Acids, Bases & pH

Acids, bases and pH

pH measures hydrogen-ion concentration in powers of ten. Add a drop of acid to a glass of pure water and watch how far one drop moves it.

Plate Add drops of 0.1 M hydrochloric acid or sodium hydroxide, or drag the pointer along the scale. The loupe shows a statistical sample of the ions expected in one cubic micrometre: H₃O⁺ (orange), OH⁻ (blue) and the Cl⁻ or Na⁺ that came with the acid or base (grey rings), so the charges balance. The 33 billion water molecules in that volume are not drawn. Below about pH 4.4 there are too many to draw, so a nested inset magnifies a sample ten times smaller on each side (a thousandth of the volume). Each step of one pH unit is a factor of ten. The solution is colored as a universal indicator would show it (an illustration, not a measurement).

Begin with the pH scale →

Pure water at 25 °C holds about six thousand trillion hydronium ions per glass. One drop of dilute acid multiplies that number by several hundred. Pour in a whole 100 mL bottle of the same acid and you gain only three more steps. Everything on this site follows from those two facts: acidity is about how many hydrogen ions are present, and pH reads that amount, as a concentration (strictly, an activity), on a scale of powers of ten.

Acids give protons; bases take them. How far each transfer goes is settled by an equilibrium constant, and the pH you measure is whatever value makes every positive charge in the solution balance every negative one. Every figure here solves that balance exactly, with no textbook shortcuts, and shows you where the shortcuts hold and where they fail.

Contents

How this is made and checked

Every number in a figure comes from one small equilibrium engine that solves the full charge balance, using equilibrium constants from NIST’s critical review of buffer ionization data and the 2024 IAPWS formulation for water. It is tested against published worked examples, and an independent test suite, written without reading the engine’s code, checks it again. Every claim on the site is listed with its source, and every simplification is named next to the figure that makes it. More about how it is checked.