Question

Solid $BaC{O}_3$ is gradually dissolved in a $1.0\times {10}^{-4}MN{a}_{2}C{O}_3$ solution. At what concentration of $B{a}^{2+}$, will a precipitate form? $(K_{sp}$ for $BaC{O}_3=5.1\times {10}^{-9})$

• A. $4.1\times {10}^{-5}M$
• B. $5.1\times {10}^{-5}M$
• C. $8.1\times {10}^{-8}M$
• D. $8.1\times {10}^{-7}M$

Answer 1

The correct option is B $5.1\times {10}^{-5}M$

$N{a}_{2}C{O}_3\to 2N{a}^{+}+C{O}_3^{2-}$

$\left[C{O}_3^{2-}\right]=1\times {10}^{-4}M$

$BaC{O}_3\to B{a}^{2+}+C{O}_3^{2-}$

$K_{sp}=\left[B{a}^{2+}\right]\left[C{O}_3^{2-}\right]$

$5.1\times {10}^{-9}=\left[B{a}^{2+}\right][1\times {10}^{-4}]$

$[B{a}^{2+}]=\frac{5.1\times {10}^{-9}}{1\times {10}^{-4}}$$=5.1\times {10}^{-5}M$