Question

If solubility product of Zr₃(PO₄)₄ is denoted by K_sp and its molar solubility is denoted by S, then which of the following relation between S and K_sp is correct?
1. \({\rm{S}} = {\left( {\frac{{{{\rm{K}}_{{\rm{sp}}}}}}{{144}}} \right)^{1/6}}\)
2. \({\rm{S}} = {\left( {\frac{{{{\rm{K}}_{{\rm{sp}}}}}}{{6912}}} \right)^{1/7}}\)
3. \({\rm{S}} = {\left( {\frac{{{{\rm{K}}_{{\rm{sp}}}}}}{{929}}} \right)^{1/9}}\)
4. \({\rm{S}} = {\left( {\frac{{{{\rm{K}}_{{\rm{sp}}}}}}{{216}}} \right)^{1/7}}\)

Answer 1

Correct Answer - Option 2 : \({\rm{S}} = {\left( {\frac{{{{\rm{K}}_{{\rm{sp}}}}}}{{6912}}} \right)^{1/7}}\)

Concept:

The oxidation of Zr₃(PO₄)₄is given as:

\({\rm{Z}}{{\rm{r}}_3}{\left( {{\rm{P}}{{\rm{O}}_4}} \right)_4}⇌3{\rm{Z}}{{\rm{r}}^{4 + }} + 4{\rm{PO}}_4^{3 - }\)

                         3S       4S

The solubility of Zr₃(PO₄)₄

\({{\rm{K}}_{{\rm{sp}}}} = {\left[ {3{\rm{Z}}{{\rm{r}}^{4 + }}} \right]^3}{\left[ {4{\rm{PO}}_4^{3 - }} \right]^4}\)

Calculation:

⇒ K_sp = [3S]³ [4S]⁴

⇒ K_sp = 27S³ × 256S⁴

⇒ K_sp = 6912S⁷

\(\Rightarrow {{\rm{S}}^7} = \frac{{{{\rm{K}}_{{\rm{sp}}}}}}{{6912}}\)

\(\therefore {\rm{S}} = {\left( {\frac{{{{\rm{K}}_{{\rm{sp}}}}}}{{6912}}} \right)^{1/7}}\)