Answer
a. $1.6 \times 10^{-5} M$
b. $9.3 \times 10^{-5}M$
c. $6.5 \times 10^{-7}M$
Work Step by Step
(a)
1. Write the $K_{sp}$ expression:
$ Ag_3PO_4(s) \lt -- \gt 3Ag^{+}(aq) + 1P{O_4}^{3-}(aq)$
$1.8 \times 10^{-18} = [Ag^{+}]^ 3[P{O_4}^{3-}]^ 1$
2. Considering a pure solution: $[Ag^{+}] = 3x$ and $[P{O_4}^{3-}] = 1x$
$1.8 \times 10^{-18}= ( 3x)^ 3 \times ( 1x)^ 1$
$1.8 \times 10^{-18} = 27x^ 4$
$6.667 \times 10^{-20} = x^ 4$
$ \sqrt [ 4] {6.667 \times 10^{-20}} = x$
$1.607 \times 10^{-5} = x$
- This is the molar solubility value for this salt.
(b)
1. Write the $K_{sp}$ expression:
$ CaCO_3(s) \lt -- \gt 1Ca^{2+}(aq) + 1C{O_3}^{2-}(aq)$
$8.7 \times 10^{-9} = [Ca^{2+}]^ 1[C{O_3}^{2-}]^ 1$
2. Considering a pure solution: $[Ca^{2+}] = 1x$ and $[C{O_3}^{2-}] = 1x$
$8.7 \times 10^{-9}= ( 1x)^ 1 \times ( 1x)^ 1$
$8.7 \times 10^{-9} = 1x^ 2$
$8.7 \times 10^{-9} = x^ 2$
$ \sqrt [ 2] {8.7 \times 10^{-9}} = x$
$9.327 \times 10^{-5} = x$
- This is the molar solubility value for this salt.
(c)
1. Write the $K_{sp}$ expression:
$ Hg_2Cl_2(s) \lt -- \gt 1Hg^{2+}(aq) + 2Cl^-(aq)$
$1.1 \times 10^{-18} = [Hg^{2+}]^ 1[Cl^-]^ 2$
2. Considering a pure solution: $[Hg^{2+}] = 1x$ and $[Cl^-] = 2x$
$1.1 \times 10^{-18}= ( 1x)^ 1 \times ( 2x)^ 2$
$1.1 \times 10^{-18} = 4x^ 3$
$2.75 \times 10^{-19} = x^ 3$
$ \sqrt [ 3] {2.75 \times 10^{-19}} = x$
$6.503 \times 10^{-7} = x$
- This is the molar solubility value for this salt.