Calculate the `pH` of `0.1M K_(3)PO_(4)`soln. The third dissociation constant of orthophosphoric acid is `1.3 xx10^(-12)`. Assume that the hydrolysis proceeds only in the first step.

Explanation

To calculate the pH of a 0.1 M K₃PO₄ solution, we will follow these steps:

### Step 1: Understand the Hydrolysis Reaction
K₃PO₄ dissociates in water to form K⁺ ions and PO₄³⁻ ions. The PO₄³⁻ ion can undergo hydrolysis to form HPO₄²⁻ and OH⁻ ions:
\[ \text{PO}_4^{3-} + \text{H}_2\text{O} \rightleftharpoons \text{HPO}_4^{2-} + \text{OH}^- \]

### Step 2: Determine the Relevant Equilibrium Constant
For the hydrolysis of PO₄³⁻, we can use the third dissociation constant (Kₐ₃) of phosphoric acid (H₃PO₄), which is given as:
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