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Concentration Terms - An Introduction (w/w etc)

Given that E0...

Question

Given that $E_{C l_{2} / C l^{-}}^{0} = 1.35 V$ and $K_{s p} (A g C l) = 10^{- 10}$ at $25^{o} C$ .

$E^{0}$ corresponding to the electrode reaction is
$\frac{1}{2} C l_{2} (g) + A g^{+} (a q) + e^{-} \to A g C l (s)$ is

A

0.75 V

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B

1.05 V

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C

2.65 V

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D

1.94 V

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Solution

The correct option is D $1.94 V$
For sparingly soluble $A g C l$
$A g C l (s) \to A g^{+} (a q) + C l^{-} (a q) . . . (e q 1)$
$K_{s p} (A g C l) = 10^{- 10}$
$Δ G_{1} = - R T ln K_{s p}$
For :
$\frac{1}{2} C l_{2} (g) + e^{-} \to C l^{-} (a q) . . . . . . (e q 2); E_{2}^{0} = 1.35 V$
$Δ G_{2} = - n F E_{2}^{0}$
Reversing eqn 1 and adding with equation 2, we get the desired equation
$\frac{1}{2} C l_{2} (g) + A g^{+} (a q) + e^{-} \to A g C l (s) . . . (e q 3)$
$Δ G_{3} = - n F E_{3}^{0} = Δ G_{2} - Δ G_{1}$
$- n F E_{3}^{0} = - n F E_{2}^{0} - (- R T ln K_{s p})$
$E_{3}^{0} = E_{2}^{0} - \frac{R T}{F} ln 10^{- 10} E_{3}^{0} = 1.35 + (0.059 \times 10) = 1.94 V$

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Concentration Terms - An Introduction (w/w etc)

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