Determine the number of moles of AgI which may be dissolved in 1.0 M CN^(-) solution. K_(sp) for AgI and K_(c)for Ag(CN)_(2)^(-) are 1.2xx10^(-7) M^(2) and 7.1xx10^(19) M^(-2) respectively.

Determine the number of moles of AgI which may be dissolved in 1.0 M C

1.	Determine the number of moles of AgI which may be dissolved in 1.0 M CN^(-) solution. K_(sp) for AgI and K_(c)for Ag(CN)_(2)^(-) are 1.2xx10^(-7) M^(2) and 7.1xx10^(19) M^(-2) respectively.
Answer» Solution :Suppose number of moles of AGI which may be dissolved in 1.0 litre of 1.0 M `CN^(-)` solution = x. Then `{:(,AgI (s) ,+ ,2CN^(-) (AQ) ,HARR,[Ag(CN)_(2)]^(-),+,I^(-)),("Initial moles " ,x,,1,," "0,,0),("Moles after reaction",0,,1-2x,," "x,,x),(,,,,,,,),(,,,,,,,):}` `K_(eq)=([Ag(CN)_(2)]^(-)[I^(-)])/([CN^(-1)]^(2))=(x^(2))/((1-2x)^(2))`...(i) Further,`AgI (s) hArr Ag^(+) (aq) + (Aq) + I^(-) (aq)` `K_(sp) = [Ag^(+)][I^(-)] = 1.2xx10^(-17) ` (Given)...(ii) `Ag^(+) (aq) + 2 (CN^(-) (aq)) hArr [Ag(CN)_(2)]^(-)` `K_(c)=([Ag(CN)_(2)]^(-))/([Ag^(+) ] [ CN^(-) ] ^(2) ) = 7.1xx10^(19) ` (Given) From eqn. (i) , (ii) and (iii) `K_(eq)=K_(sp)xxK_(c)=(1.2xx10^(-17))xx(7.1xx10^(19))= 8.52xx10^(2)` `:. (x^(2))/((1-2x)^(2)) = 8. 52xx10^(2) or (x)/(1-2x) = 29.2 or x = 29.2- 58.4x or x = 0.49 ` mole