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Q. An aqueous solution contains $0.10 \, M \, H_2S$ and $0.20 \, M \, HCl$ . If the equilibrium constants for the formation of $HS^-$ from $H_2S$ is $1.0 \times 10^{-7}$ and that of $S^{2- }$ from $HS^-$ ions is $ 1.2 \times 10^{-13}$ then the concentration of $S^{2-}$ ions in aqueous solution is -

JEE MainJEE Main 2018Equilibrium

Solution:

In presence of external $H ^{+}$,

$H _{2} S \rightleftharpoons 2 H ^{+}+ S ^{2-}, K _{ a _{1}} \cdot K _{ a _{2}}= K _{ eq }$

$\therefore \,\,\, \frac{\left[ H ^{+}\right]^{2}\left[ S ^{2-}\right]}{\left[ H _{2} S \right]}=1 \times 10^{-7} \times 1.2 \times 10^{-13} $

$\frac{[0.2]^{2}\left[ S ^{2-}\right]}{[0.1]}=1.2 \times 10^{-20} $

${\left[ S ^{2-}\right]=3 \times 10^{-20}}$