Question

The values of $K_{sp}$ of $Ca{CO}_3$ and $Ca{C}_2{O}_4$ are $4.7\times {10}^{-9}$ and $1.3\times {10}^{-9}$ respectively at ${25}^{o}C$. If the mixture of these two is washed with water, what is the concentration of ${Ca}^{2+}$ ions in water?

• A. $5.831\times {10}^{-5}M$
• B. $6.856\times {10}^{-5}M$
• C. $3.606\times {10}^{-5}M$
• D. $7.77\times {10}^{-5}M$

Answer 1

Answer: (D)

$7.77\times {10}^{-5}M$

$CaC{O}_3⟺C{a}^{+2}+C{O}_3^{-2}aaCa{C}_2{O}_4⟺C{a}^{+2}+C_2{O}_4^{-2}bb(a+b)a=4.7\times 10^{-9}(a+b)b=1.3\times {10}^{-9}\frac{a}{b}=3.62a=3.62b(a+b)a=4.7\times 10^{-9}(3.62b+b)\times 3.62b=4.7\times 10^{-9}b=1.673\times 10^{-5}(a+b)b=1.3\times {10}^{-9}a+b=\frac{1.3\times {10}^{-9}}{1.673\times 10^{-5}}=7.77\times {10}^{-5}$