Answer
(a) $1.0 \times 10^{-5}$ M
(b) $1.1 \times 10^{-10}$ M
Work Step by Step
(a)
1. Write the $K_{sp}$ expression:
$ BaSO_4(s) \lt -- \gt 1SO_4^{2-}(aq) + 1Ba^{2+}(aq)$
$1.1 \times 10^{-10} = [SO_4^{2-}]^ 1[Ba^{2+}]^ 1$
2. Considering a pure solution: $[SO_4^{2-}] = 1S$ and $[Ba^{2+}] = 1S$
$1.1 \times 10^{-10}= ( 1S)^ 1 \times ( 1S)^ 1$
$1.1 \times 10^{-10} = S^ 2$
$ \sqrt [ 2] {1.1 \times 10^{-10}} = S$
$1.0 \times 10^{-5} = S$
- This is the molar solubility value for this salt in pure water.
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(b)
1. Write the $K_{sp}$ expression:
$ BaSO_4(s) \lt -- \gt 1SO_4^{2-}(aq) + 1Ba^{2+}(aq)$
$1.1 \times 10^{-10} = [SO_4^{2-}]^ 1[Ba^{2+}]^ 1$
$1.1 \times 10^{-10} = (1 + S)^ 1( 1S)^ 1$
2. Find the molar solubility.
Since 'S' has a very small value, we can approximate: $[SO_4^{2-}] = 1$
$1.1 \times 10^{-10}= (1)^ 1 \times ( 1S)^ 1$
$ \frac{1.1 \times 10^{-10}}{1} = ( 1S)^ 1$
$1.1 \times 10^{-10} = S$
