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  4. The hydrogen ion concentration in a solution of weak acid of dissociation constant Ka and concentration C is nearly equal to:

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Q. The hydrogen ion concentration in a solution of weak acid of dissociation constant $ K_{a} $ and concentration $C$ is nearly equal to:

Rajasthan PMTRajasthan PMT 2000Equilibrium

Solution:

$HA \rightleftharpoons H ^{+}+A^{-}$
$K_{a}=\frac{C^{2} x^{2}}{C(a-x)}$
$\frac{C_{2} x^{2}}{C} $
(For weak acid $\left.1-x \cong 1\right)$
$C \cdot K_{a}=C^{2} x^{2}=C x=\sqrt{K_{a} \cdot C}$
$\therefore \left[ H ^{+}\right]= C x=\sqrt{K_{a} \cdot C }$