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11 Calculate The Ph of 0.15 M Acetic Acid

Reviewed by Calculator Editorial Team

Calculating the pH of a solution is fundamental in chemistry. For acetic acid (CH₃COOH), a weak acid, we use the Henderson-Hasselbalch equation to determine its pH when dissolved in water. This guide explains how to calculate the pH of 0.15 M acetic acid, understand the results, and interpret the acid dissociation behavior.

Introduction

The pH scale measures the acidity or basicity of a solution, ranging from 0 (very acidic) to 14 (very basic). For weak acids like acetic acid, the pH depends on the concentration of the acid and its dissociation constant (Ka).

Acetic acid is a common organic acid found in vinegar. When dissolved in water, it partially dissociates into acetate ions (CH₃COO⁻) and hydrogen ions (H⁺). The equilibrium can be represented as:

CH₃COOH ⇌ CH₃COO⁻ + H⁺

The dissociation constant (Ka) for acetic acid is approximately 1.8 × 10⁻⁵ at 25°C. The Henderson-Hasselbalch equation relates the pH of a buffer solution to the ratio of the concentrations of the conjugate base to the acid.

How to Calculate pH of Acetic Acid

The Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is:

pH = pKa + log₁₀([CH₃COO⁻]/[CH₃COOH])

Where:

  • pKa is the negative logarithm of the acid dissociation constant (-log₁₀(Ka))
  • [CH₃COO⁻] is the concentration of the acetate ion
  • [CH₃COOH] is the concentration of acetic acid

Steps to Calculate pH

  1. Determine the pKa value for acetic acid (typically 4.76 at 25°C)
  2. Calculate the ratio of [CH₃COO⁻]/[CH₃COOH]
  3. Take the logarithm (base 10) of this ratio
  4. Add the pKa value to the logarithm result

For pure acetic acid solutions, [CH₃COO⁻] is negligible compared to [CH₃COOH], so the ratio [CH₃COO⁻]/[CH₃COOH] ≈ 0. This results in a pH equal to pKa (4.76).

Example Calculation

Let's calculate the pH of 0.15 M acetic acid:

  1. Given: [CH₃COOH] = 0.15 M
  2. Assume [CH₃COO⁻] ≈ 0 (negligible for pure acid)
  3. pKa for acetic acid = 4.76
  4. Ratio [CH₃COO⁻]/[CH₃COOH] ≈ 0
  5. log₁₀(0) is undefined, but as the ratio approaches 0, pH approaches pKa
  6. Therefore, pH ≈ 4.76

This means a 0.15 M solution of acetic acid will have a pH of approximately 4.76, indicating it is a weak acid.

Interpreting the Results

The calculated pH of 4.76 for 0.15 M acetic acid shows that:

  • The solution is acidic (pH < 7)
  • It's a weak acid since the pH is close to pKa
  • Very little dissociation has occurred

To increase the dissociation and lower the pH further, you would need to:

  • Increase the concentration of acetic acid
  • Add a base to convert more acid to acetate ions
  • Increase the temperature (Ka increases with temperature)

Frequently Asked Questions

What is the pKa of acetic acid?

The pKa of acetic acid is approximately 4.76 at 25°C. This value represents the point at which half of the acid molecules are dissociated.

Why does pure acetic acid have a pH of 4.76?

Pure acetic acid has a pH of 4.76 because the concentration of acetate ions ([CH₃COO⁻]) is negligible compared to the concentration of undissociated acetic acid ([CH₃COOH]). The pH approaches the pKa value in such cases.

How does temperature affect the pH of acetic acid?

Temperature affects the pH of acetic acid because the dissociation constant (Ka) increases with temperature. This means the pH of a given concentration of acetic acid will decrease slightly as temperature increases.