pH of a Strong Acid Solution
Calculate the pH of a 0.010 M aqueous solution of hydrochloric acid, HCl, at 25 C.
Given
[HCl] = 0.010 M
HCl is a strong acid: it dissociates 100% in water
Temperature 25 C (standard pH scale).
Find
The pH of the solution.
Principle
Strong acids ionize completely in water, so the hydrogen ion concentration equals the nominal acid concentration (for a monoprotic acid). The pH is then the negative base-10 logarithm of [H+]. No equilibrium expression or approximation is required.
Formula
Solution
Write the dissociation: HCl(aq) -> H+(aq) + Cl-(aq), going to completion because HCl is a strong acid.
Set [H+] = [HCl]initial = 0.010 M (one H+ per HCl, monoprotic).
Compute pH = -log(0.010) = -(-2.00) = 2.00.
Unit check
The argument of a logarithm must be dimensionless; formally we take -log([H+] / 1 M), so pH is a pure number with no units, as required.
What this means physically
A pH of 2.00 means the solution is 100 times more acidic than a pH 3 solution — each pH unit is a factor of 10 in [H+]. Because HCl is strong, the full 0.010 M appears as H+, and no equilibrium calculation is needed.
Students sometimes take the negative log of the pH, or divide the concentration by 2 thinking both H atoms of an acid dissociate — HCl is monoprotic, so [H+] equals the acid concentration exactly once.