Question

The standard electrode potential \(E^\circ\) and its temperature coefficient \(\left(\frac{dE^\circ}{dT}\right)\) for a cell are 2 V and \(-5\times10^{-4}\ \mathrm{VK^{-1}}\) at 300 K respectively. The cell reaction is
\(\mathrm{Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)}\)
The standard reaction enthalpy \((\Delta_rH^\circ)\) at 300 K in \(\mathrm{kJ\ mol^{-1}}\) is, [Use \(R = 8\ \mathrm{JK^{-1}mol^{-1}}\) and \(F = 96{,}000\ \mathrm{C\ mol^{-1}}\)]

• A. \(-412.8\)
• B. \(-384.0\)
• C. \(192.0\)
• D. \(206.4\)

Hint:

Use \(\Delta G=-nFE\), \(\Delta S=nF\,(dE/dT)\) and \(\Delta H=\Delta G+T\Delta S\) with n = 2.

Answer 1

The Correct Option is A

For Zn + Cu²⁺ \(\rightarrow\) Zn²⁺ + Cu, n = 2.
\(\Delta G^\circ=-nFE^\circ=-2\times96000\times2=-384000\ \mathrm{J\,mol^{-1}}=-384\ \mathrm{kJ\,mol^{-1}}\).
\(\Delta S^\circ=nF\left(\frac{dE^\circ}{dT}\right)=2\times96000\times(-5\times10^{-4})=-96\ \mathrm{J\,K^{-1}mol^{-1}}\).
\(\Delta H^\circ=\Delta G^\circ+T\Delta S^\circ=-384000+300\times(-96)=-384000-28800=-412800\ \mathrm{J}\).
\(\Delta_rH^\circ=-412.8\ \mathrm{kJ\,mol^{-1}}\) (R is not needed).
Answer: (1) \(-412.8\)