Aluminum compounds are soluble in acidic solution, where aluminum(III) exists as the complex ion [Al(H₂O)₆]³⁺, which is generally represented simply as Al³⁺(aq). They are also soluble in basic solutions, where the aluminum(III) is present as the complex ion [Al(OH)₄]^-. At certain intermediate pH values, the concentration of aluminum(III) that can exist in solution is at a minimum. Thus, a plot of the total concentration of aluminum(III) in solution as a function of pH yields a U-shaped curve. Demonstrate that this is the case with a few calculations.