Calculate Ph of 0.160 M Phosphoric Acid

Introduction

The pH of a solution is a measure of its acidity or basicity, defined as the negative logarithm of the hydrogen ion concentration. For phosphoric acid, which can donate up to three protons, the pH depends on the concentration of the acid and its dissociation constants.

At low concentrations (typically less than 0.01 M), phosphoric acid behaves as a monoprotic acid, and its pH can be calculated using the formula:

Where pKa₁ is the first dissociation constant of phosphoric acid (typically 2.16 for H₃PO₄).

How to Calculate pH

Step 1: Determine the Acid Dissociation Constants

Phosphoric acid has three dissociation constants:

• pKa₁ = 2.16 (for H₃PO₄ → H⁺ + H₂PO₄⁻)
• pKa₂ = 7.21 (for H₂PO₄⁻ → H⁺ + HPO₄²⁻)
• pKa₃ = 12.32 (for HPO₄²⁻ → H⁺ + PO₄³⁻)

Step 2: Calculate the pH

For a 0.160 M solution of phosphoric acid, we can use the Henderson-Hasselbalch equation to estimate the pH:

Since the concentration of the conjugate base [HPO₄²⁻] is initially zero, the equation simplifies to:

This results in pH = pKa₁ ≈ 2.16.

Step 3: Consider the Second Dissociation

As the solution becomes more basic, the second dissociation becomes significant. The pH can be calculated using:

This requires knowing the concentrations of the mono- and dihydrogen phosphate ions, which can be determined using equilibrium calculations.

Phosphoric Acid Basics

Phosphoric acid is a weak acid that exists in several forms in aqueous solution:

• H₃PO₄ (undissociated acid)
• H₂PO₄⁻ (monohydrogen phosphate)
• HPO₄²⁻ (dihydrogen phosphate)
• PO₄³⁻ (phosphate ion)

The pH of the solution depends on which form dominates, which in turn depends on the concentration of the acid and the pH of the solution.

Calculation Example

Let's calculate the pH of a 0.160 M solution of phosphoric acid:

1. Assume the solution is initially dominated by H₃PO₄.
2. Use the simplified Henderson-Hasselbalch equation: pH = pKa₁ - log([H₃PO₄]/[HPO₄²⁻]).
3. Since [HPO₄²⁻] is initially zero, pH ≈ pKa₁ = 2.16.

For more accurate calculations, you would need to consider the equilibrium concentrations of all species, which requires solving a system of equations.