A cell reaction with $n = 2$ has $Δ_{r} H^{\circ} = - 200.0 kJ mo l^{- 1}$ and $Δ_{r} G^{\circ} = - 180.0 kJ mo l^{- 1}$ at 298 K. The temperature coefficient of the standard EMF, $(\frac{\partial E ^{\circ}}{\partial T})_{P}$ , is closest to ( $F = 96500 C mo l^{- 1}$ )

Answer: A

Δ_{r} S^{\circ} = \frac{Δ _{r} H ^{\circ} - Δ _{r} G ^{\circ}}{T} = \frac{- 200000 - ( - 180000 )}{298} = - 67.1 J K^{- 1} mo l^{- 1}

. Then

(\frac{\partial E ^{\circ}}{\partial T})_{P} = \frac{Δ _{r} S ^{\circ}}{n F} = \frac{- 67.1}{2 \times 96500} = - 3.48 \times 1 0^{- 4} V K^{- 1}

. The EMF falls with temperature because the reaction entropy is negative. Option C uses

n = 1