GATE 2026 ES – Question 51
For $SO_2(aq)\rightleftharpoons H^++HSO_3^-$ and $HSO_3^-\rightleftharpoons H^++SO_3^{2-}$,the ideal equilibrium constants are $K_{S1}=1.3\times10^{-2}$ M and $K_{S2}=6.6\times10^{-8}$ M. At pH 4.0 and $[SO_2(aq)]=1.0$ M, find $[SO_3^{2-}]$ in mM, to one decimal place.
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Correct answer: 80 to 90
Explanation
At pH 4,$[H^+]=10^{-4}$ M. Multiplying the two equilibrium relations eliminates bisulfite: $$K_{S1}K_{S2}=\frac{[H^+]^2[SO_3^{2-}]}{[SO_2(aq)]}.$$ Thus $[SO_3^{2-}]=(1.3\times10^{-2})(6.6\times10^{-8})(1)/(10^{-4})^2=.0858$ M. Multiply by 1000 to obtain **85.8 mM**. The calculation uses the ideal equilibrium assumptions explicitly given.