Calculate the e.m.f. (in V) of the cell:
$P t | H_{2} (g) | B O H (a q) | | H A (a q) | H_{2} (g) | P t; (0.1 b a r; 1 M; 0.1 M; 1 b a r$
Given: $K_{a} (H A) = 10^{- 7}, K_{b} (B O H) = 10^{- 5}$

0.43 V

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0.36 V

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0.93 V

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None of these

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Solution

The correct option is A $0.43 V$
$E = E^{0} - 2.303 R T l o g Q / n F$
$E = 0 - 2.303 R T / 2 F l o g [p_{H_{2}} \times [H^{+}]^{2} / p_{H_{2}} \times [H^{+}]^{2}] = (- 0.066 / 2) \times l o g (1 \times 10^{- 23} / 0.1 \times 10^{- 6} = - 0.033 l o g (10^{- 16})$
$= 0.43 V o l t$
( $[H^{+}] = 10^{- 14} / [O H^{-}]$ )

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