A solution is saturated with both AgCl (K_sp = 1.6x10^-10) and AgBr (K_sp = 5.0x10^-13) in pure water. Find [Ag+] in units of 10^-5 M (two decimals).

JEE Main levelNumerical answerDifficulty 2 of 3ia184

A solution is saturated with both $AgCl$ ( $K_{s p} = 1.6 \times 1 0^{- 10}$ ) and $AgBr$ ( $K_{s p} = 5.0 \times 1 0^{- 13}$ ) in pure water. Find $[Ag X^{+}]$ in units of $1 0^{- 5} M$ (two decimals).

Numerical answer type, answer in x 10^-5 M, tolerance 0.01.

Charge balance:

[Ag X^{+}] = [Cl X^{-}] + [Br X^{-}] = (K_{1} + K_{2}) / [Ag X^{+}]

. So

[Ag X^{+}]^{2} = 1.6 \times 1 0^{- 10} + 5.0 \times 1 0^{- 13} = 1.605 \times 1 0^{- 10}

, giving

[Ag X^{+}] = 1.27 \times 1 0^{- 5} M