If the standard cell potential () of a standard galvanic cell is measured to be at exactly and at ex — Electrochemistry Chemistry Question
Question
If the standard cell potential ($E^\circ_{cell}$) of a standard galvanic cell is measured to be $0.46\text{ V}$ at exactly $300\text{ K}$ and $0.50\text{ V}$ at exactly $340\text{ K}$, what is the estimated standard entropy change ($\Delta S^\circ$) for the cell reaction? Assume a $2$ -electron transfer process ($n=2$) and use Faraday's constant $F = 96500\text{ C mol}^{-1}$.
💡 Solution & Explanation
The standard entropy change is tied to the temperature coefficient via $\Delta S^\circ = nF (\frac{\partial E^\circ}{\partial T})_P$. We estimate the temperature coefficient linearly: $\frac{\Delta E^\circ}{\Delta T} = \frac{0.50\text{ V} - 0.46\text{ V}}{340\text{ K} - 300\text{ K}} = \frac{0.04}{40} = 10^{-3}\text{ V K}^{-1}$. Inserting this into the entropy equation: $\Delta S^\circ = 2 \times 96500\text{ C mol}^{-1} \times 10^{-3}\text{ V K}^{-1} = 193 \times 2 = 386\text{ J K}^{-1}\text{ mol}^{-1}$.