We wish to precipitate \(\mathrm{Al}^{+3}\) from 2.0 liters of a dilute solution of \(\mathrm{Al}(\mathrm{OH})_{3}\) in water. The concentration is \(7.0 \times 10^{-5} \mathrm{~mol} / \mathrm{L}\) and is not saturated. The concentration solubility product of \(\mathrm{Al}(\mathrm{OH})_{3}\) is \(1.1 \times 10^{-15}(\mathrm{~mol} / \mathrm{L})^{4}(\) Mullin, 2001).

a. If we add solid \(\mathrm{NaOH}\), which is very soluble, to the solution, how many moles need to be added to form a saturated solution?

b. If we add solid \(\mathrm{NaOH}\) to the original solution, how many moles need to be added to precipitate \(2 / 3\) of the \(\mathrm{Al}^{+3}\) ?

c. If we add 1.0 liter of \(0.001 \mathrm{~mol} / \mathrm{L}\) aqueous solution of \(\mathrm{NaOH}\) to the original solution, how many moles of \(\mathrm{Al}^{+3}\) precipitate?