Concise Physical Chemistry

c13 JWBS043-Rogers September 13, 2010 11:27 Printer Name: Yet to Come

204 COULOMETRY AND CONDUCTIVITY

+ –

(l)

"battery"

(0)

FIGURE 13.1 The potential drop between charged plates isV=φ(0)−φ(l).

ions of the opposite charge, a potential difference is established across the membrane.

Up to this point, expressions involving the Gibbs chemical potentialμhave been

used, assuming that there were no other potentials present; but in this section, a new

potential, theelectrical potentialφ, is introduced. The two potentials, chemical and

electrical, are additive:

μ′=μ+Fφ

whereFis a proportionality constant (see below).

Suppose that, for a dilute solution of KCl, the potassium ion is preferentially

passed through a membrane that blocks the Cl−anion. An electrical potential builds

up that is positive on the potassium-rich side of the membrane and negative on the Cl−

side. The situation is analogous to preferential passage of small molecules through a

membrane in opposition to an osmotic pressure, except that now it is the electrical

potential that opposes flow across the membrane. Just as in the case of osmotic flow,

when the chemical potential driving the transfer is equal and opposite to the electrical

potential, flow stops and an equilibrium has been established. This is the type of

preferential ion flow that occurs between the interior and exterior of mammalian cells

under certain conditions, and it is part of the mechanism of signal transmission along

nerve networks (Fig. 13.2).

If we designate the interior of the cellαand the exterior of the cellβand take into

account only the potassium ion, at equilibrium the sums of electrical and chemical

potentials on either side are equal:

μ+α+Fφα=μ+β+Fφβ

K+( ) K+( )

Cl– Cl–

FIGURE 13.2 An ion-permeable membrane (schematic).