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Calculate The Percent Ionization of A 0.15 M Benzoic

Reviewed by Calculator Editorial Team

Benzoic acid (C₇H₆O₂) is a weak organic acid that partially ionizes in aqueous solution. Calculating its percent ionization helps understand its behavior in solution. This guide explains how to determine the percent ionization of a 0.15 M benzoic acid solution using the ionization constant (Kₐ) and the Henderson-Hasselbalch equation.

Introduction

When benzoic acid dissolves in water, it partially dissociates into benzoate ions (C₇H₅O₂⁻) and hydrogen ions (H⁺). The percent ionization measures what fraction of the acid molecules have dissociated. For a weak acid like benzoic acid, the percent ionization is typically small but can be calculated using the ionization constant (Kₐ) and the initial concentration of the acid.

The ionization constant (Kₐ) for benzoic acid is approximately 6.5 × 10⁻⁵ at 25°C. This value indicates how strongly the acid dissociates in solution. The percent ionization is calculated using the formula:

Percent Ionization = (√(4Kₐ × C) / (1 + √(4Kₐ × C))) × 100

Where C is the initial concentration of the acid in molarity (M).

Formula

The percent ionization of a weak acid can be calculated using the following formula:

Percent Ionization = (√(4Kₐ × C) / (1 + √(4Kₐ × C))) × 100

This formula is derived from the quadratic equation that describes the ionization equilibrium of the weak acid. The square root term accounts for the partial dissociation of the acid.

Calculation

To calculate the percent ionization of a 0.15 M benzoic acid solution:

  1. Identify the ionization constant (Kₐ) for benzoic acid, which is approximately 6.5 × 10⁻⁵ at 25°C.
  2. Use the formula: Percent Ionization = (√(4Kₐ × C) / (1 + √(4Kₐ × C))) × 100.
  3. Plug in the values: C = 0.15 M, Kₐ = 6.5 × 10⁻⁵.
  4. Calculate the numerator: √(4 × 6.5 × 10⁻⁵ × 0.15) ≈ √(3.9 × 10⁻⁵) ≈ 6.245 × 10⁻³.
  5. Calculate the denominator: 1 + 6.245 × 10⁻³ ≈ 1.006245.
  6. Divide the numerator by the denominator: 6.245 × 10⁻³ / 1.006245 ≈ 6.215 × 10⁻³.
  7. Multiply by 100 to get the percent: 6.215 × 10⁻³ × 100 ≈ 0.6215%.

The percent ionization of a 0.15 M benzoic acid solution is approximately 0.62%.

Example

Let's calculate the percent ionization of a 0.15 M benzoic acid solution step by step.

Given:

  • Initial concentration (C) = 0.15 M
  • Ionization constant (Kₐ) = 6.5 × 10⁻⁵

Calculation:

  1. Calculate 4Kₐ × C = 4 × 6.5 × 10⁻⁵ × 0.15 ≈ 3.9 × 10⁻⁵
  2. Take the square root: √(3.9 × 10⁻⁵) ≈ 6.245 × 10⁻³
  3. Add 1 to the square root: 1 + 6.245 × 10⁻³ ≈ 1.006245
  4. Divide the square root by the sum: 6.245 × 10⁻³ / 1.006245 ≈ 6.215 × 10⁻³
  5. Multiply by 100 to get the percent: 6.215 × 10⁻³ × 100 ≈ 0.6215%

The percent ionization of the 0.15 M benzoic acid solution is approximately 0.62%. This means that only about 0.62% of the benzoic acid molecules have dissociated into ions in the solution.

FAQ

What is the percent ionization of benzoic acid?
The percent ionization of benzoic acid depends on its concentration and the ionization constant (Kₐ). For a 0.15 M solution, it's approximately 0.62%.
How does the percent ionization change with concentration?
The percent ionization increases with concentration but levels off as the concentration becomes very high. For weak acids, the percent ionization is typically small.
What factors affect the percent ionization of benzoic acid?
The percent ionization is primarily affected by the concentration of the acid and the ionization constant (Kₐ). Temperature and the presence of other ions can also influence the result.
Can the percent ionization of benzoic acid be greater than 100%?
No, the percent ionization cannot exceed 100% because it represents the fraction of acid molecules that have dissociated. For weak acids, it's typically much less than 100%.
How is the percent ionization different from the degree of dissociation?
The percent ionization and the degree of dissociation are related but not identical. The percent ionization is calculated based on the initial concentration, while the degree of dissociation is the actual fraction of molecules that have dissociated.