pH and pKₐ

8.7 pH & pKₐ

Slide pH across sigmoidal HA and A⁻ speciation curves and watch a particulate beaker flip its mix at pKₐ. Compare 8 weak acids to see how each 1-unit gap shifts the ratio 10×.

Speciation Curve8 Weak AcidsDominant FormpH − pKₐ

Topic 8.7

pH and pK_a

Explain the relationship between the predominant form of a weak acid or base in solution at a given pH and the pK_a of the conjugate acid or the pK_b of the conjugate base.

The protonation state of an acid or base — the relative concentrations of HA and A⁻ — can be predicted by comparing the solution pH to the pK_a of the acid in that solution:

pH < pK_a → the acid form (HA) has the higher concentration.
pH > pK_a → the base form (A⁻) has the higher concentration.
pH = pK_a → equal concentrations.

The rule follows immediately from Henderson–Hasselbalch: pH − pK_a = log([A⁻]/[HA]). A positive difference means the log is positive, so the ratio exceeds 1. Every unit of difference is a factor of ten in the ratio — at pH two units above pK_a, the base form outnumbers the acid form 100 to 1.

A memory aid: low pH means lots of protons around, so the species holds onto its proton.

Indicators are substances that exhibit different properties, such as color, in their protonated versus deprotonated states — which makes that property respond to the pH of the solution. An indicator is itself a weak acid: HIn ⇌ H⁺ + In⁻, with the two forms differently colored.

EK 8.7.A.3 gives the selection rule: to ensure accurate results in a titration, choose an indicator whose pK_a is close to the pH at the equivalence point. An indicator changes color over roughly pK_a ± 1, so matching it to the equivalence pH makes the endpoint coincide with the equivalence point.

Practical consequences: phenolphthalein (pK_a ≈ 9.4) suits weak acid/strong base titrations; methyl red (pK_a ≈ 5.1) suits weak base/strong acid titrations; either works for strong/strong because the pH jump there is so steep.

Key points

pH below pK_a → protonated form dominates. pH above pK_a → deprotonated form dominates.
Each pH unit away from pK_a is a factor of ten in the [A⁻]/[HA] ratio.
Indicators are weak acids whose two protonation states differ in color.
Choose an indicator with pK_a near the equivalence-point pH.

Equations

$pH - p K_{a} = lo g \frac{[ A ^{-} ]}{[ HA ]}$
not on the sheetA rearrangement of the Henderson–Hasselbalch equation on the sheet.

Common mistakes

Reversing the rule. Low pH favors the acid (protonated) form.
Picking an indicator by color preference rather than by pK_a.
Assuming any indicator works for any titration. A mismatched indicator gives a systematically wrong endpoint.
Forgetting that indicators are themselves weak acids — which is why adding too much perturbs the titration.

Worked example

Benzoic acid has pK_a = 4.20. (a) In a solution buffered at pH 6.20, what is the ratio of benzoate to benzoic acid? (b) Which form predominates in the stomach at pH 2.0? (c) Would phenolphthalein (pK_a ≈ 9.4) or methyl red (pK_a ≈ 5.1) be the better indicator for titrating benzoic acid with NaOH?

(a) Ratio at pH 6.20.
pH − pK_a = log([A⁻]/[HA])
6.20 − 4.20 = 2.00 = log(ratio)
ratio = 10² = 100 : 1 benzoate to benzoic acid

(b) At pH 2.0. pH (2.0) is below pK_a (4.20), so the protonated form, benzoic acid (HA), predominates. Quantitatively, 2.0 − 4.20 = −2.20, so [A⁻]/[HA] = 10⁻²·²⁰ ≈ 0.0063 — about 160 molecules of benzoic acid for each benzoate ion.

(c) Indicator choice: phenolphthalein. Titrating a weak acid with a strong base gives an equivalence point above pH 7, typically around pH 8.5–9, because the conjugate base benzoate remains in solution and reacts with water to produce hydroxide. Phenolphthalein’s pK_a of about 9.4 places its color change in that region, so its endpoint nearly coincides with the equivalence point. Methyl red would change color around pH 5, far too early — the endpoint would occur well before the equivalence point and the calculated acid concentration would be too low.

Full notes for topic 8.7 →