The pH scale and what it measures
What pH actually measures: the concentration of H₃O⁺ ions
pH is related to concentration
pH is not an arbitrarily invented quantity: it measures the concentration of oxonium ions (H₃O⁺) present in the solution. The more H₃O⁺ ions there are per litre of solution, the lower the pH (acidic solution); the fewer there are, the higher the pH (basic solution).
The origin of H₃O⁺ ions
In water, H₃O⁺ ions (also known as hydronium ions) are formed when an acid species donates an H⁺ ion to a water molecule: H⁺ + H₂O → H₃O⁺. An acidic solution therefore has a higher concentration of H3O+ than pure water (10⁻⁷ mol/L at 25°C).
A precise mathematical relationship
The exact relationship, discussed in detail in the following chapter, is:
pH = -log[H3O+]
where [H3O+] denotes the concentration of H3O+ ions, expressed in mol/L. The ‘minus’ sign is important: as [H₃O⁺] is always less than 1 mol/L in typical cases, its logarithm is negative, and the minus sign makes the pH positive.
Practical example
A solution with an H3O+ concentration of 1.0 × 10⁻³ mol/L has a pH of 3 (since -log(10⁻³) = 3). This is a distinctly acidic solution.
Common mistake
The most common misconception is to believe that pH and the [H₃O⁺] concentration vary in the same direction. The opposite is true: when [H₃O⁺] INCREASES, the pH DECREASES. A solution with a very high concentration of H₃O⁺ ions is very acidic, so its pH is low, not high.