It has been found that the $pH$ of a $0.01 \ M$ solution of an organic acid is $4.15$. Calculate the concentration of the anion,the ionization constant of the acid and its $pK_a$.

Let the organic acid be $HA$.
$HA \longleftrightarrow H^{+} + A^{-}$
Concentration of $HA = 0.01 \ M$
$pH = 4.15$
$-\log [H^{+}] = 4.15$
$[H^{+}] = 10^{-4.15} = 7.08 \times 10^{-5} \ M$
Since $[H^{+}] = [A^{-}]$,the concentration of the anion $[A^{-}] = 7.08 \times 10^{-5} \ M$.
Now,$K_a = \frac{[H^{+}][A^{-}]}{[HA]} = \frac{(7.08 \times 10^{-5})^2}{0.01} = 5.01 \times 10^{-7}$.
$pK_a = -\log K_a = -\log (5.01 \times 10^{-7}) = 6.30$.