Question

If the solubility of calcium phosphate (molecular weight $=M$) in water at ${25}^{o}C$ is $wg/100mL$, its solubility product at ${25}^{o}C$ is

• A. ${10}^9{\left(\frac{w}{M}\right)}^5$
• B. ${10}^7{\left(\frac{w}{M}\right)}^5$
• C. ${10}^5{\left(\frac{w}{M}\right)}^5$
• D. ${10}^3{\left(\frac{w}{M}\right)}^5$

Answer 1

The correct option is B ${10}^7{\left(\frac{w}{M}\right)}^5$

Solubility $S=wg/100mL=10wg/1000mL=10wg/1L$
Solubility $S=\frac{10w}{M}mol/L$
Calcium phosphate is $C{a}_3(P{O}_4{)}_2$
$\left[C{a}^{2+}\right]=3\left[C{a}_3\right(P{O}_4{)}_2]=3S$

$\left[P{O}_4^{3-}\right]=2C{a}_3(P{O}_4{)}_2=2S$
The solubility product, $K_{sp}=\left[C{a}^{2+}{]}^3\right[P{O}_4^{3-}{]}^2$

$K_{sp}=\left(3S{)}^3\right(2S{)}^2$

$K_{sp}=108S^5$
$K_{sp}=108(\frac{10w}{M}{)}^5$ [Note: $108\approx {10}^2$]

$K_{sp}={10}^7{\left(\frac{w}{M}\right)}^5$