According to the Gibbs-Helmholtz equation and electrochemical thermodynamics, which of the following — Electrochemistry Chemistry Question
Question
According to the Gibbs-Helmholtz equation and electrochemical thermodynamics, which of the following mathematical expressions correctly relates the standard enthalpy change ($\Delta H$) of a cell reaction to the cell potential ($E$) and its temperature coefficient $(\partial E/\partial T)_P$?
💡 Solution & Explanation
The fundamental thermodynamic identity is $\Delta G = \Delta H - T\Delta S$. In an electrochemical cell, $\Delta G = -nFE$. Additionally, the entropy change is related to the temperature derivative of the free energy, giving $\Delta S = nF (\partial E/\partial T)_P$. Substituting these into the first equation yields $-nFE = \Delta H - T \cdot nF(\partial E/\partial T)_P$. Rearranging for $\Delta H$ provides $\Delta H = -nFE + nFT (\partial E/\partial T)_P$.