To find $-\left[H^{+}\right]=$?

$\quad\quad\quad\quad HA \rightleftharpoons H ^{+}+ A ^{-}$

$t=0 \quad\quad c \quad\quad\quad0\quad \quad 0$

$t=t_1 \quad c-x \quad\quad x \quad\quad x$

For very weak acid $\Rightarrow x\,<<<,1$

$K_a =\frac{\left[H^{+}\right]\left[A^{-}\right]}{[H A]}$

$=\frac{x \times x}{c-x}$

where,$K_a =\text { Dissociation censtent }$

$c =[H A]$

$x =H^{+} \text {concentration }$

As $\quad x\,<<<\,1$ so $c-x \approx c$

$\therefore k_a =\frac{x^2}{c}$

$\Rightarrow x=\sqrt{k_a C}$