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Derive the equation of following sparingly soluble salt :
$(i)$ Two ions having $MX$ formula
$(ii)$ Three ions having $M{X_2}$ or ${M_2}X$ types
$(iii)$ Four ions having $AX_{3}$ or ${A_3}X$ type salts.
$(iv)$ Five ions ${A_2}{X_3}$ or ${A_3}{X_2}$ type salts.
Solution
$(i)$ Examples of salts form by two ions and its $K_{s p}$ :
Example : $\mathrm{AgBr}, \mathrm{AgCl}, \mathrm{BaSO}_{4}, \mathrm{SrSO}_{4}, \mathrm{AlPO}_{4}, \mathrm{AgI}, \mathrm{CaCO}_{3}, \mathrm{CaC}_{2} \mathrm{O}_{4},$
$\mathrm{CaSO}_{4}, \mathrm{SrSO}_{4}, \mathrm{CdS}, \mathrm{CuS}, \mathrm{CuBr}$, $\mathrm{CuCO}_{3}, \mathrm{FeCO}_{3}, \mathrm{FeO}, \mathrm{CuO}, \mathrm{ZnS}, \mathrm{FeS}, \mathrm{HgSO}_{4}, \mathrm{HgS}, \mathrm{MgCO}_{3},$
$\mathrm{MnCO}_{3},\mathrm{MnS}, \mathrm{ZnCO}_{3}, \mathrm{NiS}, \mathrm{PbCO}_{3}$, $\mathrm{PbSO}_{4}$ etc. MX salts.
$(ii)$
Example of sperigly soluble salts form by three ions and $\mathrm{K}_{s p}$ :
$\mathrm{MX}_{2}$ type $: \mathrm{Mg}(\mathrm{OH})_{2}, \mathrm{BaF}_{2}, \mathrm{Ca}(\mathrm{OH})_{2}, \mathrm{Zn}(\mathrm{OH})_{2}, \mathrm{Sn}(\mathrm{OH})_{2}, \mathrm{Cd}(\mathrm{OH})_{2},$
$\mathrm{Fe}(\mathrm{OH})_{2}, \mathrm{MgF}_{2}, \mathrm{Ni}(\mathrm{OH})_{2}$,
$\mathrm{Pb}(\mathrm{OH})_{2}$
$\mathrm{M}_{2} \mathrm{X}$ type : $\mathrm{Ag}_{2} \mathrm{CO}_{3}, \mathrm{Ag}_{2} \mathrm{CrO}_{4}, \mathrm{Ag}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}, \mathrm{Ag}_{2} \mathrm{SO}_{4}, \mathrm{Hg}_{2} \mathrm{SO}_{4}, \mathrm{Hg}_{2} \mathrm{~S}$ etc. $\left.\begin{array}{lcc}\text { Equilibrium } \mathrm{MX}_{2 \text { (s) }} \square & \mathrm{M}_{\text {(aq) }}^{2+}+2 \mathrm{X}_{\text {(aq) }}^{-} \\ & \mathrm{SM} & 2 \mathrm{~S} \mathrm{M} \\ \text { Equilibrium } \mathrm{M}_{2} \mathrm{X}_{\text {(aq) }} \square & 2 \mathrm{M}_{\text {(aq) }}^{+}+\mathrm{X}_{\text {(aq) }}^{2-} \\ \mathrm{K}_{s p}=\text { (S) }(2 \mathrm{~S})^{2}=4 \mathrm{~S}^{3} & 2 \mathrm{~S} & \mathrm{~S}\end{array}\right\} \ldots$ $(Eq-ii)$
$(iii)$
Example of salts form by four ions and its $\mathrm{K}_{s p}$ :
$\mathrm{MX}_{3}: \mathrm{Cr}(\mathrm{OH})_{3}, \mathrm{Al}(\mathrm{OH})_{3}, \mathrm{Fe}(\mathrm{OH})_{3}, \mathrm{Bi}(\mathrm{OH})_{3}$
$\mathrm{M}_{3} \mathrm{X}: \mathrm{Ag}_{3} \mathrm{PO}_{4}, \mathrm{Hg}_{3} \mathrm{PO}_{4}$
$\left.\begin{array}{lcc}\mathrm{MX}_{3(\mathrm{~s})} \square & \begin{array}{c}\mathrm{M}_{(\mathrm{aq})}^{3+}+3 \mathrm{X}_{(\mathrm{aq})}^{-} \\ \mathrm{s} \mathrm{M}\end{array} \\ \mathrm{M}_{3} \mathrm{X}_{(\mathrm{s})} \square & \begin{array}{c}3 \mathrm{M}^{+}+\mathrm{X}_{(\mathrm{aq})}^{3-} \\ 3 \mathrm{~S}\end{array} \\ \mathrm{~K}_{s p}=(3 \mathrm{~S})^{3} & (\mathrm{~S})=27 \mathrm{~S}^{4}\end{array}\right\}$
$\ldots($ Eu.-$iii$)
$(iv)$ $\mathrm{M}_{2} \mathrm{X}_{3}: \mathrm{Bi}_{2} \mathrm{~S}_{3}, \mathrm{Cr}_{2} \mathrm{~S}_{3}, \mathrm{Fe}_{2} \mathrm{~S}_{3}$
$\mathrm{M}_{3} \mathrm{X}_{2}: \mathrm{Zn}_{3}\left(\mathrm{PO}_{4}\right)_{2}, \mathrm{Cd}_{3}\left(\mathrm{PO}_{4}\right)_{2}, \mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2}, \mathrm{Mn}_{3}\left(\mathrm{AsO}_{4}\right)_{2}$
$\mathrm{M}_{2} \mathrm{X}_{3(\mathrm{~s})} \square \quad 2 \mathrm{M}_{\text {(aq) }}^{3+}+3 \mathrm{X}_{\text {(aq) }}^{2-}$
$\quad 2 \mathrm{~S} \quad 3 \mathrm{~S}$
$\mathrm{M}_{3} \mathrm{X}_{2(\mathrm{~s})} \square \quad 3 \mathrm{M}_{\text {(qq) }}^{2+}+2 \mathrm{X}_{\text {(aq) }}^{3-}$
$\quad 3 \mathrm{~S}$
$\mathrm{~K}_{s p}=(3 \mathrm{~S})^{3}(2 \mathrm{~S})^{2}=108 \mathrm{~S}^{5}$