Answer
(a) $Solubility = 2.3 \times 10^{-5}$
(b) $Solubility = 4.2 \times 10^{-9}$
Work Step by Step
(a)
1. Write the $K_{sp}$ expression:
$ Sr(NO_3)_2(s) \lt -- \gt 1Sr^{2+}(aq) + 1CO{_3}^{2-}(aq)$
$5.4 \times 10^{-10} = [Sr^{2+}]^ 1[CO{_3}^{2-}]^ 1$
2. Considering a pure solution: $[Sr^{2+}] = 1S$ and $[CO{_3}^{2-}] = 1S$
$5.4 \times 10^{-10}= ( 1S)^ 1 \times ( 1S)^ 1$
$5.4 \times 10^{-10} = 1S^ 2$
$5.4 \times 10^{-10} = S^ 2$
$ \sqrt [ 2] {5.4 \times 10^{-10}} = S$
$2.3 \times 10^{-5} = S$
- This is the molar solubility value for this salt.
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(b)
1. Write the $K_{sp}$ expression:
$ Sr(NO_3)_2(s) \lt -- \gt 1Sr^{2+}(aq) + 1CO{_3}^{2-}(aq)$
$5.4 \times 10^{-10} = [Sr^{2+}]^ 1[CO{_3}^{2-}]^ 1$
$5.4 \times 10^{-10} = (0.13 + S)^ 1( 1S)^ 1$
2. Find the $CO{_3}^{2-}$ concentration.
Since 'S' has a very small value, we can approximate: $[Sr^{2+}] = x$
$5.4 \times 10^{-10}= (0.13)^ 1 \times ( 1S)^ 1$
$5.4 \times 10^{-10}= (0.13)^ 1 \times ( 1S)^ 1$
$5.4 \times 10^{-10}= 0.13 \times ( 1S)^ 1$
$ \frac{5.4 \times 10^{-10}}{0.13} = ( 1S)^ 1$
$4.2 \times 10^{-9} = ( 1S)^ 1$
$ \sqrt [ 1] {4.2 \times 10^{-9}} = 1S$
$4.2 \times 10^{-9} = 1S$
