0.10 M aqueous ammonia (initial concentration) is shaken with excess AgCl. K_sp(AgCl) = 1.6x10^-10, K_f([Ag(NH3)2]^+) = 1.6x10^7. Allowing for the ammonia consumed in forming the complex, the solubility of AgCl is

JEE Advanced levelSingle correct optionDifficulty 3 of 3ia207

$0.10 M$ aqueous ammonia (initial concentration) is shaken with excess $AgCl$ . $K_{s p} (AgCl) = 1.6 \times 1 0^{- 10}$ , $K_{f} ([Ag (NH X_{3}) X_{2}]^{+}) = 1.6 \times 1 0^{7}$ . Allowing for the ammonia consumed in forming the complex, the solubility of $AgCl$ is

K = K_{s p} K_{f} = 2.56 \times 1 0^{- 3}

, so

K = 0.0506

. With

[NH X_{3}] = 0.10 - 2 s

s / (0.10 - 2 s) = 0.0506

, so

s = 0.10 \times 0.0506/ (1 + 2 \times 0.0506) = 4.59 \times 1 0^{- 3} M

. Ignoring the

2 s

correction gives

5.06 \times 1 0^{- 3}

, which is too high.