pH, acids and bases
Acid–base chemistry is proton-transfer chemistry plus equilibrium. pH is a logarithmic measure of hydronium activity; pKₐ measures the position of an acid-dissociation equilibrium. Keeping those roles distinct makes buffers and titrations much easier to understand.
Brønsted acids and bases
A Brønsted acid donates a proton; a Brønsted base accepts one. In water:
HA + H₂O ⇌ H₃O⁺ + A⁻
HA/A⁻ are a conjugate acid–base pair. Water can act as acid or base depending on its partner.
Strong acids are essentially fully ionized in dilute water; weak acids establish equilibria. “Strong” refers to equilibrium position, not concentration.
pH, pOH and water autoionization
pH = −log a(H₃O⁺)
At 25 °C in dilute solution: Kw ≈ 1.0×10⁻¹⁴, so pH + pOH ≈ 14.
The familiar 0–14 range is not a fundamental boundary. Concentrated solutions can have pH below 0 or above 14, and Kw changes with temperature.
Kₐ and pKₐ
For HA:
Kₐ = a(H₃O⁺)a(A⁻)/a(HA) pKₐ = −log Kₐ
Smaller pKₐ means a stronger acid. Comparing pKₐ values is often more useful than memorizing acid labels because equilibrium direction favors formation of the weaker acid/base pair.
Buffers and Henderson–Hasselbalch
For an idealized weak-acid buffer:
pH = pKₐ + log([A⁻]/[HA])
The equation is most reliable when both conjugate forms are present in substantial amounts and activities are approximated by concentrations. Buffer capacity is greatest when concentrations are reasonably high and the ratio is near 1.
pH / pKₐ ratio explorer
Estimated pH =
Titration and equivalence
In a strong-acid/strong-base titration, equivalence is set by stoichiometric neutralization, not by “pH = 7” as a universal rule. Weak-acid/strong-base equivalence solutions contain the conjugate base and are typically basic.
At half-equivalence in a simple weak-acid titration, [A⁻] = [HA], so pH = pKₐ. This is a chemically meaningful point, not merely a shortcut.
Acid–base reasoning beyond one formula
Conjugate strength follows equilibrium
A strong acid has a very weak conjugate base because proton loss lies strongly toward products. Conversely, the conjugate base of a weak acid retains appreciable proton affinity. Comparing pKₐ values therefore predicts proton-transfer direction.
For B⁻ + HA ⇌ HB + A⁻, equilibrium favors the side containing the weaker acid—the acid with the larger pKₐ—under comparable solvent conditions.
Polyprotic acids ionize stepwise
H₂CO₃, H₃PO₄ and other polyprotic acids have successive Kₐ values. The first proton is generally lost more easily than the second because removing a proton from an increasingly negative species is less favorable.
Each step has its own pKₐ and can create its own buffer region in a titration curve.
Activities matter in concentrated solutions
Rigorous pH uses hydronium activity rather than bare molar concentration. In dilute solutions activity and concentration are close enough for introductory calculations; at higher ionic strength, electrostatic interactions make activity coefficients important.
This is another reason pH is not simply “the number of H⁺ ions.” It is a thermodynamic measure connected to chemical potential.
Worked example: a weak-acid buffer
An acetate buffer contains 0.20 M CH₃COOH and 0.10 M CH₃COO⁻. With pKₐ = 4.76:
pH = 4.76 + log(0.10/0.20) = 4.46.
The result is below pKₐ because the acid form is more abundant. If equal amounts of acid and conjugate base were present, the logarithm would be zero and pH would equal pKₐ.
When Henderson–Hasselbalch should not be the first move
A pure weak acid before any conjugate base has been added is better treated with the Kₐ equilibrium directly. The buffer equation is a rearranged equilibrium relation, not a universal pH formula.
Strong-acid calculation before equilibrium approximations
For 1.0×10⁻³ M HCl in sufficiently dilute water, complete dissociation gives [H₃O⁺] ≈ 1.0×10⁻³ M and pH ≈ 3.00. At much lower acid concentrations, water autoionization can no longer be ignored; simply taking −log of the formal acid concentration eventually becomes wrong.
Indicators and titration curves
An acid–base indicator is itself a weak acid/base pair whose two forms absorb visible light differently. Its useful transition range lies near its pKₐ, typically within roughly one pH unit. A good titration indicator changes color within the steep region around the equivalence point.
A pH electrode avoids subjective color matching and measures an electrochemical potential related to hydrogen-ion activity. Calibration with known buffers is essential for quantitative work.
Exercises
Tenfold change
How does [H₃O⁺] change when pH rises from 3 to 4?
Solution
It becomes ten times smaller.
Buffer midpoint
What is pH when [A⁻] = [HA]?
Solution
pH = pKₐ.
Strong versus concentrated
Can a weak acid solution be more concentrated than a strong acid solution?
Solution
Yes. Strength is an equilibrium property; concentration is amount per volume.