pKa

pKa measures how strong a weak acid is. It is the negative logarithm of the acid dissociation constant: pKa = −log₁₀ Ka. The lower the pKa, the more the acid dissociates and the stronger it is. Ethanoic acid (acetic acid) has a pKa of 4.74, while hydrocyanic acid, a much weaker acid, has a pKa of 9.31.

The Ka equation: the acid dissociation constant

A weak acid HA only partly dissociates in water. AQA's A-level specification defines Ka as the dissociation constant for a weak acid, the equilibrium constant for:

HA(aq) ⇌ H⁺(aq) + A⁻(aq)

Its unit is mol dm⁻³. A bigger Ka means more of the acid has split into ions at equilibrium, so it is a stronger acid. The trouble is that Ka values are tiny and awkward, like 1.8 × 10⁻⁵ or 4.9 × 10⁻¹⁰. That is why chemists use pKa.

What is pKa?

Taking −log turns those powers of ten into simple numbers, the same way pH does for [H⁺]. Because of the minus sign, the scale runs backwards: a lower pKa means a larger Ka and a stronger acid. Each step of 1 in pKa is a factor of 10 in Ka. pKa has no unit.

How to calculate pKa from Ka

Hypochlorous acid, HOCl, has Ka = 2.9 × 10⁻⁸ mol dm⁻³. On a calculator: pKa = −log₁₀(2.9 × 10⁻⁸) = 7.54.

How to calculate Ka from pKa

Methanoic acid (formic acid) has pKa = 3.74. Ka = 10⁻³·⁷⁴ = 1.8 × 10⁻⁴ mol dm⁻³. AQA lists converting Ka into pKa and back as a skill you need.

pKa values of common acids

The Ka values are from OpenStax's table of ionisation constants of weak acids, at 25 °C; the pKa values are worked out from them.

Hydrofluoric acid's Ka is 6.4 × 10⁻⁴ ÷ 4.9 × 10⁻¹⁰, about 1.3 million times bigger than hydrocyanic acid's, yet their pKa values differ by only about 6. Strong acids such as hydrochloric acid dissociate completely, so their pH calculations don't need Ka at all.

pKa vs pH

pH describes a solution: how many H⁺ ions it has right now. pKa describes an acid: how readily it gives up H⁺. A bottle of ethanoic acid always has pKa 4.74, but its pH depends on how concentrated it is.

The two link up neatly. Rearranging the Ka expression gives pH = pKa + log₁₀([A⁻] ÷ [HA]). So:

Worked examples

Example 1: pH of a weak acid from its pKa

Find the pH of 0.050 mol dm⁻³ ethanoic acid, pKa 4.74.

1. Ka = 10⁻⁴·⁷⁴ = 1.8 × 10⁻⁵ mol dm⁻³.
2. Each HA that dissociates gives one H⁺ and one A⁻, so [H⁺] = [A⁻]. So little dissociates that [HA] stays about 0.050. Then Ka = [H⁺]² ÷ 0.050.
3. [H⁺] = √(1.8 × 10⁻⁵ × 0.050) = 9.5 × 10⁻⁴ mol dm⁻³.
4. pH = −log₁₀(9.5 × 10⁻⁴) = 3.02.

Example 2: pKa from a measured pH

A 0.25 mol dm⁻³ solution of a weak acid has pH 2.70. Find Ka and pKa.

1. [H⁺] = 10⁻²·⁷⁰ = 2.0 × 10⁻³ mol dm⁻³.
2. Ka = [H⁺]² ÷ [HA] = (2.0 × 10⁻³)² ÷ 0.25 = 1.6 × 10⁻⁵ mol dm⁻³.
3. pKa = −log₁₀(1.6 × 10⁻⁵) = 4.80.

Example 3: pKa at half-neutralisation

AQA suggests finding Ka by measuring the pH at half-neutralisation. Titrate a weak acid with sodium hydroxide and note the volume at the end point. Halfway there, half the HA has become A⁻, so [HA] = [A⁻] and they cancel in the Ka expression: Ka = [H⁺], so pH = pKa.

If the end point is at 24.0 cm³ and the pH at 12.0 cm³ is 4.62, then pKa = 4.62 and Ka = 10⁻⁴·⁶² = 2.4 × 10⁻⁵ mol dm⁻³. The concentration of the acid doesn't matter.

Example 4: the pH of a buffer

A buffer contains 0.40 mol dm⁻³ hypochlorous acid (pKa 7.54) and 0.10 mol dm⁻³ sodium hypochlorite. Find its pH.

1. In a buffer the salt supplies almost all the A⁻, so [A⁻] = 0.10 and [HA] = 0.40.
2. pH = pKa + log₁₀([A⁻] ÷ [HA]) = 7.54 + log₁₀(0.10 ÷ 0.40).
3. log₁₀(0.25) = −0.60, so pH = 7.54 − 0.60 = 6.94.

You can also work straight from Ka: [H⁺] = Ka × [HA] ÷ [A⁻] = 2.9 × 10⁻⁸ × 0.40 ÷ 0.10 = 1.16 × 10⁻⁷, and −log₁₀ of that is also 6.94. A buffer works best when its pH is close to the acid's pKa, where there is plenty of both HA and A⁻. The pH Calculator checks weak acid and buffer answers, and the pH calculator guide has more examples.

Try it

pH Calculator

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Common mistakes

• Thinking a higher pKa is a stronger acid. It is the other way round: lower pKa, stronger acid.
• Forgetting the minus sign. pKa = −log₁₀ Ka. Without it, pKa comes out negative for every weak acid.
• Confusing pKa with pH. pKa belongs to the acid and doesn't change with concentration; pH does.
• Using the weak acid formula on a strong acid. Strong acids dissociate completely, so [H⁺] is just the acid concentration for a monoprotic one.
• Putting the salt concentration into Ka for a lone weak acid. [H⁺] = [A⁻] only when no salt has been added. In a buffer, [A⁻] comes from the salt.
• Giving units to pKa. Ka has units of mol dm⁻³; pKa has none.

Acids and bases are A-level only in AQA's specification, so practise them on today's A-level Chemistry: Year 2 short timed paper. For the basics of pH, see how to calculate pH, and for equilibrium constants in general, dynamic equilibrium.

Read next

Chemistry · Acids and basespH calculator: strong and weak acids, bases and buffersFree pH calculator: the pH of strong and weak acids and bases from molarity, buffers by Henderson-Hasselbalch, and Ka from a measured pH, with steps.