Calculated using an ICE table and Ka, often with the small-x approximation.
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To find the pH of a weak acid solution, set up an ICE table with the initial, change and equilibrium concentrations and write the Ka expression in terms of the unknown x. If x is much smaller than the initial concentration, typically less than 5 percent of it, the term C - x can be approximated as C, which gives x equal to the square root of Ka times C. Otherwise the full quadratic must be solved, and the approximation should be checked afterwards. Water's own contribution to hydrogen ions is negligible for weak acids that are not extremely dilute. This method is the standard approach in general chemistry and analytical work.
Key ideas: Set up HA with initial C, change -x, +x, +x, then Ka = x^2/(C - x). If C/Ka exceeds about 400 (or x under 5 percent of C), approximate x = sqrt(Ka C). Otherwise solve x^2 + Ka x - Ka C = 0 using the quadratic formula. Then pH = -log x.
Common mistakes and connections: Mistakes: not verifying the approximation, rejecting the wrong quadratic root (take the positive one smaller than C), and ignoring water for extremely dilute acids. Check that pH is above the strong-acid value. The same method works for weak bases with Kb and OH-.
Hydrofluoric acid starts near pH 2.1 at 0.1 M because it is only partly ionized, then buffers at its pKa 3.17 before the steep rise to equivalence. The interactive lesson shows this as a live animation or chart.
For 0.10 M HF with Ka 6.8 x 10^-4, x is about 8.2 x 10^-3 M, which is more than 5 percent of the initial concentration, so the quadratic must be used.
Calculated using an ICE table and Ka, often with the small-x approximation.
pH of Weak Acid Solutions is a intermediate topic in Acids, Bases & Electrochemistry. It builds on the vocabulary of beginner topics in this area.
Study these earlier topics in Acids, Bases & Electrochemistry first: Acid Dissociation Constant, Ka and Kb Relationship, Percent Ionization.
The next topics in Acids, Bases & Electrochemistry are Polyprotic Acids and Acid Strength and Structure.
Yes. The interactive lesson includes a self-check question on pH of Weak Acid Solutions, and the Acids, Bases & Electrochemistry quiz draws on every topic in this area.
pH of Weak Acid Solutions is topic 16 of 105 in Acids, Bases & Electrochemistry.