Two hydrogen-hydrogen ion half cells are connected to make a single voltaic cell. In one of that half cells, the pH is 1.0, but the pH of the other half cell is not known. The measured voltage delivered by the combination is 0.16 V, and the electrode in the half cell of known concentration is positive. Is the unknown concentration of H greater or less than 0.1 M? The unknown concentration of $H^{\oplus}$ ions is $1.9 \times 10^{- x} M$ .
Value of x is ______.

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Solution

$E_{c e l l} = 0.16 V; [R H E] = 10^{- 1} M, [L H E] = ?$
$0.16 = 0 - \frac{0.059}{1} l o g \frac{[H^{\oplus}]}{10^{- 1}}$
$\Rightarrow - \frac{0.16}{0.059} = 1 + l o g [H^{\oplus}]$
$\Rightarrow l o g [H^{\oplus}] = - \frac{0.16}{0.059} - 1 = - 3.70 = ¯ 4 .3$
$\Rightarrow [H^{\oplus}] < 0.1 M$ and $[H^{\oplus}] = 1.9 \times 10^{- 4} M$

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