The equilibrium constant for ionization constant of acetic acid in an aqueous solution of concentration ‘C’ is given by

We have

$C{H}_{3}COOH\rightleftharpoons C{H}_{3}CO{O}^{-}+H^{+}$

$c(1-\alpha )$                 $c\alpha$                  $c\alpha$

$K=\frac{\left[C{H}_{3}COO\left[H^{+}\right]\right]}{\left[C{H}_{3}COOH\right]}=\frac{c{\alpha }^2}{(1-\alpha )}$

since $\alpha ={\wedge }_c/{\wedge }_{\infty },wegetK=\frac{c{({\wedge }_c/{\wedge }^{\infty })}^2}{1-({\wedge }_c/{\wedge }_{\infty })}=\frac{c{\wedge }_c^2}{{\wedge }^{\infty }({\wedge }^{\infty }-{\wedge }_c)}$