A galvanic cell with n = 2 has E deg = 1.000 V at 298 K, and the cell reaction has Delta_r H deg = -200.0 kJ mol^-1. Take F = 96500 C mol^-1 and assume Delta_r H deg and Delta_r S deg are temperature independent. Which statements are correct?

Delta_r G deg at 298 K is -193.0 kJ mol^-1

Delta_r S deg is about -23.5 J K^-1 mol^-1

((partial E deg)/(partial T))_P is about -1.22 x 10^-4 V K^-1

Delta_r G deg at 298 K is -193.0 kJ mol^-1

Delta_r S deg is about -23.5 J K^-1 mol^-1

((partial E deg)/(partial T))_P is about -1.22 x 10^-4 V K^-1

At 348 K the standard EMF is about 1.006 V

JEE Advanced levelOne or more correct optionsDifficulty 3 of 3ec062

A galvanic cell with $n = 2$ has $E^{\circ} = 1.000 V$ at 298 K, and the cell reaction has $Δ_{r} H^{\circ} = - 200.0 kJ mo l^{- 1}$ . Take $F = 96500 C mo l^{- 1}$ and assume $Δ_{r} H^{\circ}$ and $Δ_{r} S^{\circ}$ are temperature independent. Which statements are correct?

A $Δ_{r} G^{\circ}$ at 298 K is $- 193.0 kJ mo l^{- 1}$
B $Δ_{r} S^{\circ}$ is about $- 23.5 J K^{- 1} mo l^{- 1}$
C $(\frac{\partial E ^{\circ}}{\partial T})_{P}$ is about $- 1.22 \times 1 0^{- 4} V K^{- 1}$
DAt 348 K the standard EMF is about $1.006 V$

Δ_{r} G^{\circ} = - n F E^{\circ} = - 2 \times 96500 \times 1.000 = - 193000 J = - 193.0 kJ

(A).

Δ_{r} S^{\circ} = (Δ_{r} H^{\circ} - Δ_{r} G^{\circ}) / T = (- 200000 + 193000) /298 = - 23.5 J K^{- 1}

(B).

(\partial E^{\circ} / \partial T)_{P} = Δ_{r} S^{\circ} / (n F) = - 23.5/193000 = - 1.22 \times 1 0^{- 4} V K^{- 1}

(C). Over 50 K the EMF changes by

- 1.22 \times 1 0^{- 4} \times 50 = - 0.006 V

, so at 348 K

E^{\circ} \approx 0.994 V

, not

1.006 V

; D is wrong.