Page 219 - Modern physical chemistry

212 Electrochemistry

For the anion in the anode compartment, we have

dnelectrolysis = 0
since anions are not oxidized at the electrode. But from the electrical neutrality condi-
tion, the change in equivalents of the cation equals the change in equivalents of the anion.
For either ion,
dn = 0.9972 _ 0.7532 = 0.2440 e uiv.
31.773 31.773 31.773 q
Combining these results as in equation (9.26) gives us

0.2440 .
dnmigration = -- eqmv
31.773
for the anion. Dividing the equivalents migrating by the equivalents reduced at the cathode,
as in (9.21), leads to
L = 0.2440/31.773 = 0.6100.
0.4000/31.773
Because the transference numbers of the ions add up to 1, we have

t+ = 1- L = 0.3900.
On the other hand, for the cation in the anode compartment, we have

0.4000 .
dnelectrolysis = -- eqmv.
31.773
As before, the change in equivalents in the compartment is

0.2440 .
dn=-- eqmv.
31.773
So for the equivalents of cation migrating into the anode compartment, equation (9.26)
yields
dn. . - 0.2440 _ 0.4000 = _ 0.1560 e uiv
nugration - 31.773 31.773 31.773 q .

To get the amount migrating out, one changes the sign. Dividing the result by the equiv-
alents oxidized at the electrode then gives us

t = 0.1560/31.773 = 0.3900.
+ 0.4000 / 31.773
whence
L = I-t+ = 0.6100.

9.4 Moving Ion Clouds and Boundaries
How a configuration of ions moves can be determined from the movement of a suit-
able boundary. This provides a second method for measuring transference numbers.
Through a region where an electrolyte is uniform, an imposed electric intensity E
causes the cations to drift in the same direction at the average velocity u+ and the anions
to drift in the opposite direction at the average velocity u .. In unit time, the cations travel
distance u+ on average, while the anions travel distance u. in the opposite direction on