$Ni(OH{)}_2$ is a sparingly soluble solid with $K_{ep}=1\mathrm{.}6{10}^{-16}.$

$Ni(OH{)}_2(s)-N{i}^{2+}(aq)+2O{H}^{-}(aq),K_{xp}=1\mathrm{.}6{10}^{-16}$

$N{i}^{2+}$ ions form a complex with $N{H}_3$ with $K_f=4\mathrm{.}1{10}^8$ according to the following equation:

$N{i}^{2+}(aq)+6N{H}_3(aq)=[Ni(N{H}_3{)}_6^{2+}](aq),K_f=4\mathrm{.}1{10}^8$

a$.$ Calculate the molar solubility of $Ni(OH{)}_2$ in pure water.

b$.$ Write the equilibrium constant expression for the formation of $Ni(N{H}_3{)}_6^{2+}.$

c$.$ Calculate the molar solubility of $Ni(OH{)}_2$ in $1\mathrm{.}0MN{H}_3.$ You may ignore any equilibrium

other than the two mentioned above.