How to Calculate pH and Acidity
Learn how to calculate pH from hydrogen ion concentration using the formula pH = −log[H⁺]. This guide covers the pH scale, buffer calculations, and real-world chemistry applications.
What is pH?
pH is a logarithmic scale that measures the concentration of hydrogen ions (H⁺) in a solution, indicating how acidic or basic it is. The scale typically runs from 0 to 14: values below 7 are acidic, 7 is neutral (pure water), and above 7 is basic (alkaline). Each whole number change represents a 10-fold change in H⁺ concentration because the scale is logarithmic.
The pH Formula
pH = −log₁₀[H⁺], where [H⁺] is the molar concentration of hydrogen ions in mol/L (also written as M). A solution with [H⁺] = 0.001 M = 10⁻³ M has a pH of −log(10⁻³) = 3, which is mildly acidic (similar to vinegar). The negative sign ensures that higher H⁺ concentration gives a lower (more acidic) pH value.
Calculating [H⁺] from pH
Rearranging gives [H⁺] = 10^(−pH). A solution with pH 5 has [H⁺] = 10⁻⁵ = 0.00001 mol/L. This is the inverse operation: while pH compresses wide ranges into a manageable scale, this formula expands them back to actual concentrations used in stoichiometry and reaction rate calculations.
pOH and the Relationship to pH
pOH measures hydroxide ion concentration: pOH = −log₁₀[OH⁻]. At 25°C, pH + pOH = 14 (the water dissociation constant Kw = 10⁻¹⁴). If a solution has pOH = 4, then pH = 14 − 4 = 10, indicating a basic solution. This relationship allows you to calculate either H⁺ or OH⁻ concentration from a single pH measurement.
Strong vs. Weak Acids
Strong acids (HCl, H₂SO₄, HNO₃) dissociate completely in water, so [H⁺] equals the initial acid concentration. A 0.01 M HCl solution has [H⁺] = 0.01 M and pH = 2. Weak acids (acetic acid, carbonic acid) only partially dissociate; their pH is calculated using the acid dissociation constant Ka: [H⁺] = √(Ka × C), where C is the initial concentration.
Buffer Solutions
A buffer resists pH change and is calculated using the Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA]), where [A⁻] is the conjugate base concentration and [HA] is the weak acid concentration. A buffer is most effective when pH ≈ pKa and the acid-to-base ratio is between 0.1 and 10. Biological systems such as blood rely on the bicarbonate buffer system to maintain pH near 7.4.
Real-World pH Applications
Soil pH affects nutrient availability — most crops prefer pH 6–7. Swimming pool water should be maintained at pH 7.2–7.6 for comfort and disinfectant effectiveness. Industrial processes from food production to pharmaceutical synthesis require precise pH control. pH meters measure voltage across a glass electrode to determine [H⁺] electronically, offering precision far better than paper litmus strips.
Try These Calculators
Put what you learned into practice with these free calculators.
Related Guides
How to Calculate Molar Mass
Learn how to calculate the molar mass of any compound by summing atomic masses from the periodic table. Includes worked examples for simple and complex molecules.
How to Calculate Density
Learn how to calculate density using the formula density = mass / volume. Covers units, measurement techniques, buoyancy, and real-world applications with worked examples.
How to Calculate Wavelength and Frequency
Learn how to calculate wavelength and frequency of electromagnetic and sound waves using the wave equation v = fλ. Understand how these properties relate to the electromagnetic spectrum and acoustics.