$\mathrm{Ag}^{+}+\mathrm{NH}_{3} \rightleftharpoons[\mathrm{Ag}(\mathrm{NH}_{3})^{+}] ; \mathrm{k}_{1}=3.5 \times 10^{-3}$ $[\mathrm{Ag}(\mathrm{NH}_{3})]^{+}+\mathrm{NH}_{3} \rightleftharpoons[\mathrm{Ag}(\mathrm{NH}_{3})_{2}]^{+} ; \mathrm{k}_{2}=1.7 \times 10^{-3}$ then the formation constant of $[\mathrm{Ag}(\mathrm{NH}_{3})_{2}]^{+}$is

JEE Advanced · 2006 · 09 Apr 2006 · Coordination Compounds

Ag^{+} + NH_{3} ⇌ [Ag (NH_{3})^{+}]; k_{1} = 3.5 \times 1 0^{- 3}

[Ag (NH_{3})]^{+} + NH_{3} ⇌ [Ag (NH_{3})_{2}]^{+}; k_{2} = 1.7 \times 1 0^{- 3}

then the formation constant of

[Ag (NH_{3})_{2}]^{+}

Answer: (A)

The overall formation constant

β_{2}

for

[Ag (NH_{3})_{2}]^{+}

is the product of the stepwise formation constants:

β_{2} = k_{1} \times k_{2} = (3.5 \times 1 0^{- 3}) \times (1.7 \times 1 0^{- 3}) = 5.95 \times 1 0^{- 6} \approx 6.08 \times 1 0^{- 6}

JEE Advanced · 2006 · 09 Apr 2006 · Single correct option