The hydrogen ion concentration in a weak acid | vedclass

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Question

(A) For a weak acid $HA$ dissociating as $HA \rightleftharpoons H^{+} + A^{-}$,the dissociation constant is given by $K_a = \frac{[H^{+}][A^{-}]}{[HA]

Vedclass · Accepted Answer

$\sqrt{K_a c}$

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(A) For a weak acid $HA$ dissociating as $HA ightleftharpoons H^{+} + A^{-}$,the dissociation constant is given by $K_a = \frac{[H^{+}][A^{-}]}{[HA]}$.Let the initial concentration be $c$ and the degree of dissociation be $\alpha$.Then $[H^{+}] = c\alpha$,$[A^{-}] = c\alpha$,and $[HA] = c(1-\alpha)$.$K_a = \frac{(c\alpha)(c\alpha)}{c(1-\alpha)} = \frac{c\alpha^2}{1-\alpha}$.Since the acid is weak,$\alpha Thus,$K_a \approx c\alpha^2$,which gives $\alpha = \sqrt{K_a/c}$.Therefore,$[H^{+}] = c\alpha = c 	imes \sqrt{K_a/c} = \sqrt{K_a c}$.

The hydrogen ion concentration in a weak acid of dissociation constant $K_a$ and concentration $c$ is nearly equal to:

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