pH and pOH of Strong Acids and Bases

pH is just a compressed way of writing [H+]. Water solutions span concentrations from about 10 M down to 10⁻¹⁴ M, a range too awkward to graph or compare by eye. Taking -log of that number turns multiplying by ten into subtracting one. That's why a pH of 3 means ten times more H+ than a pH of 4: each whole pH unit is a factor of 10 in concentration, not a fixed amount.

For a strong acid like HNO3, dissociation is complete, so every molecule hands off its proton: [H+] equals the acid's molarity exactly, no equilibrium calculation needed. pH = -log[H+] follows directly. Strong bases work the same way but through OH-. For Ba(OH)2, each formula unit releases two OH- ions, so [OH-] = 2 x the base's molarity. Find pOH = -log[OH-], then use pH + pOH = 14 to get pH. The 14 comes from water's own equilibrium, Kw = [H+][OH-] = 1.0 x 10⁻¹⁴ at 25 C.

This is the simplest case in the unit because there's no equilibrium to solve, just stoichiometry and a logarithm. It sets up everything else: weak acids and bases need an equilibrium expression because they don't fully dissociate, and buffers build on both ideas at once. Get strong acid and base pH down cold, because every other calculation in the unit compares back to this baseline.