Answer
(a) $1.1 \times 10^{-5}M$
(b) $1.1 \times 10^{-4}M$
(c) $1.6 \times 10^{-5}M$
Work Step by Step
(a)
1. Write the $K_{sp}$ expression:
$ Ba(CrO_4)(s) \lt -- \gt 1Ba^{2+}(aq) + 1Cr{O_4}^{2-}(aq)$
$1.2 \times 10^{-10} = [Ba^{2+}]^ 1[Cr{O_4}^{2-}]^ 1$
2. Considering a pure solution: $[Ba^{2+}] = 1x$ and $[Cr{O_4}^{2-}] = 1x$
$1.2 \times 10^{-10}= ( 1x)^ 1 \times ( 1x)^ 1$
$1.2 \times 10^{-10} = 1x^ 2$
$1.2 \times 10^{-10} = x^ 2$
$ \sqrt [ 2] {1.2 \times 10^{-10}} = x$
$1.1 \times 10^{-5} = x$
- This is the molar solubility value for this salt.
(b)
1. Write the $K_{sp}$ expression:
$ Mg(OH)_2(s) \lt -- \gt 1Mg^{2+}(aq) + 2{OH}^{-}(aq)$
$5.6 \times 10^{-12} = [Mg^{2+}]^ 1[{OH}^{-}]^ 2$
2. Considering a pure solution: $[Mg^{2+}] = 1x$ and $[{OH}^{-}] = 2x$
$5.6 \times 10^{-12}= ( 1x)^ 1 \times ( 2x)^ 2$
$5.6 \times 10^{-12} = 4x^ 3$
$1.4 \times 10^{-12} = x^ 3$
$ \sqrt [ 3] {1.4 \times 10^{-12}} = x$
$1.1 \times 10^{-4} = x$
(c)
1. Write the $K_{sp}$ expression:
$ Ag_2SO_3(s) \lt -- \gt 2Ag^{+}(aq) + 1{SO_3}^{2-}(aq)$
$1.5 \times 10^{-13} = [Ag^{+}]^ 2[{SO_3}^{2-}]^ 1$
2. Considering a pure solution: $[Ag^{+}] = 2x$ and $[{SO_3}^{2-}] = 1x$
$1.5 \times 10^{-13}= ( 2x)^ 2 \times ( 1x)^ 1$
$1.5 \times 10^{-13} = 4x^ 3$
$3.8 \times 10^{-25} = x^ 3$
$ \sqrt [ 3] {3.8 \times 10^{-25}} = x$
$1.6 \times 10^{-5} = x $
