By Robert Boumis – Updated Aug 30, 2022
The pH scale quantifies how acidic or basic a substance is, a cornerstone concept in chemistry, biology, geology, and many applied sciences. Mastery of pH allows scientists to communicate critical properties of materials with precision.
pH, always written in lowercase, measures the concentration of hydrogen ions (H⁺) in a solution. The scale ranges from 0 to 14, with 7 representing neutral pure water. Values below 7 denote increasing acidity, while values above 7 indicate increasing alkalinity. Extremely acidic or basic solutions can be corrosive.
The scale is logarithmic, meaning each unit change corresponds to a ten‑fold difference in hydrogen ion concentration. For instance, a solution with a pH of 4 contains ten times more H⁺ than a solution with a pH of 5.
Mathematically, pH is defined as the negative base‑10 logarithm of the hydrogen ion concentration (expressed in moles per liter, or molarity):
pH = –log₁₀[H⁺]
This conversion simplifies the representation of hydrogen ion levels, making it easier to compare solutions.
Suppose you have 1 L of a solution containing 0.02 g of hydrogen. Since one mole of hydrogen is approximately 1 g, the molarity is 0.02 mol L⁻¹ (or 2 × 10⁻² M). Taking the negative log gives:
pH = –log₁₀(2 × 10⁻²) ≈ 1.7 (rounded to 2 for simplicity). Thus, the solution is strongly acidic.
pOH, the negative log of hydroxide ion concentration, provides an indirect route to pH:
pOH = –log₁₀[OH⁻]
Because [H⁺][OH⁻] = 1 × 10⁻¹⁴ at 25 °C, pH and pOH are related by:
pH + pOH = 14 → pH = 14 – pOH
For example, a pOH of 12 yields a pH of 2. The reverse calculation uses 14 – pH = pOH.
