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Question

One liter of NH3 solution dissolves 0.10 mole of AgCl. Its concentration is: (Ksp of AgCl and Kf of [Ag(NH3)2]+ are 1010 and 1.6×107 respectively)

A
2.5 M
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B
2.7 M
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C
2.5×103 M
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D
6.25 M
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Solution

The correct option is B 2.7 M
To dissolve 0.1 mole of AgCl in 1 L, let conc of NH3 be C and when simultaneous equilibria will be established, conc of Cl will be 0.1 M and of complex will be also almost 0.1 M as Kf is large. Let conc Ag+ left over be x.
AgCl(s)Ksp=1010Ag+aq+Claq x 0.1
Ag+aq+2NH3Kf=1.6×107[Ag(NH3)2]+
x C0.1×2 0.1

So, Ksp=1010=x×0.1x=109 M
And Kf=1.6×107=0.1x×(C0.1×2)2=0.1109×(C0.1×2)2
(C0.1×2)2=10.16C0.1×2=10.4C=2.7 M

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