The hydrogen ion concentration in weak acid of dissociation constant Ka and concentration c is nearly equal to

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The hydrogen ion concentration in weak acid of dissociation constant $K_{a}$ and concentration c is nearly equal to

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$\sqrt{K_{a} / c}$

$C / K_{a}$

$K_{a} C$

$\sqrt{K_{a} c}$

answer is D.

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Detailed Solution

$HA ⇄ H_{3} O^{+} + A^{-}$

At equilibrium $C (1 - α)$ $C α$ $C α$

$[H_{3} O^{+}] = Cα and K_{a} = \frac{Cα \times Cα}{C (1 - α)} = {Cα}^{2} \Rightarrow α = \sqrt{\frac{K_{a}}{c}}$

$So [H_{3} O^{+}] = C \sqrt{\frac{K_{a}}{c}} = \sqrt{K_{a} c}$

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