The values of K_(sp) of two sparingly soluble salts NI(OH)_2 and AgCN are 2.0xx10^(-15)and 6xx10^(-17) respectively . Which salt is more soluble ? Explain .

The values of K_(sp) of two sparingly soluble salts NI(OH)_2 and AgCN

1.	The values of K_(sp) of two sparingly soluble salts NI(OH)_2 and AgCN are 2.0xx10^(-15)and 6xx10^(-17) respectively . Which salt is more soluble ? Explain .
Answer» Solution :Value of `K_(sp)` is more than solubility is more according to this , Solubility of `Ni(OH)_2 gt` solubility of AGCN. Suppose , solubility of `Ni(OH)_2=S_1` solubility of AgCN = `S_2` CALCULATION of solubility `S_1` of `Ni(OH)_2` : EQUILIBRIUM in concentrated solution of `Ni(OH)_2` . `{:(Ni(OH)_(2(s)) hArr , Ni_((aq))^(2+) + , 2OH_((aq))^(-)),("Molarity in solution:", S_1,2S_1):}` `therefore K_(sp) [Ni(OH)_2] = [Ni^(2+)] [OH^-]^2` `=(S_1)(2S_1)^2` `=(4S_1)^3=2.0xx10^(-15)` `therefore S=(2.0/4.0 xx 10^(-15) )^(1/3)= (0.5 xx 10^(-15) )^(1/3)` `= 0.7937 xx 10^(-5) "mol L"^(-1)` `=7.937xx10^(-6)` The calculation of solubility of `S_2` in AgCN : `{:(AgCN_((s)) hArr , Ag_((aq))^(+) +, CN_((aq))^(-)),("Molar concentration", S_2,S_2):}` `therefore K_(sp)=[Ag^+][CN^-]` `=(S_2)(S_2)=S^2 =6xx10^(-17) = 60XX10^(-18)` `therefore S_2=sqrt(60xx10^(-18))=7.745xx10^(-8)` Thus solubility of `Ni(OH)_2` is `S_1= 7.937xx10^(-6)` solubility of AgCN is `S_2= 7.745xx10^(-8)` The solubility of `Ni(OH)_2` is more and the solubility of AgCN is less than it.