1 \({\rm{s}} = {\left( {{{\rm{K}}_{{\rm{sp }}}}} \right)^{1/3}}\)
2 \({\rm{s}} = {\left( {{{\rm{K}}_{{\rm{sp}}}}/2} \right)^{1/3}}\)
3 \({\rm{s}} = {\left( {{{\rm{K}}_{{\rm{sp}}}}/4} \right)^{1/3}}\)
4 \({\rm{s}} = {\left( {{{\rm{K}}_{{\rm{sp}}}}/2} \right)^{1/2}}\)
Explanation:
It is ternary electrolyte,
\(\mathrm{CaF}_{2} \rightleftharpoons \mathrm{Ca}^{2+}+2 \mathrm{~F}^{-}\)
Let solubility of \(\mathrm{CaF}_{2}\) be \(\mathrm{s\,mol\,L}^{-1}\), then
\({{\text{Ca}}{{\text{F}}_{\text{2}}} \rightleftharpoons {{\mathop {{\text{Ca}}}\limits_{\text{S}} }^{{\text{2 + }}}} + \mathop {{\text{2F}}_2^ - }\limits_{2{\text{S}}} }\)
\({{\rm{Let }}\,{{\rm{K}}_{{\rm{sp}}}} = \left[ {{\rm{C}}{{\rm{a}}^{2 + }}} \right]{{\left[ {{{\rm{F}}^ - }} \right]}^2}}\)
\({\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = ({\rm{S}}) \times {{({\rm{2S}})}^2} = 4{{\rm{S}}^3}}\)
\({{\rm{S}} = \sqrt[3]{{\frac{{{{\rm{K}}_{{\rm{sp}}}}}}{4}}}}\)