PHYSICAL CHEMISTRY IN BRIEF

CHAP. 11: ELECTROCHEMISTRY [CONTENTS] 357

Example

(Acidified) water is electrolyzed in a coulometry monitor for explosive gas. The volume of the dis-

charged stoichiometric mixture of oxygen and hydrogen, the so-called explosive gas, is measured.

Determine the volume of the discharged explosive gas if a charge of 1Fpasses through the circuit

at a temperature of 300 K and pressure 100 kPa. Assume that under the given conditions, the

equation of state of an ideal gas can be applied.

Solution

The following reactions occur during the electrolysis of water:

H 2 O = H++ OH− dissociation of water,

H++ e− =^12 H 2 reduction at the cathode,

OH− =^12 H 2 O +^14 O 2 + e− oxidation at the anode.

A total of 1/2 mole of H 2 and 1/4 mole of O 2 , i.e. 3/4 moles of electrolytic gas were discharged

by a charge of 1F. From the state equation of an ideal gas we obtain

V =

nRT

p

=

3 / 4 × 8. 314 × 300

100

= 18. 706 dm^3.

11.2.4 Transport numbers

During electrolysis, the electric charge is carried in the electrolyte by both cations and anions,
but the amount of charge they transport is different. Thecation transport numbert+is
defined as the ratio of the charge carried by the cationsQ+and the total chargeQ=Q++Q−

t+=

Q+

Q

. (11.11)

Similarly, theanion transport numberis defined as

t−=

Q−

Q

. (11.12)

It is obvious that
t++t−= 1. (11.13)