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Relation between Cp and Cv

For the react...

Question

For the reaction $A g^{+} (a q) + C l^{-} (a q) ⇌ A g C l (s)$ ; the $Δ G^{o}$ values for $A g^{+} (a q), C l^{-} (a q)$ and $A g C l (s)$ are + 77, -129 and -109 kJ mol $^{- 1}$ . Write the cell representation of above reaction and calculate $K_{s p}$ of AgCl at 298 K.
(Multiply the ans by $10^{10}$ )

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Solution

$Δ G = Δ G (A g C l (s)) - [Δ G (A g^{+}) + Δ G (C l^{-})] = - 109 k J / m o l - [77 k J / m o l - 129 k J / m o l] = - 57 k J / m o l$
$Δ G = - n F E$
$E = \frac{- Δ G}{n F} = \frac{- 57000 J / m o l}{1 \times 96500} = 0.591 V$
$E^{0} = 0.222 V$
$E = E^{0} - \frac{0.0592}{n} l o g \frac{1}{[A g^{+}] [C l^{-}]}$
$0.59 V = 0.222 V - \frac{0.0592}{1} l o g \frac{1}{K_{s p}}$
$l o g \frac{1}{K_{s p}} = 6.2276$
$\frac{1}{K_{s p}} = 1.688 \times 10^{6}$
$K_{s p} = 5.9 \times 10^{- 7}$
The molar mass of AgCl is 143.5 g/mol.
$K_{s p} = \frac{5.9 \times 10^{- 7}}{143.5} = 4 \times 10^{- 9}$
Hence, $K_{s p} \times 10^{10} ≃ 40$

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Δ G^{o}

A g C l (s) + 1 / 2 H_{2} (g) \to A g (s) + H^{+} (a q .) + {C l}^{-} (a q)

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2 A g C l (c) + H_{2} (g) \to A g (s) + 2 H^{+} (a q .) + 2 {C l}^{-} (a q .)

Δ G_{f}^{⊖}

A g^{\oplus} (a q) + C l^{⊖} (a q) \to A g C l (s)

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