Electrochemistry

Background:
Consider the maximum work that can be obtained when 1 mole of of hydrogen combines with half a mole of of oxygen to form water vapor at $25^\circ$C.

$$\input{equations/27-1A}$$ (34-1)

The entropy of the thermal surroundings of the reaction increase by

$$\input{equations/27-1B}$$ (34-2)

So the total entropy of the universe increases¹ by $953 - 163 = 790 {\ensuremath{\frac{\mbox{J}}{\mbox{mole} {}^\circ\mbox{K}}}}$

WHAT a WASTE! In order not to violate the second law, only only $q_{min}$ amount of heat needs to be transfered.

$$\input{equations/27-2A}$$ (34-3)

which leaves

$$\input{equations/27-2B}$$ (34-4)

Apparently, $\Delta G^{rx}$ represents the maximum work that can be extracted from a system.

How can this work be extracted? In principle it could be harnessed to drive an electric motor. To do this, a source of electrons is needed and those can be generated those by the reactions:

$$\input{equations/27-3A}$$ (34-5)

The work done by the electric motor is the potential drop between the source and sink of the electrons, multiplied by the net charge that they carry:

$$\input{equations/27-3B}$$ (34-6)

or

$$\input{equations/27-3C}$$ (34-7)

The maximum potential is related to the molar Gibbs free energy of the reaction.