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For a weak acid, the concentration of H⁺ ions is given by

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$\large \sqrt {{K_a}.C}$

$\sqrt {\frac{C}{{{K_a}}}}$

$\sqrt {\frac{{{K_a}}}{C}}$

$\frac{{{K_a}}}{C}$

answer is A.

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Detailed Solution

$C{H_3}COOH$ $\rightleftharpoons$ ${H^ + }$ $+$ $C{H_3}CO{O^ - }$

t=0	C₀	0	0
t=t_eq	C₀-C₀α	C₀α	C₀α

${K_a} = \frac{{\left ({C_0}\alpha \right ) \left ({C_0}\alpha \right )}}{{{C_0} - {C_0}\alpha }}$ $= \frac{{{C_0}{\alpha ^2}}}{{1 - \alpha }}$ $\rightarrow$ (1)

For a weak acid, 1 - α ~ 1

${C_0}\left( {{K_a}} \right) = {C_0}{\alpha ^2} \times {C_0}$

${C_0}\left( {{K_a}} \right) = {\left( {{C_0}\alpha } \right)^2}=[H^+]^2$

$[H^+]=\sqrt{K_aC_0}$

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