# 10.2: The connection to ΔG

Recall that in addition to being used as a criterion for spontaneity, $$\Delta G$$ also indicated the maximum amount of non p-V work a system could produce at constant temperature and pressure. And since we is non p-V work, it seems like a natural fit that

$\Delta G = -nFE$

If all of the reactants and products in the electrochemical cell are in their standard states, it follows that

$\Delta G^o = -nFE^o$

where $$E^o$$ is the standard cell potential. Noting that the molar Gibbs function change can be expressed in terms of the reaction quotient $$Q$$ by

$\Delta G = \Delta G^o + RT \ln Q$

it follows that

$-nFE = -nFE^o + RT \ln Q$

Dividing by $$–nF$$ yields

$E = E^o - \dfrac{RT}{nF} \ln Q$

which is the Nernst equation. This relationship allows one to calculate the cell potential of a electrochemical cell as a function of the specific activities of the reactants and products. In the Nernst equation, n is the number of electrons transferred per reaction equivalent. For the specific reaction harnessed by Volta in his original battery, Eo = 0.763 V (at 25 oC) and $$n = 2$$. So if the Zn2+ and H+ ions are at a concentration that gives them unit activity, and the H2 gas is at a partial pressure that gives it unit fugacity:

$E = 0.763\,V - \dfrac{RT}{nF} \ln (1) = 0/763$