J. Phys. Chern. 1981,85,3952-3954
3952
T A B L E VI:
E x p e r i m e n t a l Slopes a n d I n t e r c e p t s for P l o t s of e o - ( R / F )In rn vs. rn”‘
acid
mean temp/”C
no. of runs
HC1 HC1 HC1 HBr HBr HBr
25 20 30 25 15 35
15 19 11 14
I 8
max m
std error of est
0.0196
0.0191 0.0212 0.0138 0.0122 0.0168
0.96 1.06 1.28 0.90 0.38 0.50
i n t e r c e p t / ( p V K-’) 520.92 510.31 531.55 522.69 501.70 541.60
f f
*
f f 2
0.72 0.69 1.02 0.57 0.39 0.47
s l o p e / ( F V K-’ mol-”’ dm3’z) -83.8 % 6.8 -18.4 f 1.8 -95.6 z 10.0 -18.2 t 1.8 -56.9 f 5.2 -84.9 * 5.3
’76 agreementa 1.1 1.5 8.3 6.1 21.6
10.4
P e r c e n t a g r e e m e n t is calculated f r o m t h e experimental slopes of T a b l e VI (after dividing t h e m by t h e s q u a r e root of t h e density o f water to c o n v e r t these slopes to t h e e”’ basis) c o m p a r e d w i t h t h e theoretical slopes o f Table 111. a
eq 1 at infinite dilution with the left-hand side egual to 522.69 f 0.57 PV K-l. This results in a value of QoHBr = 3399 f 38 cal mol-l. The last term of eq 2 can be expressed in terms of the concentration dependence of the transport number for the anion given by t i - = B’eF(2t0A-- 1)/6(299.79)~qo(XO~+ + XoA-) (7)
No correction was used for the lowering of water vapor pressure due to the presence of solute because of the extreme dilution of each acid used. The experimental results for HC1 and HBr and the agreement of the experimental limiting slopes with the theoretical limiting slopes are given in Table VI. Hydrochloric acid is in excellent agreement. Hydrobromic acid is in good agreement, considering the experimental error and the *3% error in the theoretical limiting slopes where qo is the viscosity of water. Equation 7 was derived due mainly to the &lo% error22in the electrophoretic by taking the infinite-dilution limit of the expression for terms, eq 5 and 6. the concentration variation of the transport number due The present difficulty with the theory lies in the electo first-order electrophoretic terms according to Robinson trophoretic terms, eq 5 and 6. The contributions from the and Stokes.20 The values of constants used in the theodirect terms, eq 3 and 4, as well as eq 7, are fairly certain. retical calculations are found in Tables I and 11. If one examines the experimental slopes minus the conWe can now calculate the limiting slopes by substituting tributions of eq 3,4, and 7, i.e., [(experimental slope) - (eq the values for eq 3-7 into eq 2. The numerical values and 3 + eq 4 eq 7)23],compared with the sum of eq 5 and units for eq 3-7 and the theoretical limiting slopes are eq 6, one sees how well the theory for the electrophoretic given in Table 111. terms explains the experimental results. The present Data and Results theory very satisfactorily explains HC1, but for HBr, the We present in Tables IV-V thermoelectric powers at theoretical electrophoretic terms are already too large. The very dilute (
