Using the Gibbs' energy change, = + 63 . 3 kJ , for the following reaction, Ag 2 CO 3 () ? 2 Ag + + CO 3 2 - the of 2 3 in water at 25 C o is ( = 8 . 314 J K - 1 mol - 1 ) [2014]

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Solution

Q.
Using the Gibbs' energy change, $Δ G ° = + 63.3$ $kJ$ , for the following reaction, ${Ag}_{2} {CO}_{3 (s)} ⇌ 2 {Ag}_{(a q)}^{+} + {CO}_{3}^{2 -}_{(a q)}$

the $K_{s p}$ of $A g_{2} C O_{3 (s)}$ in water at $25 {}^{o}C$ is ( $R = 8.314$ $J$ $K^{- 1}$ ${mol}^{- 1}$ ) [2014]

1 $3.2 \times 10^{- 26}$

2 $8.0 \times 10^{- 12}$

3 $2.9 \times 10^{- 3}$

4 $7.9 \times 10^{- 2}$

Ans.
(2)

$Δ G ° = - 2.303 R T \log K_{s p}$

$63.3 \times 10^{3} J = - 2.303 \times 8.314 \times 298 \log K_{s p}$

$63.3 \times 10^{3} J = - 5705.84 \log K_{s p}$

$\log K_{s p} = - \frac{63.3 \times 10^{3}}{5705.84} = - 11.09$

$K_{s p} = antilog (- 11.09) = 8.128 \times 10^{- 12}$

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