Calculate Ph of 0.2 M Aqueous Solution of Sodium Butyrate

Sodium butyrate (C₄H₇NaO₂) is a weak organic acid that dissociates in water to form butyric acid (C₄H₆O₂) and sodium ions (Na⁺). The pH of a solution depends on the concentration of hydrogen ions (H⁺) and the dissociation constant (Kₐ) of the weak acid. This guide explains how to calculate the pH of a 0.2 molar aqueous solution of sodium butyrate.

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 = -log[H⁺]

For weak acids like sodium butyrate, the pH cannot be directly calculated from the initial concentration because the acid partially dissociates in water. Instead, we use the dissociation constant (Kₐ) and the initial concentration to determine the equilibrium concentration of hydrogen ions.

How to Calculate pH

Step 1: Determine the Dissociation Constant (Kₐ)

The dissociation constant for butyric acid (C₄H₆O₂) is approximately 1.55 × 10⁻⁵ at 25°C. This value represents the equilibrium between the undissociated acid (HA) and its dissociated ions (H⁺ and A⁻):

HA ⇌ H⁺ + A⁻

Kₐ = [H⁺][A⁻]/[HA]

Step 2: Set Up the Ice Table

Assume the initial concentration of sodium butyrate is 0.2 M. Let x be the concentration of hydrogen ions formed at equilibrium. The ice table helps track the changes in concentrations:

Species	Initial (M)	Change (M)	Equilibrium (M)
HA	0.2	-x	0.2 - x
H⁺	0	+x	x
A⁻	0	+x	x

Step 3: Apply the Dissociation Constant

Substitute the equilibrium concentrations into the Kₐ expression:

Kₐ = [H⁺][A⁻]/[HA] = x * x / (0.2 - x)

1.55 × 10⁻⁵ = x² / (0.2 - x)

Step 4: Solve for x

This is a quadratic equation that can be solved using the quadratic formula:

x = [Kₐ + √(Kₐ² + 4Kₐ[HA])] / 2

x = [1.55 × 10⁻⁵ + √((1.55 × 10⁻⁵)² + 4 × 1.55 × 10⁻⁵ × 0.2)] / 2

x ≈ 0.000123 M

Step 5: Calculate the pH

Using the hydrogen ion concentration at equilibrium:

pH = -log[H⁺] = -log(0.000123) ≈ 3.91

Example Calculation

Let's calculate the pH of a 0.2 M aqueous solution of sodium butyrate step-by-step:

Given: [HA] = 0.2 M, Kₐ = 1.55 × 10⁻⁵
Assume x = [H⁺] at equilibrium
Set up the equation: 1.55 × 10⁻⁵ = x² / (0.2 - x)
Solve the quadratic equation to find x ≈ 0.000123 M
Calculate pH: -log(0.000123) ≈ 3.91

The pH of a 0.2 M solution of sodium butyrate is approximately 3.91, indicating a weak acid solution.

Interpreting Results

A pH of 3.91 means the solution contains more hydrogen ions than a neutral solution (pH 7) but fewer than a strong acid like hydrochloric acid (pH 0). This is typical for weak acids, which do not fully dissociate in water.

To verify your calculations, you can use our pH calculator or consult chemistry reference tables for weak acid dissociation constants.

FAQ

What is the dissociation constant for butyric acid?

The dissociation constant (Kₐ) for butyric acid is approximately 1.55 × 10⁻⁵ at 25°C.

Why doesn't the pH of a weak acid solution equal the negative logarithm of its initial concentration?

Weak acids only partially dissociate in water, so the equilibrium concentration of hydrogen ions is lower than the initial concentration.

How does temperature affect the pH calculation?

The dissociation constant (Kₐ) changes with temperature, so the pH calculation should use the Kₐ value at the relevant temperature.