118
I - K ‘ Acsf/c Aud
108
4 1.4
shown in the previous paper to be valid 2 for potassium chloride, applies equally well to potassium acetate. The value of A,(KAc) a t 100% DzO calculated either 0.9 from equation (1) or (7) is 94.7 K. U. Dissociation Constant of Acetic Acid. -The stoichiometric constant for approximately 0.02 N acetic acid, has been 0. calculated using the MacInnes-Shedlovsky’ method for each H20-D20 0 mixture (Table I), by omitting the last (empirical) term in the equation A,(HAc) = ii0 - A + BC (1 - a
