Question

The solubility of $B{a}_3(As{O}_4{)}_2$ (formula mass$=690$) is $6.9\times {10}^{-2}g/L$. What is the $K_{sp}$?

• A. $1.08\times {10}^{-11}$
• B. $1.08\times {10}^{-13}$
• C. $1.0\times {10}^{-15}$
• D. $6.0\times {10}^{-13}$

Answer 1

Answer: (A)

$1.08\times {10}^{-11}$

The reaction will be:

${Ba}_3(As{O}_4{)}_2\to {3Ba}^{2+}+2As{O}_4^{3-}$

The expression for $K_{SP}$for ${Ba}_3(As{O}_4{)}_2$is-

$K_{Sp}=\left[{Ba}^{2+}{]}^3\right[As{O}_4^{3-}{]}^2$

${Ba}^{2+}=3SAs{O}_4^{3-}=2S$

$K_{SP}=(3S{)}^3\times (2S{)}^2=27\times 4\times S^5=108S^5$

$S=\frac{6.9\times {10}^{-2}}{690}=1\times {10}^{-4}$

$K_{SP}=108\times (1\times {10}^{-4}{)}^5=108\times {10}^{-9}=1.08\times {10}^{-11}$