pH Calculations
Learning Objectives
The ionic product of water, the pH scale and the use of pH in the measurement and calculations of strengths of acids and bases and dilutions of solutions (calculations involving acidity constants are not required)
Summary Notes
The pH scale (istockphoto)
The strength of an acid or base solution can be measured along the pH scale.
pH is the measure of the concentration of hydronium (H₃O⁺) ions present.
To find the concentration of hydronium ions, given the pH:
Eg. 0.0005 M solution of H₂SO₄ is prepared by adding water. Calculate pH of solution.
H₂SO₄ (l) + 2H₂O (l) → 2H₃O⁺(aq) + SO₄⁻² (aq)
[H₃O⁺] = 2 x [H₂SO₄] pH = -log₁₀[H₃O⁺]
[H₃O⁺] = 0.001 M pH = -log 0.001
pH = 3
Dilution of Acids
When an acid undergoes dilution, it's concentration changes which then affects the value of the pH.
The method for calculating dilution of acids and bases is using the equation:
Eg. 250.0 mL of a solution of HCl of pH 2 is diluted to a new pH of 5. How much water has been added into the solution?
[H₃O⁺] = 10⁻² c₁v₁ = c₂v₂ v₂ = v₁ + water
[H₃O⁺] = 0.01 M 0.01 x (25/1000) = 0.00001 x v₂ water = v₂ - v₁
[H₃O⁺] = 10⁻⁵ v₂ = 250 L water = 250 - 0.25
[H₃O⁺] = 0.00001 M water = 249.8 L
Ionic Product of Water
In every aqueous solution there will always be some hydronium (H₃O⁺) ions and some hydroxide (OH⁻) ions.
The product of their concentrations is always equals 10⁻¹⁴.
This means that you can always find the concentration of hydronium or hydroxide ions in a given solution if you have information about the other ion.
Eg. A solution of Mg(OH)₂ is found to have a concentration of 0.015 M. What is the pH of this solution?
[OH⁻] = 2 x [Mg(OH)₂] 2. [H₃O⁺] x [OH⁻] = 10⁻¹⁴ 3. pH = -log [H₃O⁺]
[OH⁻] = 0.030 M [H₃O⁺] = 10⁻¹⁴/0.030 pH = -log (3.33 x 10⁻¹³ )
[H₃O⁺] = 3.33 x 10⁻¹³ M pH = 12.48 = 12.5 (3sf)
The ionic product of water exists because water can ionise itself using the following equation:
Videos to help build your understanding
Sample pH Calculations
Practice Material
Teacher's Tips:
Make sure you familiarise yourself with which buttons to press on your scientific calculator to give you the correct functions. Often students make mistakes in their calculations because they are not making full use of their calculator's functionality
Remember to check if your acids are polyprotic. You will need to utilise stoichiometry/mole ratios to solve for those that are