Calculate The Ph of Each of The Following Buffered Solutions.

This guide explains how to calculate the pH of buffered solutions using the Henderson-Hasselbalch equation. Buffered solutions resist changes in pH when small amounts of acid or base are added, making them essential in biological systems and chemical applications.

Introduction

The pH of a buffered solution can be calculated using the Henderson-Hasselbalch equation, which relates the pH to the ratio of the concentrations of a conjugate acid-base pair. This equation is fundamental in chemistry and biology for understanding how buffers maintain stable pH levels.

Buffers are solutions that resist changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base, or a weak base and its conjugate acid. The effectiveness of a buffer depends on the concentrations of these components and the pKa of the weak acid or base.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is given by:

pH = pKa + log₁₀([A^-]/[HA])

Where:

pH is the negative logarithm of the hydrogen ion concentration
pKa is the negative logarithm of the acid dissociation constant
[A^-] is the concentration of the conjugate base
[HA] is the concentration of the weak acid

This equation allows you to calculate the pH of a buffered solution when you know the pKa of the weak acid, the concentration of the conjugate base, and the concentration of the weak acid.

Worked Examples

Example 1: Acetic Acid Buffer

Consider a buffer solution containing 0.1 M acetic acid (CH₃COOH) and 0.1 M sodium acetate (CH₃COO^-). The pKa of acetic acid is 4.76.

Using the Henderson-Hasselbalch equation:

pH = 4.76 + log₁₀([CH₃COO^-]/[CH₃COOH]) = 4.76 + log₁₀(0.1/0.1) = 4.76 + log₁₀(1) = 4.76 + 0 = 4.76

The pH of this buffer solution is 4.76.

Example 2: Phosphate Buffer

A phosphate buffer contains 0.2 M H₂PO₄^- and 0.3 M HPO₄^2-. The pKa of H₂PO₄^- is 7.2.

Using the Henderson-Hasselbalch equation:

pH = 7.2 + log₁₀([HPO₄^2-]/[H₂PO₄^-]) = 7.2 + log₁₀(0.3/0.2) = 7.2 + log₁₀(1.5) ≈ 7.2 + 0.176 ≈ 7.38

The pH of this buffer solution is approximately 7.38.

FAQ

What is the Henderson-Hasselbalch equation used for?: The Henderson-Hasselbalch equation is used to calculate the pH of buffered solutions. It helps determine the pH when the concentrations of a conjugate acid-base pair and the pKa of the weak acid are known.
How do you prepare a buffer solution?: A buffer solution is prepared by mixing a weak acid with its conjugate base or a weak base with its conjugate acid. The ratio of these components affects the pH of the solution.
What factors affect the effectiveness of a buffer?: The effectiveness of a buffer depends on the concentrations of the weak acid and its conjugate base, as well as the pKa of the weak acid. A buffer is most effective when the concentrations of the acid and base are equal.
Can the Henderson-Hasselbalch equation be used for any buffer?: The Henderson-Hasselbalch equation is most accurate for buffers that follow the ideal buffer behavior, where the concentrations of the weak acid and its conjugate base are not too different. For extreme ratios, other equations may be more appropriate.
How does temperature affect the pKa and pH of a buffer?: Temperature can affect the pKa of a weak acid, which in turn affects the pH of the buffer. The Henderson-Hasselbalch equation assumes a constant pKa, so temperature changes may require adjustments to the pKa value.