Gibbs Energy Change and Cell EMF

A spontaneous chemical reaction can, in principle, be harnessed to do useful work, and the maximum non-expansion (e.g. electrical) work obtainable from a reaction at constant temperature and pressure is given by its Gibbs energy change, $\Delta G$. In a galvanic cell, the electrical work delivered when $n$ moles of electrons pass through a potential difference $E_{cell}$ is $nFE_{cell}$ (charge, $nF$, times potential difference). Equating the two, with a sign flip because $\Delta G$ is negative for a spontaneous process while the work delivered is treated as positive, gives the central relation of electrochemical thermodynamics: $\Delta G^{\circ} = -nFE^{\circ}_{cell}$

For the Daniell cell, with $n=2$ and $E^{\circ}_{cell}=1.10\ \text{V}$, this gives $\Delta G^{\circ} = -(2)(96500\ \text{C mol}^{-1})(1.10\ \text{V}) = -212{,}300\ \text{J mol}^{-1} = -212.3\ \text{kJ mol}^{-1}$, a large negative value confirming the reaction is strongly thermodynamically favoured under standard conditions.

Because $n$ and $F$ are always positive, this relation forces $\Delta G^{\circ}$ and $E^{\circ}_{cell}$ to always carry opposite signs: whenever $E^{\circ}_{cell}$ is positive (the cell can genuinely deliver a current), $\Delta G^{\circ}$ must be negative (the reaction is spontaneous); whenever $E^{\circ}_{cell}$ is negative, $\Delta G^{\circ}$ must be positive (the reaction, as written, is non-spontaneous, and it is instead the reverse reaction that is favoured). This gives a direct, purely-electrical way to judge the spontaneity of any redox reaction: simply check the sign of the calculated $E^{\circ}_{cell}$ for the reaction as written. …