Question

The standard free energy for the neutralization of HCl with NaOH at 25C is -79.9 kj/mol. Calculate the equilibrium constant for the reaction.

Answer 1

We are interested in the Gibbs free energy and assume constant pressure (Helmholtz if we hold volume constant):\[\Large \Delta G=\Delta G ^{\Theta}+RT \ln \left( K \right)\]Where \(K\) is the equilibrium constant. At equilibrium \(\Delta G=0\):\[\Large 0=\Delta G ^{\Theta}+RT \ln \left( K \right) \rightarrow \Delta G^{\Theta}=-RT \ln(K)\]Solve for the equilibrium constant:\[\Large \frac{ - \Delta G^\Theta }{ RT }=\ln(K)\]\[\Large \frac{ [P] }{ [S] }=K=\exp \left( \frac{ -\Delta G^\Theta }{ RT } \right)\]Just put into the equation and calculate the equilibrium constant \(K\).