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Types of Solutions Based on the Concentration of the Solution

Calculate the...

Question

Calculate the ${log}_{10} K_{s p}$ value for $C d S$ at $25^{o} C$
Given:
$C d^{2 +} (a q) + 2 e^{-} \to C d (s); E^{o} = - 0.403 V$
$C d S (s) + 2 e^{-} \to C d (s) + S^{2 -} (a q); E^{o} = - 1.21 V$

(here $K_{s p}$ is solubility product)

A

+ 13.65

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B

- 13.65

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C

+ 27.3

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D

- 27.3

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Solution

The correct option is D $- 27.3$
It is a metal-metal insoluble salt electrode.

Here,
$C d^{2 +} (a q) + 2 e^{-} \to C d (s) . . . . (1); E^{o} = - 0.403 V$
$C d S (s) + 2 e^{-} \to C d (s) + S^{2 -} (a q) . . . . . (2); E^{o} = - 1.21 V$

Reversing equation (2), we get,
$C d (s) + S^{2 -} (a q) \to C d S (s) + 2 e^{-} . . . . . . (3); E^{o} = 1.21 V$
Add equation (1) and (3)
$C d^{2 -} (a q) + S^{2 -} (a q) \to C d S (s) . . . . . (4); E^{0} = 0.807$

Reverse equation (4)
$\Rightarrow C d S (s) \to C d^{2 -} (a q) + S^{2 -} (a q) . . . . (5); E^{o} = - 0.807 V$

For equation (5), standard free energy will be (at equilibrium)
$Δ G^{0} = - R T l n K_{s p}$
Also,
$Δ G^{0} = - n F E^{0}$
$∴$
$- R T l n K_{s p} = - n F E^{0}$

$R T l n K_{s p} = n F E^{0}$

$E^{0} = \frac{2.303 \times R T}{n F} {log}_{10} K_{s p}$

$E^{0} = \frac{0.0592}{2} \times {log}_{10} K_{s p}$

${log}_{10} K_{s p} = \frac{- 0.807 \times 2}{0.0591} \approx - 27.3$

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Types of Solutions Based on the Concentration of the Solution

Standard VIII Chemistry

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