Find the solubility of AgBr in 0.10 M Na2S2O3 solution, using AgBr(s) + 2S2O3^2- leftharpoons [Ag(S2O3)2]^3- + Br- with K_sp(AgBr) = 5.0 x 10^-13 and K_f([Ag(S2O3)2]^3-) = 2.9 x 10^13. Give the answer in units of 10^-2 mol L^-1 (two decimals).

JEE Main levelNumerical answerDifficulty 2 of 3ia082

Find the solubility of $AgBr$ in $0.10 M$ $Na X_{2} S X_{2} O X_{3}$ solution, using $AgBr (s) + 2 S X_{2} O X_{3} X^{2 -} ⇌ [Ag (S X_{2} O X_{3}) X_{2}] X^{3 -} + Br X^{-}$ with $K_{s p} (AgBr) = 5.0 \times 1 0^{- 13}$ and $K_{f} ([Ag (S X_{2} O X_{3}) X_{2}] X^{3 -}) = 2.9 \times 1 0^{13}$ . Give the answer in units of $1 0^{- 2} mol L^{- 1}$ (two decimals).

Numerical answer type, answer in x 10^-2 mol/L, tolerance 0.01.

K = K_{s p} K_{f} = 14.5

. With

s = [Ag (S X_{2} O X_{3}) X_{2} X^{3 -}] = [Br X^{-}]

and

[S X_{2} O X_{3} X^{2 -}] = 0.10 - 2 s

s / (0.10 - 2 s) = K = 3.808

, so

s = 0.10 \times 3.808/ (1 + 2 \times 3.808) = 0.0442 M

, i.e. 4.42 in units of

1 0^{- 2} M