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$The pH of a 0.1 M solution of a weak acid HA is 3 . What is the dissociation constant K_{a} of the acid?$

A. $1 \times 1 0^{- 3}$
B. $1 \times 1 0^{- 4}$
C. $1 \times 1 0^{- 5}$
D. $1 \times 1 0^{- 6}$

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Correct answer: C — $1 \times 1 0^{- 5}$

Solution

$Given pH = 3, the concentration of hydrogen ions is [H^{+}] = 1 0^{- pH} = 1 0^{- 3} M .$
$For a weak acid, [H^{+}] = K_{a} \cdot C .$
$Substitute the values: 1 0^{- 3} = K_{a} \cdot 0.1 .$
$Square both sides: 1 0^{- 6} = K_{a} \cdot 0.1 .$
$Solve for K_{a} : K_{a} = \frac{1 0 ^{- 6}}{0.1} = 1 0^{- 5} .$
$Hence the answer is (C).$

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The pH of a 0.1 M solution of a weak acid HA is 3. What is the dissociation constant Ka​ of the acid?

Solution

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$The pH of a 0.1 M solution of a weak acid HA is 3 . What is the dissociation constant K_{a} of the acid?$