Maths Skill: Calculating pH

Question 1

If the hydrogen ion (H+) concentration of a solution is known, the pH can be calculated using the equation:

Answer 1

pH = (minus)log₁₀ [H⁺]

You can find the ‘log’ function on your calculator (‘log’ is the same as ‘log10’ so don’t worry if your calculator doesn’t say ‘log10’)

Question 2

example The hydrogen ion concentration of a solution is 1.6 x 10-4 mol dm-3. Find the pH of this solution.

Answer 2

pH = -log₁₀ [H⁺]

pH = -log₁₀ 1.6 x 10-4 = 3.796

pH = 3.8

Question 3

The hydrogen ion concentration of a solution of sodium hydroxide is 3.5 x 10-11 mol dm-3. Find the pH of this solution.

Answer 3

pH = -log₁₀ [H⁺]

pH = -log₁₀ 3.5 x 10-11 = 10.456

pH = 10.5

Question 4

Don’t forget the minus sign in the formula: pH = -log₁₀ [H⁺]. This is easy to overlook and is a common mistake that students make in exams. Remember: pH must fall between 0 and 14 so if your answer is outside of this range, something has gone wrong!