Answer
(a) $Mg(OH)_2(s) \lt -- \gt Mg^{2+}(aq) + 2OH^-(aq)$
$K_{sp} = [Mg^{2+}][OH^-]^2$
(b) $FeCO_3(s) \lt -- \gt Fe^{2+}(aq) + CO_3^{2-}(aq)$
$K_{sp} = [Fe^{2+}][CO_3^{2-}]$
(c) $PbS(s) \lt -- \gt Pb^{2+}(aq) + S^{2-}(aq)$
$K_{sp} = [Pb^{2+}][S^{2-}]$
(d) $PbSO_4(s) \lt -- \gt Pb^{2+}(aq) + SO_4^{2-}(aq)$
$K_{sp} = [Pb^{2+}][SO_4^{2-}]$
Work Step by Step
The equation for when the compound dissolves in water:
Reactant: Compound in solid form.
Products: Aqueous ions that form the compound.
The $K_{sp}$ expression have the pattern:
$K_{sp} = \frac{[Products]}{[Reactants]}$
** Do not forget to put the balancing coefficients as the exponents of the concentrations.
But, since the reactant is solid, there will be only the multiplication of the ion concentrations.