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

JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Redox Reactions and Electrochemistry

Consider an electrochemical cell:

A (s) ∣ A^{n +} (aq, 2 M) ∣∣ B^{2 n +} (aq, 1 M) ∣ B (s)

. The value of

Δ H^{⊖}

for the cell reaction is twice that of

Δ G^{⊖}

at 300 K. If the emf of the cell is zero, the

Δ S^{⊖}

(in

J K^{- 1} mol^{- 1}

) of the cell reaction per mole of B formed at 300 K is ____.

(Given:

ln (2) = 0.7

R

(universal gas constant) =

8.3 J K^{- 1} mol^{- 1}

H

S

and

G

are enthalpy, entropy and Gibbs energy, respectively.)

Answer: -11.62

Cell reaction:

2 A (s) + B^{2 n +} \to 2 A^{n +} + B (s)

. Reaction quotient

Q = \frac{[ A ^{n +} ] ^{2}}{[ B ^{2 n +} ]} = \frac{4}{1} = 4

. Since

E_{cell} = 0

E_{cell}^{\circ} = \frac{R T}{2 n F} ln 4

. Then

Δ G^{\circ} = - 2 n F \times E_{cell}^{\circ} = - R T ln 4

. Given

Δ H^{\circ} = 2Δ G^{\circ}

, using

Δ G^{\circ} = Δ H^{\circ} - T Δ S^{\circ}

Δ G^{\circ} = 2Δ G^{\circ} - T Δ S^{\circ}

, so

Δ S^{\circ} = \frac{Δ G ^{\circ}}{T} = \frac{- R T l n 4}{T} = - R ln 4 = - 8.3 \times 2 ln 2 = - 8.3 \times 1.4 = - 11.62

J K

^{- 1}

mol

^{- 1}

JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Numerical answer