Consider an electrochemical cell- -A s - An- aq- 2 M - B2n- aq- 1 M - B s- The value of - H0for the cell reaction is thrice that of - G0 at- 300 K- If the emf of the cell is zero- the - S0 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 - 8-3 J K-1 mol-1- -H- S and G are enthalpy- entropy and Gibbs energy- respectively-

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Standard Electrode Potentials

Consider an e...

Question

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 thrice that of $Δ G^{0}$ at 300 K. 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 300 K is:
Given:
$l n (2) = 0.7$ ,
$R = 8.3 J K^{- 1} m o l^{- 1}$ .
H, S and G are enthalpy, entropy and Gibbs energy, respectively.

- 23.24 J m o l^{- 1} K^{- 1}

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- 0.77 J m o l^{- 1} K^{- 1}

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- 122 J m o l^{- 1} K^{- 1}

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- 0.11 J m o l^{- 1} K^{- 1}

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Solution

The correct option is A $- 23.24 J m o l^{- 1} K^{- 1}$
$A (s) \to A^{n +} + n e^{-} . . . (e q 1)$
$B^{2 n +} + 2 n e^{-} \to B (s) . . (e q 2)$
Multiplying eq 1 by 2 and adding to eq 2
Overall reaction:
$2 A (s) + B^{2 n +} \to 2 A^{n +} + B (s)$

$E_{c e l l} = E_{c e l l}^{0} - \frac{R T}{2 n F} ln \frac{[A^{n +}]^{2}}{[B^{2 n +}]}$

$0 = E_{c e l l}^{0} - \frac{R T}{2 n F} ln \frac{2^{2}}{1}$
$E_{c e l l}^{0} = \frac{R T}{n F} ln 2$
$Δ G^{0} = - 2 n F E_{c e l l}^{0} = - 2 n F \times \frac{R T}{n F} ln 2$
$Δ G^{0} = - 2 R T ln 2$
$Δ G^{0} = Δ H^{0} - T Δ S^{0}$
$Δ S^{0} = \frac{Δ H^{0} - Δ G^{0}}{T}$
$Δ S^{0} = \frac{3 Δ G^{0} - Δ G^{0}}{T}$
$Δ S^{0} = \frac{2 Δ G^{0}}{T}$
$Δ S^{0} = \frac{2 \times - 2 R T ln 2}{T}$
$Δ S^{0} = - 4 R ln 2 = - 4 \times 8.3 \times 0.7 = - 23.24 J m o l^{- 1} K^{- 1}$

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