Consider an electrochemical cell: \(\mathrm{A}(\mathrm{s})\left|\mathrm{A}^{\mathrm{n}+}(\mathrm{aq}, 2 \mathrm{M}) \| \mathrm{B}^{2 \mathrm{n}+}(\mathrm{aq}, 1 \mathrm{M})\right| \mathrm{B}(\mathrm{s})\). The value of \(\Delta H^{\ominus}\) for the cell reaction is twice that of \(\Delta G^{\theta}\) at \(300 \mathrm{~K}\). If the emf of the cell is zero, the \(\Delta S^{\theta}\) (in \(\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}\) ) of the cell reaction per mole of \(\mathrm{B}\) formed at \(300 \mathrm{~K}\) is (Given: \(\ln (2)=0.7, R\) (universal gas constant) \(=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \cdot H, S\) and \(G\) are enthalpy, entropy and Gibbs energy, respectively.)

In electrochemistry, understanding thermodynamics is crucial because it reveals how energy changes during chemical reactions in an electrochemical cell. An electrochemical cell uses chemical reactions to produce electrical energy, and the thermodynamics of these reactions tell us whether the process is spontaneous and how efficient it can be.

Thermodynamics ties into electrochemistry primarily through the study of energy changes involving Gibbs free energy (\( \triangle G \)), enthalpy (\( \triangle H \bar{\theta} \bar{\theta}= -RT\text{ln}Q \triangle S \theta \triangle H \ominus \triangle S \theta \triangle H \ominus \triangle G \theta \triangle G \theta \triangle S \theta \bar{\theta} \bar{\theta} \bar{\theta} \triangle S \theta \bar{\theta} \bar{\theta} \)

At the heart of predicting spontaneity in electrochemical reactions is Gibbs free energy (\( \triangle G \bar{\theta} = \triangle H \ominus - T\triangle S \theta \triangle G \theta \triangle H \ominus = \frac{\triangle H \ominus}{2} \bar{\theta} \triangle G \theta \bar{\theta} \ominus \ominus \theta \triangle S \theta \triangle S \theta = \frac{\triangle H \ominus}{T} \bar{\theta} = \frac{2\triangle G \theta}{T} \triangle G \theta \)

A powerful tool in the study of electrochemistry is the Nernst equation, vital for calculating the electromotive force (EMF) of a cell under non-standard conditions. However, it can also inform us about the change in Gibbs free energy (\( \triangle G \theta = -RT\text{ln}Q \bar{\theta} = -RT\text{ln}Q \triangle G \theta \theta = -RT\text{ln}Q \bar{\theta} = -8.3 \times 300 \times 0.7 = -1743 \text{J/mol} \ominus \ominus \ominus \bar{\theta} \)

Entropy (\( \triangle S \triangle H \triangle S \triangle G = \triangle H - T\triangle S \triangle H \ominus \triangle G \theta \triangle S \theta \theta \triangle S \theta \ominus \ominus \ominus \triangle S \theta = \frac{2 \times (-1743)}{300} = \frac{-3486}{300} = -11.62 \text{J K}^{-1} \text{mol}^{-1} \ominus \ominus \ominus \bar{\theta} \triangle S \theta \bar{\theta} = \frac{\triangle H \ominus}{T} \)