Calculate the equilibrium constants for the reactions with water of `H_(2)PO_(4)^(Theta), HPO_(4)^(2-)`, and `PO_(4)^(3-)` as ase. Comparing the relative values of two equilibrium constants of `H_(2)PO_(4)^(Theta)` with water, deduce whether solutions of this ion in water are acidic or base, Deduce whether solutions of `HPO_(4)^(2-)` are acidic or bases. Given `K_(1),K_(2)`,and `K_(3)` for `H_(3)PO_(4)` are `7.1 xx 10^(-3), 6.3 xx 10^(-8)`, and `4.5 xx 10^(-13)` respectively.

Explanation

To solve the problem, we will calculate the equilibrium constants for the hydrolysis reactions of the ions \( H_2PO_4^- \), \( HPO_4^{2-} \), and \( PO_4^{3-} \) with water, and then deduce whether their solutions are acidic or basic.

### Step 1: Calculate the hydrolysis constant for \( H_2PO_4^- \)

The reaction for the hydrolysis of \( H_2PO_4^- \) with water is:
\[ H_2PO_4^- + H_2O \rightleftharpoons H_3PO_4 + OH^- \]
...