PHYSICAL CHEMISTRY IN BRIEF

CHAP. 11: ELECTROCHEMISTRY [CONTENTS] 358

The amount of the transported charge relates to the velocity with which the ions travel through
the electrolyte. We have

t+=

v+

v++v−

, t−=

v−

v++v−

, (11.14)

wherev+is the velocity of the cation andv−is that of the anion.
The velocity of ions in a solution of a given concentration, temperature and pressure depends
on the voltage between the two electrodes and on the distance between them. The higher the
voltage and the closer the electrodes to each other, the higher is the ions velocity. Theionic
mobilityis defined as the velocity of an ion at a potential gradient of 1 V m−^1.

u+=

`

E

v+, u−=

`

E

v−, (11.15)

whereu+is the cation mobility,u−is the anion mobility,Eis the voltage and`is the distance
between the electrodes. The same relations as (11.14) apply between transport numbers and
ionic mobilities

t+=

u+

u++u−

, t−=

u−

u++u−

. (11.16)

Relations (11.11) through (11.16) can be easily extended to cases when there are more kinds
of anions and cations in an electrolyte. For example, generalized equation (11.13) becomes

∑

i

t+i +

∑

j

t−j = 1. (11.17)

Transport numbers and ionic mobilities depend on the concentration of the electrolyte,
temperature and (to a small extent) pressure.

11.2.5 Concentration changes during electrolysis.

In consequence of unequal velocity of ions, concentration changes in the vicinity of the electrodes
occur during electrolysis. If the ions are discharged at the electrode, their concentration in the
vicinity of the opposite electrode decreases. If the ions reaction at the electrode is such that
they return to the solution, their concentration in the vicinity of the given electrode increases.
In both cases, the condition of local electroneutrality, relation (11.3), is always fulfilled.