pH and Hydrogen Ion Concentration

Defining pH

The pH scale provides a convenient way to express the acidity or alkalinity of a solution. It was introduced by Søren Sørensen in 1909 and is defined as:

pH = -log₁₀[H⁺]

where [H⁺] is the concentration of hydrogen ions in mol dm⁻³. Because the logarithm is base 10, each unit change in pH represents a tenfold change in hydrogen ion concentration.

The reverse calculation is equally important:

[H⁺] = 10⁻ᵖᴴ

These two equations are the foundation of every pH calculation you will meet at A-Level.

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Worked Example: pH of a Strong Acid

Calculate the pH of a 0.050 mol dm⁻³ solution of HCl.

HCl is a strong acid, so it fully dissociates:

HCl → H⁺ + Cl⁻

Therefore [H⁺] = 0.050 mol dm⁻³.

pH = -log₁₀(0.050) pH = -(-1.30) pH = 1.30

This is straightforward because the strong acid fully dissociates — every molecule of HCl produces one H⁺ ion.

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Worked Example: [H⁺] from pH

A solution has a pH of 3.40. Calculate the hydrogen ion concentration.

[H⁺] = 10⁻³·⁴⁰ [H⁺] = 3.98 × 10⁻⁴ mol dm⁻³

Always give your answer to the appropriate number of significant figures (usually 3 s.f. for Edexcel).