Question

$CaC{O}_3$ and $BaC{O}_3$ have solubility product values $1\times {10}^{-8}and5\times {10}^{-9}$, respectively. If water is shaken up with both solids till equilibrium is reached, the concentration of $C{O}_3^{2-}$ ion is:

• A. $1.5\times {10}^{-8}$
• B. $1.225\times {10}^{-4}$
• C. $2.25\times {10}^{-9}$
• D. None of these

Answer 1

The correct option is B $1.225\times {10}^{-4}$

Both the carbonates will dissociate in water. Let the concentration of ions be x and y respectively
$CaC{O}_3\to C{a}^{2+}+C{O}_3^{2-}$
x x+y
$K_{sp}=x(x+y)={10}^{-8}$...(1)
$BaC{O}_3\to B{a}^{2+}+C{O}_3^{2-}$
y x+y
Total concentration of $C{O}_3^{2-}$ = x + y
$K_{sp}=y(x+y)=5\times {10}^{-9}$...(2)
divide eq. 1 by eq 2
$\frac{x}{y}=2$ ; x =2y
Substituting:
$2y(2y+y)={10}^{-8}$ y = $0.4083\times {10}^{-4}$
and concentration of carbonate ion =
x + y = $1.225\times {10}^{-4}$