10.5 Electrical Conduction in Electrolyte Solutions
477
for the anions. The current density can be written
j z + N Av e c + v + + z − N Av e c − v − j + + j −
(10.5-8)
Although v + and v − are in opposite directions, z + and z − 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)
where v + and v − are the magnitudes of the drift velocities, and where F is Faraday’s
constant, equal to the charge on 1 mol of protons:
F e N Av 96485 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 if c is its stoichiometric concentration (the concentration that the electrolyte would have if no dissociation or ionization occurred), then
c + ν + c and c − ν − c
(10.5-11)
where ν + is the number of cations in the formula of the solute and ν − 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
j Fcz + 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 charge ze in an
electric field E E E is
F elec ze E E E
(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:
F elec −F friction f v
(10.5-15)
where f is the friction coefficient. For the case that ν + ν − 1 (as with a uniunivalent electrolyte such as sodium chloride), we obtain
j FcE E E e
1
f +
+
1
f −
(if ν + ν − 1)
(10.5-16)
477
for the anions. The current density can be written
j z + N Av e c + v + + z − N Av e c − v − j + + j −
(10.5-8)
Although v + and v − are in opposite directions, z + and z − 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)
where v + and v − are the magnitudes of the drift velocities, and where F is Faraday’s
constant, equal to the charge on 1 mol of protons:
F e N Av 96485 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 if c is its stoichiometric concentration (the concentration that the electrolyte would have if no dissociation or ionization occurred), then
c + ν + c and c − ν − c
(10.5-11)
where ν + is the number of cations in the formula of the solute and ν − 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
j Fcz + 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 charge ze in an
electric field E E E is
F elec ze E E E
(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:
F elec −F friction f v
(10.5-15)
where f is the friction coefficient. For the case that ν + ν − 1 (as with a uniunivalent electrolyte such as sodium chloride), we obtain
j FcE E E e
1
f +
+
1
f −
(if ν + ν − 1)
(10.5-16)