Consider an electrochemical cell: A(s) $|A^{n +} (a q, 2 M)| |B^{2 n +} (a q, 1 M)| B (s)$ . The value of $Δ H^{0}$ for the cell reaction is twice that of $Δ G^{0}$ at 300K. If the EMF of the cell is zero, the $Δ S^{0}$ (in $J K^{- 1} m o l^{- 1}$ ) of the cell reaction per mole of B formed at 300K is___
(Given : ln (2) = 0.7, R (universal gas constant) = 8.3 J $K^{- 1} m o l^{- 1}$ . H, S and G are enthalpy, entropy and Gibbs energy, respectively.)

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$\begin{aligned} A (s) |A^{+ n} (aq, 2 M) ∥ B^{+ 2 n} (aq, 1 M)| B (s) \\ {ΔH}^{\circ} = 2 {ΔG}_{0}^{\circ} E_{cell} = 0 \\ Cell Rx A \to A^{+ n} + {ne}^{-}] \times 2 \\ B^{+ 2 n} + 2 {ne}^{-} \to B (s) \\ 2 A (s) + B_{1 M}^{+ 2 n} (aq) \to 2 A^{+ n} (aq) + B (s) \\ ΔG = {ΔG}^{\circ} + RTln \frac{{[A^{+ n}]}^{2}}{[B^{+ 2 n}]} \\ {ΔG}^{\circ} = - RTln \frac{{[A^{+ n}]}^{2}}{[B^{+ 2 n}]} = - RT . \ln \frac{2^{2}}{1} = - RT \cdot \ln 4 \\ {ΔG}^{\circ} = {ΔH}^{\circ} - {TΔS}^{\circ} \\ {ΔG}^{\circ} = 2 {ΔG}^{\circ} - {TΔS}^{\circ} \\ {ΔS}^{\circ} = \frac{{ΔG}^{\circ}}{T} = - \frac{RTln 4}{T} \\ = 8.3 \times 2 \times 0.7 = - 11.62 J / K \cdot mol \end{aligned}$