Introduction

In chemistry, pH is a measure of the acidity or basicity of a solution. It is essential for various applications, from biological processes to industrial practices. Understanding how to calculate the pH of mixtures of acids and bases is crucial for achieving desired chemical properties. Below, we present three diverse and practical examples of calculating the pH of a mixture of acids or bases.

Example 1: Calculating pH of a Mixture of Hydrochloric Acid and Acetic Acid

Context

In a laboratory setting, a chemist is tasked with determining the pH of a solution created by mixing hydrochloric acid (HCl) and acetic acid (CH₃COOH). This example demonstrates how to calculate the pH of a solution containing two different acids with distinct strengths.

To calculate the pH, we first need to determine the concentration of hydrogen ions contributed by each acid. Hydrochloric acid is a strong acid, while acetic acid is a weak acid.

• Concentration of HCl: 0.1 M
• Concentration of CH₃COOH: 0.1 M

For HCl, since it’s a strong acid, we can assume that it completely dissociates:

• [H⁺] from HCl = 0.1 M

For acetic acid, we need to use its dissociation constant (Ka) to find the concentration of hydrogen ions:

• Ka for acetic acid = 1.8 × 10⁻⁵
• The dissociation reaction is CH₃COOH ⇌ H⁺ + CH₃COO⁻.

Using the formula:

• [H⁺] = √(Ka * [CH₃COOH]) = √(1.8 × 10⁻⁵ * 0.1) = 0.00134 M

Now, add the contributions of both acids:

• Total [H⁺] = 0.1 + 0.00134 = 0.10134 M

Finally, we can calculate the pH:

• pH = -log(0.10134) ≈ 0.994

Notes

• This example illustrates the dominance of a strong acid’s effect on pH in a mixture.
• For weak acids, consider their dissociation constants for accurate calculations.

Example 2: Determining the pH of a Sodium Hydroxide and Ammonium Chloride Solution

Context

In an environmental chemistry project, a researcher is examining the pH of a solution formed by mixing sodium hydroxide (NaOH), a strong base, and ammonium chloride (NH₄Cl), a salt derived from a weak base and strong acid.

For this example, we have:

• Concentration of NaOH: 0.05 M
• Concentration of NH₄Cl: 0.1 M

NaOH dissociates completely in solution:

• [OH⁻] from NaOH = 0.05 M

Ammonium chloride dissociates into NH₄⁺ and Cl⁻. The ammonium ion (NH₄⁺) can act as a weak acid:

• The dissociation reaction: NH₄⁺ ⇌ H⁺ + NH₃
• Ka for NH₄⁺ = 5.56 × 10⁻¹⁰

To find the [H⁺] from NH₄⁺, we can use the equation:

• [H⁺] = √(Ka * [NH₄⁺]) = √(5.56 × 10⁻¹⁰ * 0.1) = 0.000745 M

Next, we need to convert [OH⁻] to [H⁺]:

• pOH = -log(0.05) = 1.3, thus [H⁺] = 10⁻⁴.⁷ = 0.00001995 M

The total [H⁺] in the solution is the sum of contributions from NH₄⁺ and the converted [OH⁻]:

• Total [H⁺] = 0.000745 + 0.00001995 = 0.000764 M

Finally, we calculate the pH:

• pH = -log(0.000764) ≈ 3.12

Notes

• This example highlights how a strong base interacts with a weak acid’s conjugate base in a salt, affecting the pH.
• Always consider the equilibrium reactions and dissociation constants when working with weak acids and bases.

Example 3: Mixing Strong Acid and Strong Base

Context

An industrial chemist needs to neutralize 0.2 M sulfuric acid (H₂SO₄) with 0.2 M sodium hydroxide (NaOH) to achieve a neutral pH for a waste treatment process. This example illustrates how to calculate the pH of a strong acid and strong base mixture.

Sulfuric acid is a strong acid that dissociates completely:

• [H⁺] from H₂SO₄ = 0.2 M

Sodium hydroxide is also a strong base:

• [OH⁻] from NaOH = 0.2 M

In a neutralization reaction, H⁺ ions from the acid react with OH⁻ ions from the base:

• H⁺ + OH⁻ → H₂O

Since the concentrations are equal, they will completely neutralize each other:

• Remaining [H⁺] = 0.2 M - 0.2 M = 0 M
• Remaining [OH⁻] = 0.2 M - 0.2 M = 0 M

The resulting solution contains only water, which has a neutral pH:

• pH = 7

Notes

• This example demonstrates the straightforward calculation of pH in a strong acid-strong base neutralization.
• For mixtures where the concentrations of acids and bases differ, further calculations are required to determine the excess H⁺ or OH⁻ ions for pH evaluation.