$(1)$ Silver chromate:

$Ag _{2} CrO _{4} \longrightarrow 2 Ag ^{+}+ CrO _{4}^{2-}$

Then,

${K_{sp}} = {\left[ {A{g^ + }} \right]^2}\left[ {CrO_4^{2 – }} \right]$

Let the solubility of $Ag _{2} CrO _{4}$ bes.

$\Rightarrow\left[ Ag ^{+}\right] 2 s$ and $\left[ CrO _{4}^{2-}\right]=s$

Then

$K_{s p}=(2 s)^{2} s=4 s^{3}$

$\Rightarrow 1.1 \times 10^{-12}=4 s^{3}$

$.275 \times 10^{-12}=s^{3}$

$s=0.65 \times 10^{-4} \,M$

Molarity of $Ag ^{+}$  $=2 s=2 \times 0.65 \times 10^{-4}=1.30 \times 10^{-4}\, M$

Molarity of $CrO _{4}^{2-}$ $=s=0.65 \times 10^{-4} \,M$

$(2)$ Barium chromate:

$BaCrO _{4} \longrightarrow Ba ^{2+}+ CrO _{4}^{2-}$

Then, $K_{s p}=\left[ Ba ^{2+}\right]\left[ CrO _{4}^{2-}\right]$

Let the solubility of $BaCrO _{4}$. be s.

So , $\quad\left[ Ba ^{2+}\right]= s$ and  $\left[ CrO _{4}^{2-}\right]= s$

$\Rightarrow K_{S P}=s^{2}$

$\Rightarrow 1.2 \times 10^{-10}=s^{2}$

$\Rightarrow s=1.09 \times 10^{-5}\, M$

Molarity of $\quad Ba ^{2+}=$ Molarity of $CrO _{4}^{2-}=s=1.09 \times 10^{-5} \,M$

$(3)$ Ferric hydroxide:

$Fe ( OH )_{3} \longrightarrow Fe ^{2+}+3 OH$

$K_{s p}=\left[ Fe ^{2+}\right]\left[ OH ^{-}\right]^{3}$

Let s be the solubility of $\operatorname{Fe}( OH )_{3}$

Thus, $\left[ Fe ^{3+}\right]=s$ and $\left[ OH ^{-}\right]=3 s$

$\Rightarrow K_{s p}=s \cdot(3 s)^{3}$

$\quad=s .27 s^{3}$

$K_{s p}=27 s^{4}$

$1.0 \times 10^{-38}=27 s^{4}$

$.037 \times 10^{-38}=s^{4}$

$.00037 \times 10^{-36}=s^{4}$   $\Rightarrow 1.39 \times 10^{-10} \,M = S$

Molarity of $Fe ^{3+}=s=1.39 \times 10^{-10} \,M$

Molarity of $OH ^{-}=3 s=4.17 \times 10^{-10} \,M$

$(4)$ Lead chloride:

$PbCl _{2} \longrightarrow Pb ^{2+}+2 Cl ^{-}$

$K_{S P}=\left[P b^{2+}\right]\left[C l^{-}\right]^{2}$

Let $K_{S P}$ be the solubility of $PbCl _{2}$

$\left[ PB ^{2+}\right]=s$ and $\left[ Cl ^{-}\right]=2 s$

Thus, $K_{x p}=s .(2 s)^{2}$

$=4 s$

$\Rightarrow 1.6 \times 10^{-5}=4 s^{3}$

$\Rightarrow 0.4 \times 10^{-5}=s^{3}$

$4 \times 10^{-6}=s^{3} \Rightarrow 1.58 \times 10^{-2} \,M = S .1$

Molarity of $P B^{2+}=s=1.58 \times 10^{-2} \,M$

Molarity of chloride $=2 s=3.16 \times 10^{-2}\, M$

$(5)$ Mercurous iodide:

$Hg _{2} I _{2} \longrightarrow Hg ^{2+}+2 I ^{-}$

$K_{s p}=\left[ Hg _{2}^{2+}\right]^{2}\left[ I ^{-}\right]^{2}$

Let s be the solubility of $Hg _{2} I _{2}$

$\Rightarrow\left[ Hg _{2}^{2+}\right]=s$ and $\left[ I ^{-}\right]=2 s$

Thus, ${K_{sp}} = s{(2s)^2} \Rightarrow {K_{sq}} = 4{s^3}$

$4.5 \times 10^{-29}=4 s^{3}$

$1.125 \times 10^{-29}=s^{3}$

$\Rightarrow s=2.24 \times 10^{-10} \,M$

Molarity of $Hg _{2}^{2+}=s=2.24 \times 10^{-10}\, M$

Molarity of $I^{-}=2 s=4.48 \times 10^{-10} \,M$