A solution of a monoprotic weak acid has acidity constant $K_{a}$ . The minimum initial concentration ‘c’ such that the concentration of the undissociated acid can be equated to ‘c’ within a $10 %$ limit of error, is y $K_{a}$ . What is the value of $\frac{y}{10}$ ?
(Report the value to nearest integer)

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answer is 9.

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Detailed Solution

$H A (a q) ⇌ H^{+} (a q) + A^{-} (a q)$
Initially c 0 0
At equilib. $c (1 - α) c α c α$

$K_{a} = \frac{{(c α)}^{2}}{c (1 - α)} = \frac{{(0.1 c)}^{2}}{0.9 c} = \frac{0.01 c}{0.9} K_{a} = \frac{0.1 c}{9}; c = \frac{9 K_{a}}{0.1} = 90 K_{a}$

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