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Calculate Ph of 0.160 M Phosphoric Acid

Reviewed by Calculator Editorial Team

Phosphoric acid (H₃PO₄) is a triprotic acid that dissociates in water to form multiple hydrogen ions. Calculating its pH at a specific concentration requires understanding acid dissociation constants and equilibrium calculations. This guide explains the process step-by-step, including the formula, assumptions, and practical applications.

Introduction

The pH of a solution is a measure of its acidity or alkalinity, defined as the negative logarithm of the hydrogen ion concentration:

pH Formula

pH = -log₁₀[H⁺]

For phosphoric acid (H₃PO₄), which is a triprotic acid, the pH calculation involves multiple dissociation steps. The first dissociation is:

First Dissociation

H₃PO₄ ⇌ H⁺ + H₂PO₄⁻

K₁ = [H⁺][H₂PO₄⁻]/[H₃PO₄] ≈ 7.5 × 10⁻³

At a concentration of 0.160 M, we can calculate the pH using the Henderson-Hasselbalch equation for the first dissociation step.

How to Calculate pH

To calculate the pH of 0.160 M phosphoric acid:

  1. Identify the dissociation constant (K₁) for the first dissociation step.
  2. Assume the solution is dilute enough that the water autoionization can be neglected.
  3. Use the Henderson-Hasselbalch equation to estimate the pH.

Assumptions

This calculation assumes:

  • The solution is at 25°C.
  • The concentration of H₂PO₄⁻ is negligible compared to H₃PO₄.
  • The activity coefficients are close to 1 (ideal solution behavior).

Phosphoric Acid Basics

Phosphoric acid is a weak acid with three dissociable protons. Its dissociation steps are:

  1. First dissociation (K₁ ≈ 7.5 × 10⁻³)
  2. Second dissociation (K₂ ≈ 6.2 × 10⁻⁸)
  3. Third dissociation (K₃ ≈ 4.2 × 10⁻¹³)

At low concentrations, only the first dissociation contributes significantly to the pH.

Calculation Example

For 0.160 M H₃PO₄:

  1. Assume x = [H⁺] = [H₂PO₄⁻] (from the first dissociation).
  2. Initial [H₃PO₄] = 0.160 M.
  3. After dissociation: [H₃PO₄] = 0.160 - x.
  4. Set up the equilibrium expression: x² / (0.160 - x) = 7.5 × 10⁻³.
  5. Solve for x (typically x ≈ 0.012 M).
  6. Calculate pH = -log₁₀(0.012) ≈ 1.92.

Result Interpretation

A pH of approximately 1.92 indicates a moderately acidic solution. The result is consistent with the first dissociation step dominating at this concentration.

FAQ

What is the pH of 0.160 M phosphoric acid?

The pH of 0.160 M phosphoric acid is approximately 1.92, calculated using the first dissociation constant and the Henderson-Hasselbalch equation.

Why does phosphoric acid have multiple pH values?

Phosphoric acid is a triprotic acid, meaning it can donate three protons. Each dissociation step occurs at a different pH, resulting in multiple pH values across the titration curve.

How does temperature affect the pH calculation?

The dissociation constants (K₁, K₂, K₃) are temperature-dependent. For precise calculations at temperatures other than 25°C, use temperature-corrected K values.