Physical Chemistry Third Edition

10.5 Electrical Conduction in Electrolyte Solutions 477

for the anions. The current density can be written

jz+NAvec+v++z−NAvec−v−j++j− (10.5-8)

Althoughv+andv−are in opposite directions,z+andz−also have opposite signs so

the two contributions have the same sign. The magnitude of the current density is

j|j|F(z+c+v++|z−|c−v−) (10.5-9)

wherev+andv−are the magnitudes of the drift velocities, and whereFis Faraday’s

constant, equal to the charge on 1 mol of protons:

FeNAv96485 C mol−^1 (10.5-10)

Exercise 10.18

Show that Eq. (10.5-8) is correct.

If dissociation or ionization of an electrolyte solute is complete and ifcis its stoi-

chiometric concentration (the concentration that the electrolyte would have if no dis-

sociation or ionization occurred), then

c+ν+c and c−ν−c (10.5-11)

whereν+is the number of cations in the formula of the solute andν−is the number of

anions in the formula. (In some fonts the Greek “nu” and the English “vee” look quite

similar. Please try to keep them straight.) If there is a single electrolyte solute these

quantities must obey the electrical neutrality relation

ν+z++ν−z− 0 (10.5-12)

For a single electrolyte we can write

jFcz+ν+(v++v−) (10.5-13)

If the ions experience a frictional force according to Eq. (10.4-1), Ohm’s law is

obeyed by an electrolyte solution. The electrostatic force on an ion of chargezein an

electric fieldEEE is

FeleczeEEE (10.5-14)

On the average, the ions are not accelerated if a steady current is flowing, so that the

electrical force and the frictional force cancel:

Felec−Ffrictionfv (10.5-15)

wheref is the friction coefficient. For the case thatν+ν−1 (as with a uni-

univalent electrolyte such as sodium chloride), we obtain

jFcEEEe

(

1

f+

+

1

f−

)

(ifν+ν−1) (10.5-16)