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Nernst Equation

The emf of th...

Question

The emf of the following cell is 0.7995 V.
$P t | H_{2} (1 a t m) | H N O_{3} (1 M) | | A g N O_{3} (1 M) | A g$
If we add enough $K C l$ to the $A g$ half cell so that the final $C l^{-}$ is 1M, then the measured emf of the cell is 0.222V. The $K_{s p}$ of AgCl would be :

1 \times 10^{- 9.8}

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1 \times 10^{- 19.6}

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2 \times 10^{- 10}

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2.64 \times 10^{- 14}

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Solution

The correct option is B $1 \times 10^{- 9.8}$
$2 A g^{+} + H_{2} ⇌ 2 H^{+} + 2 A g$
$E = E^{o} - \frac{0.0591}{2} l o g \frac{(H^{+})^{2}}{P_{H_{2}} \times (A g^{+})^{2}}$ ---- 1

Substitute $E = 0.222 V, E^{o} = 0.7995 V, P_{H_{2}} = 1 a t m$ and $[H^{+}] = 1 M$ to get,
$[A g^{+}] = 10^{- 9.8}$ from equation 1.
Now,

$K s p = [A g^{+}] [C l^{-}] = (10^{- 9.8}) \times (1) = 1 \times 10^{- 9.8}$

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Similar questions

P t | H_{2} (1 a t m) | N a O H (x M) | | N a C l (x M) | A g C l (s) | A g

E_{C l^{-} / A g C l / A g}^{0} = 0.222 V

Consider the cell : $A g_{(s)} | A g C l (saturated solution) | A g N O_{3 (a q)} 1.0 M | A g_{(s)}$

EMF of the above cell is given by:

(K_{s p}

A g C l

= 1.0 \times 10^{- 10} M^{2})

A g (s) | A g B r (x) | B r^{-} (a q) | | C l^{-} (a q) | A g C l (s) | A g (s)

^{o}

A g B r

A g C l

5 \times 10^{- 13}

1 \times 10^{- 10}

^{-}

^{-}

E_{c e l l} = 0.0860 V

[C l^{-}]

K_{s p}

A g C l

A g I

1.8 \times 10^{- 10}

8.5 \times 10^{- 17}

A g (s) | A g^{+} [S a t . A g I (a q)] | | A g^{+} (S a t . A g C l, M C l^{-}) | A g (s)

A g | A g B r (s) B r^{-} | | A g C l (s) C l^{-} | A g

25^{o}

1 \times 10^{- 10}

5 \times 10^{- 13}

B r^{-}

C l^{-}

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