Total Current at Equilibrium

Equations (A-12), (A-11), (A-10) and (A-3) can be combined into the form of Equation (A-2) to give

f

dC

dV)

uAZF

RT

— + ZFC-

V

d x

d x v

This requires that

f d C >

f — 1

RT

= -ZFC

1 d x V

Equation (A-14) can be rearranged to give a differential equation that can be solved for the equilibrium voltage gradient:

f RT 1

r dc 1

v ZF y

This can be solved for V by integrating across the membrane. Using the nomenclature of Figure A-1, the integrals are

RT ZF

The solution to these definite integrals is RT,

Mn vout ^m

Equation (A-18) is the Nernst equation.

out appendix

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