A solution is 0.30 M in HCl and is saturated with H2S ([H2S] = 0.10 M; overall K = [H+]^2[S^2-]/[H2S] = 1.0x10^-21). It contains cadmium(II) and K_sp(CdS) = 8.0x10^-27. Taking [H+] equal to the HCl concentration, find the equilibrium [Cd^2+] left in solution after CdS precipitation, in units of 10^-6 M, to two decimals.

JEE Advanced levelNumerical answerDifficulty 3 of 3qc180

A solution is $0.30 M$ in HCl and is saturated with $H X_{2} S$ ( $[H X_{2} S] = 0.10 M$ ; overall $K = [H X^{+}]^{2} [S X^{2 -}] / [H X_{2} S] = 1.0 \times 1 0^{- 21}$ ). It contains cadmium(II) and $K_{s p} (CdS) = 8.0 \times 1 0^{- 27}$ . Taking $[H X^{+}]$ equal to the HCl concentration, find the equilibrium $[Cd X^{2 +}]$ left in solution after CdS precipitation, in units of $1 0^{- 6} M$ , to two decimals.

Numerical answer type, answer in x 10^-6 M, tolerance 0.01.

[S X^{2 -}] = 1.0 \times 1 0^{- 21} \times 0.10/ (0.30)^{2} = 1.11 \times 1 0^{- 21} M

. Then

[Cd X^{2 +}] = K_{s p} / [S X^{2 -}] = 8.0 \times 1 0^{- 27} /1.11 \times 1 0^{- 21} = 7.20 \times 1 0^{- 6} M

. Answer 7.20.