Question

In a saturated solution of calcium phosphate, the concentration of $PO _4^{-3}$ ions is $3.3 \times 10^{-7}$. The $K_{s p}$ of $Ca _3\left( PO _4\right)_2$ will be

• A. $1.32 \times 10^{-31}$
• B. $1.32 \times 10^{-32}$
• C. $1.32 \times 10^{-33}$
• D. $1.32 \times 10^{-33}$.

Answer 1

Answer: (B)

$\left[ PO _4^{-3}\right]=3.3 \times 10^{-7} M$
$\left[ Ca ^{2+}\right]=\frac{3}{2} \times\left[ PO _4^{-3}\right]=\frac{3}{2} \times 3.3 \times 10^{-7}=5 \times 10^{-7} M$
$K_{s p} Ca _3\left( PO _4\right)_2=\left[ Ca ^{2+}\right]^3\left[ PO _4^{-3}\right]^2$
$\Rightarrow\left(5 \times 10^{-7}\right)^3\left(3.3 \times 10^{-7}\right)^2=1.32 \times 10^{-32}$