0.010 M AgNO3 is dissolved in 1.0 M aqueous NH3 (both are final concentrations before complexation; no volume change). Assume essentially all Ag+ becomes [Ag(NH3)2]+ (K_f = 1.6x10^7). Use the free ammonia concentration remaining after complexation (not 1.0 M). Find [Ag+] at equilibrium in units of 10^-10 M (two decimals).

JEE Advanced levelNumerical answerDifficulty 3 of 3ia208

$0.010 M$ $AgNO X_{3}$ is dissolved in $1.0 M$ aqueous $NH X_{3}$ (both are final concentrations before complexation; no volume change). Assume essentially all $Ag X^{+}$ becomes $[Ag (NH X_{3}) X_{2}] X^{+}$ ( $K_{f} = 1.6 \times 1 0^{7}$ ). Use the free ammonia concentration remaining after complexation (not $1.0 M$ ). Find $[Ag X^{+}]$ at equilibrium in units of $1 0^{- 10} M$ (two decimals).

Numerical answer type, answer in x 10^-10 M, tolerance 0.02.

Complex

\approx 0.010 M

uses

0.020 M

NH X_{3}

, leaving

[NH X_{3}] = 0.98 M

[Ag X^{+}] = [complex] / (K_{f} [NH X_{3}]^{2}) = 0.010/ (1.6 \times 1 0^{7} \times 0.9 8^{2}) = 6.51 \times 1 0^{- 10} M