# 1.4.9 Maths Skill: Calculating pH

### Maths Skill: Calculating pH

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

pH = -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’)

#### Worked Example

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

The pH of the solution is:

pH = -log₁₀ [H⁺]

pH = -log₁₀ 1.6 x 10-4 = 3.796

pH = 3.8

#### Worked Example

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.

The pH of the solution is:

pH = -log₁₀ [H⁺]

pH = -log₁₀ 3.5 x 10-11 = 10.456

pH = 10.5

#### Worked Example

Ethanoic acid (also known as acetic acid) is a weak acid produced by wood ants that they can spray at predators as a defence mechanism. The hydrogen ion concentration of a sample of ethanoic acid taken from some wood ants was 8.39 x 10-6 mol dm-3. Find the pH of the ethanoic acid produced by wood ants.

The pH of the solution is:

pH = -log₁₀ [H⁺]

pH = -log₁₀ 8.39 x 10-6 = 5.076

pH = 5.08

#### Exam Tip

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! Also, as seen in worked examples above, the question may give you a clue as to what your answer should roughly be. For example, we know that sodium hydroxide is an alkali, so a pH of 10.5 makes sense and we are told that the ethanoic acid produced by wood ants is a weak acid, so 5.08 makes sense too! ### Author: Amelia

While studying Biochemistry at Oxford University, Amelia started her own tutoring service, helping to connect Science tutors with students in her local area. Amelia has experience teaching the sciences and Maths at all levels to UK and international students and, as well as being our Biology Lead, designs revision resources for Chemistry.
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