pH Calculation Examples for Mixed Solutions

Learn how to determine the final pH after mixing two solutions with different pH values through practical examples.
By Jamie

Introduction

Determining the final pH after mixing two solutions with different pH values is a common task in chemistry, particularly in fields like pharmaceuticals, environmental science, and food chemistry. The final pH of a mixture depends on the volumes and pH values of the solutions being mixed, as well as their acid-base strengths. Below are three practical examples that illustrate how to perform these calculations.

Example 1: Mixing Hydrochloric Acid and Water

Context

In a laboratory setting, a chemist needs to dilute a strong acid to achieve a specific pH level for an experiment. This example illustrates how to calculate the final pH after mixing hydrochloric acid (HCl) with water.

To begin, we have:

  • Volume of HCl = 50 mL
  • pH of HCl = 1.0 (which corresponds to a hydrogen ion concentration of 0.1 M)
  • Volume of water = 150 mL

Calculating the final pH:

  1. Calculate the moles of H+ in HCl:
  • Moles = 0.1 M * 0.050 L = 0.005 moles

  1. Total volume after mixing:

    • Total volume = 50 mL + 150 mL = 200 mL = 0.200 L

  2. Final concentration of H+:

    • Final concentration = Moles / Total volume = 0.005 moles / 0.200 L = 0.025 M

  3. Calculate the final pH:

    • pH = -log(0.025) = 1.60

Notes

  • This example demonstrates dilution of a strong acid. The final pH is significantly higher than the original pH of the acid, indicating the effect of dilution.

Example 2: Mixing Acetic Acid and Sodium Acetate

Context

In food science, understanding the pH of vinegar mixtures is essential. This example shows how to calculate the final pH when mixing acetic acid (vinegar) with sodium acetate, a common buffer system.

Given data:

  • Volume of acetic acid (pH 2.9) = 100 mL
  • Volume of sodium acetate (pH 9.0) = 50 mL

Calculating the final pH:

  1. Calculate the hydrogen ion concentration for acetic acid:
  • H+ concentration from acetic acid (pH 2.9) = 0.001258 M
  • Moles of H+ = 0.001258 M * 0.100 L = 0.000126 moles

  1. Calculate the hydroxide ion concentration for sodium acetate:

    • OH- concentration from sodium acetate (pH 9.0) = 0.0000001 M
    • Moles of OH- = 0.0000001 M * 0.050 L = 0.000005 moles

  2. Determine the net moles of H+ and OH-:

    • Since H+ neutralizes OH-, we have 0.000126 - 0.000005 = 0.000121 moles of H+ remaining.

  3. Total volume after mixing:

    • Total volume = 100 mL + 50 mL = 150 mL = 0.150 L

  4. Final concentration of H+:

    • Final concentration = 0.000121 moles / 0.150 L = 0.000807 M

  5. Final pH calculation:

    • pH = -log(0.000807) = 3.09

Notes

  • This example illustrates the use of a buffer system and how pH changes can occur when mixing an acid and a base. The resulting pH shows that even when stronger acids and bases are mixed, the pH does not shift drastically due to the buffer action.

Example 3: Mixing Citric Acid and Sodium Bicarbonate

Context

In culinary applications, chefs often mix citric acid with sodium bicarbonate to create fizzy drinks. This example calculates the final pH of this mixture.

Given:

  • Volume of citric acid solution (pH 3.0) = 200 mL
  • Volume of sodium bicarbonate solution (pH 8.4) = 100 mL

Calculating the final pH:

  1. Determine the concentration of H+ from citric acid:
  • H+ concentration = 0.001 M
  • Moles of H+ = 0.001 M * 0.200 L = 0.0002 moles

  1. Determine the concentration of OH- from sodium bicarbonate:

    • OH- concentration = 0.0000004 M
    • Moles of OH- = 0.0000004 M * 0.100 L = 0.000004 moles

  2. Calculate the net moles of H+ and OH-:

    • H+ left = 0.0002 - 0.000004 = 0.000196 moles

  3. Total volume after mixing:

    • Total volume = 200 mL + 100 mL = 300 mL = 0.300 L

  4. Final concentration of H+:

    • Final concentration = 0.000196 moles / 0.300 L = 0.000653 M

  5. Final pH calculation:

    • pH = -log(0.000653) = 3.18

Notes

  • This example demonstrates how the interaction between a weak acid and a weak base can affect the final pH. The resulting pH shows a slight increase from the original acid, but not significantly high due to the buffering effect of the bicarbonate.

By understanding these examples of determining the final pH after mixing two solutions with different pH values, you can apply these calculations in various practical settings.