Auto-ionization of $\mathrm{liq}{\mathrm{NH}}_3$  is $2{\mathrm{NH}}_3\rightleftharpoons {\mathrm{NH}}_4^{+}+{\mathrm{NH}}_2^{-}$  with ${\mathrm{K}}_{{\mathrm{NH}}_3}=\left({\mathrm{NH}}_4^{+}\right)\left({\mathrm{NH}}_2^{-}\right)={10}^{-30}$ $\mathrm{at}-{50}^0\mathrm{C}$  Number of amine ions $\left({\mathrm{NH}}_2^{-}\right)$  present per ${\mathrm{mm}}^3$ of pure liquid ${\mathrm{NH}}_3$ is

(A)  $2N{H}_3\rightleftharpoons N{H}_4^{+}+N{H}_2^{-}$
 $\left[N{H}_4^{+}\right]=\left[N{H}_2^{-}\right]=\sqrt{K_{N{H}_3}}={10}^{-15}M$
$1d{m}^3$ of solution contain ${10}^{15}$ moles$=6.023\times {10}^{23}\times {10}^{-15}$  molecules of  $N{H}_2^{\Theta }$
$1m{m}^3$ of solution contain  $6.023\times {10}^{23}\times {10}^{-15}\times {10}^{-6}=602$