Question #f4fb3
1 Answer
Explanation:
Magnesium hydroxide,
Instead, an equilibrium is established between the undissolved solid and the dissociated ions.
#"Mg"("OH")_ (color(red)(2)(s)) rightleftharpoons "Mg"_ ((aq))^(2+) + color(red)(2)"OH"_ ((aq))^(-)#
Notice that every mole of magnesium hydroxide that dissociates produces
In other words, the saturated solution will contain twice as many moles of hydroxide anions than on magnesium cations. This means that the equilibrium concentration of the magnesium cations will be half that of the hydroxide anions
#["Mg"^(2+)] = 1/color(red)(2) xx ["OH"^(-)] -># equilibrium concentrations
In your case, you will have
#["Mg"^(2+)] = 1/2 * 4.0 * 10^(-4)"M" = 2.0 * 10^(-4)"M"#
Now, the solubility product constant,
#K_(sp) = ["Mg"^(2+)] * ["OH"^(-)]^color(red)(2)#
Plug in your values to find
#K_(sp) = 2.0 * 10^(-4)"M" * (4.0 * 10^(-4)"M")^color(red)(2)#
#K_(sp) = 3.2 * 10^(-11)"M"^3#
The units are usually omitted from the expression of the solubility product constant, which means that your answer will be
#K_(sp) = color(green)(|bar(ul(color(white)(a/a)color(black)(3.2 * 10^(-11))color(white)(a/a)|)))#
The answer is rounded to two sig figs.