Answer
(a) Solubility = $3.1 \times 10^{-4}M$
(b) Solubility = $4.2 \times 10^{-3}M$
Work Step by Step
(a)
1. Write the $K_{sp}$ expression:
$ Ag_2SO_4(s) \lt -- \gt 2Ag^{+}(aq) + 1SO{_4}^{2-}(aq)$
$1.5 \times 10^{-5} = [Ag^{+}]^ 2[SO{_4}^{2-}]^ 1$
$1.5 \times 10^{-5} = (0.22 + S)^ 2( 1S)^ 1$
2. Find the molar solubility.
Since 'S' has a very small value, we can approximate: $[Ag^{+}] = 0.22$
$1.5 \times 10^{-5}= (0.22)^ 2 \times ( 1S)^ 1$
$1.5 \times 10^{-5}= (0.22)^ 2 \times ( 1S)^ 1$
$1.5 \times 10^{-5}= 0.048 \times ( 1S)^ 1$
$ \frac{1.5 \times 10^{-5}}{0.048} = ( 1S)^ 1$
$3.1 \times 10^{-4} = S$
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(b)
3. Write the $K_{sp}$ expression:
$ Ag_2SO_4(s) \lt -- \gt 1S{O_4}^{2-}(aq) + 2Ag^{+}(aq)$
$1.5 \times 10^{-5} = [S{O_4}^{2-}]^ 1[Ag^{+}]^ 2$
$1.5 \times 10^{-5} = (0.22 + S)^ 1( 2S)^ 2$
4. Find the molar solubility.
Since 'S' has a very small value, we can approximate: $[S{O_4}^{2-}] = 0.22$
$1.5 \times 10^{-5}= (0.22)^ 1 \times ( 2S)^ 2$
$1.5 \times 10^{-5}= (0.22)^ 1 \times ( 2S)^ 2$
$1.5 \times 10^{-5}= 0.22 \times ( 2S)^ 2$
$ \frac{1.5 \times 10^{-5}}{0.22} = ( 2S)^ 2$
$6.8 \times 10^{-5} = ( 2S)^ 2$
$ \sqrt [ 2] {6.8 \times 10^{-5}} = 2S$
$8.3 \times 10^{-3} = 2S$
$4.2 \times 10^{-3} = S$
