Answer
$[Au^+] = 4.5 \times 10^{-7}M$
Work Step by Step
1. Write the $K_{sp}$ expression:
$ AuCl(s) \lt -- \gt 1Au^{+}(aq) + 1Cl^-(aq)$
$2 \times 10^{-13} = [Au^{+}]^ 1[Cl^-]^ 1$
2. Considering a pure solution: $[Au^{+}] = 1S$ and $[Cl^-] = 1S$
$2 \times 10^{-13}= ( 1S)^ 1 \times ( 1S)^ 1$
$2 \times 10^{-13} = S^ 2$
$ \sqrt [ 2] {2 \times 10^{-13}} = S$
$4.5 \times 10^{-7} = S$
- This is the molar solubility value for this salt.
Molar solubility $[Au^+] = 1S = 4.5 \times 10^{-7}M$
