Which of the following is most soluble?

${\mathrm{Bi}}_2{\mathrm{S}}_3({\mathrm{K}}_{\mathrm{Sp}}=1\times {10}^{-17})$

2S           3S

${\mathrm{K}}_{\mathrm{Sp}}={\left(2\mathrm{s}\right)}^2{\left(3\mathrm{s}\right)}^3=108 {\mathrm{S}}^5={10}^{-17}$

$\Rightarrow \mathrm{S}{\left(\frac{{10}^{-17}}{{10}^8}\right)}^{\frac{1}{5}}=9.25\times {10}^{-4}$

$\mathrm{MnS}\rightleftharpoons {\mathrm{Mn}}^{+}+{\mathrm{S}}^{-}$

S          S

${\mathrm{K}}_{\mathrm{Sp}}={\mathrm{S}}^2=7\times {10}^{-16}\Rightarrow \mathrm{S}=\sqrt{7\times {10}^{-16}}=2.64\times {10}^{-8}$

$\mathrm{CuS}\rightleftharpoons {\mathrm{Cu}}^{+}+{\mathrm{S}}^{-}$

${\mathrm{K}}_{\mathrm{Sp}}={\mathrm{S}}^2=8\times {10}^{-37}\Rightarrow \mathrm{S}=\sqrt{8\times {10}^{-37}}=0.894\times {10}^{18}$

$\mathrm{Ag}2\mathrm{S}\rightleftharpoons {\mathrm{Ag}}^{+}+{\mathrm{S}}^{-2}$

   2S      S   

${\mathrm{K}}_{\mathrm{Sp}}=4{\mathrm{S}}^3=6\times {10}^{-51}$

$\mathrm{s}=0.25\times {10}^{17}$

$\mathrm{Hence},{\mathrm{Bi}}_2{\mathrm{S}}_3$ is mostly soluble.