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10.2: The connection to ΔG

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  • 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:

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

    Contributors and Attributions

    • Patrick E. Fleming (Department of Chemistry and Biochemistry; California State University, East Bay)

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