Last updated: 18 August 2026
Saying that one acid is “stronger” than another is useful, but at A-Level we need a quantitative way to describe that difference. Hydrochloric acid and ethanoic acid, for example, can both donate H⁺ ions in water, yet they do so to very different extents.
This is where the acid dissociation constant, Ka, becomes important. Instead of simply labelling an acid as strong or weak, Ka allows us to compare acid strengths numerically and to calculate equilibrium concentrations such as [H⁺].
The related quantity pKa makes very small Ka values easier to compare. Once the relationships between Ka, pKa, acid strength and [H⁺] are secure, calculations involving weak acids, conjugate bases and later buffer systems become much more systematic.
Diagnostic Quiz
Try these five questions before reading the chapter. They check the equilibrium, logarithm and acid–base ideas that will be used when working with Ka and pKa.
- 5 quick starting-point questions
- Focus on common acid-strength misconceptions
- Every answer option is explained
Strong and weak acids: what does acid strength mean?
Acid strength describes the extent to which an acid dissociates in water. It does not describe how much acid happens to be present in a particular solution.
Consider a monoprotic acid represented by HA:
A strong acid is treated as essentially completely dissociated in aqueous solution. A weak acid, by contrast, only partially dissociates, so significant amounts of both the undissociated acid and its ions remain at equilibrium.
| Feature | Strong acid | Weak acid |
|---|---|---|
| Extent of dissociation | Essentially complete in aqueous solution | Partial |
| Equilibrium description | Products are overwhelmingly favoured | An appreciable amount of undissociated acid remains |
| Typical equation | HCl(aq) → H⁺(aq) + Cl⁻(aq) | CH₃COOH(aq) ⇌ H⁺(aq) + CH₃COO⁻(aq) |
| Routine Ka calculations | Usually unnecessary | Used to describe the dissociation equilibrium |
Strength describes the extent of dissociation. Concentration describes the amount of acid present per unit volume of solution. A concentrated weak acid and a dilute strong acid are both perfectly possible.
Why can we not use the acid concentration directly as [H⁺]?
Suppose a 0.100 mol dm⁻³ solution of CH₃COOH is prepared. It would be incorrect to assume that [H⁺] = 0.100 mol dm⁻³ because only a small fraction of the CH₃COOH molecules dissociate.
At equilibrium, most CH₃COOH remains as undissociated molecules while smaller concentrations of H⁺ and CH₃COO⁻ are present. We therefore need an equilibrium constant to connect these concentrations.
Incorrect idea: a 0.100 mol dm⁻³ monoprotic acid must contain 0.100 mol dm⁻³ H⁺.
Correct reasoning: this approximation is suitable for a strong monoprotic acid that is treated as completely dissociated, but not for a weak acid. For a weak acid, [H⁺] is determined from its dissociation equilibrium.
The acid dissociation constant, Ka
For the general weak monoprotic acid HA:
the acid dissociation constant is:
The square brackets represent equilibrium concentrations. This point is important: the concentrations substituted into an equilibrium expression are the concentrations after equilibrium has been established.
Where does this expression come from?
Acid dissociation in water can be written more explicitly as:
H₂O is the solvent and is present in very large excess. Its effective concentration is essentially constant and is incorporated into the value of Ka. The expression is therefore normally written using H⁺ as convenient shorthand:
For the usual aqueous acid dissociation equilibrium, the pure liquid solvent is omitted from the equilibrium expression. H⁺ is commonly used as shorthand for the hydrated proton in aqueous solution.
What does the magnitude of Ka tell us?
Ka compares the amount of dissociated acid with the amount that remains undissociated at equilibrium.
| Ka | Position of equilibrium | Extent of dissociation | Relative acid strength |
|---|---|---|---|
| Larger | Further towards H⁺ and A⁻ | Greater | Stronger acid |
| Smaller | Further towards HA | Smaller | Weaker acid |
We can therefore summarise the relationship as:
Does Ka change when the acid is diluted?
No. For a particular acid, the value of Ka is fixed at a given temperature. Dilution changes the equilibrium concentrations and causes the equilibrium position to adjust, but the new concentrations still satisfy the same Ka expression.
Like other equilibrium constants, Ka is temperature-dependent. Changing concentration or diluting the solution does not by itself change Ka.
Using pKa to express acid strength
Ka values for weak acids are often very small. Values such as 1.8 × 10⁻⁵ or 6.3 × 10⁻⁸ are manageable individually, but comparing many acids becomes easier if the values are converted onto a logarithmic scale.
The pKa scale is defined by:
To convert back:
Why does a lower pKa mean a stronger acid?
The negative sign reverses the numerical trend. If Ka becomes larger, pKa becomes smaller.
| Ka | pKa | Relative acid strength |
|---|---|---|
| 1.0 × 10⁻³ | 3.00 | Strongest of the three |
| 1.0 × 10⁻⁵ | 5.00 | Intermediate |
| 1.0 × 10⁻⁷ | 7.00 | Weakest of the three |
Ka scale: larger Ka = stronger acid.
pKa scale: smaller pKa = stronger acid.
The two quantities describe the same acid strength; only the numerical direction is reversed.
Worked example: converting Ka to pKa
An acid has Ka = 2.50 × 10⁻⁴. Calculate its pKa.
pKa = 3.60
Worked example: converting pKa to Ka
A weak acid has pKa = 4.20. Calculate Ka.
Ka = 6.31 × 10⁻⁵ mol dm⁻³
Calculating the pH of a weak acid
For a strong monoprotic acid, [H⁺] can often be obtained directly from the concentration because the acid is treated as completely dissociated. A weak acid requires an equilibrium calculation because only part of it dissociates.
Consider a weak monoprotic acid HA with initial concentration c mol dm⁻³:
Build the equilibrium concentrations first
Suppose x mol dm⁻³ of HA dissociates. Each mole of HA that dissociates forms one mole of H⁺ and one mole of A⁻.
| HA | H⁺ | A⁻ | |
|---|---|---|---|
| Initial / mol dm⁻³ | c | Approximately 0 | 0 |
| Change / mol dm⁻³ | −x | +x | +x |
| Equilibrium / mol dm⁻³ | c − x | x | x |
The small H⁺ concentration initially present from water is normally negligible compared with the H⁺ produced by the acid in these calculations.
Substituting the equilibrium concentrations into the Ka expression gives:
Since x = [H⁺], this equation can be solved exactly if necessary.
The two approximations commonly used
For many weak-acid calculations, two simplifications are useful.
- [H⁺] ≈ [A⁻] because each molecule of a simple monoprotic acid that dissociates produces one H⁺ and one A⁻, while the contribution of H⁺ from water is negligible.
- [HA]equilibrium ≈ [HA]initial if only a small fraction of the weak acid dissociates.
The second approximation means:
Therefore:
and hence:
Once [H⁺] is known:
It is not a separate acid formula. It comes from the full equilibrium expression Ka = x²/(c − x) after assuming that x is small compared with c.
Worked example: pH of ethanoic acid
Calculate the pH of 0.100 mol dm⁻³ CH₃COOH when Ka = 1.74 × 10⁻⁵ mol dm⁻³.
Using the weak-acid approximation:
Therefore:
pH = 2.88
Notice that the pH is not 1.00. If 0.100 mol dm⁻³ of a strong monoprotic acid were treated as completely dissociated, [H⁺] would be approximately 0.100 mol dm⁻³. Ethanoic acid is weak, so its [H⁺] is much smaller.
Checking whether the approximation is valid
The amount dissociated in the previous example is approximately 1.32 × 10⁻³ mol dm⁻³ compared with an initial concentration of 0.100 mol dm⁻³.
Only a small fraction of the acid has dissociated, so treating c − x as approximately c is reasonable.
A commonly used practical check is the 5% rule: if the amount dissociated is less than about 5% of the initial concentration, the approximation is usually sufficiently accurate for this type of calculation.
If x is small compared with c: use c − x ≈ c and therefore [H⁺] ≈ √(Kac).
If x is not small compared with c: retain c − x and solve Ka = x²/(c − x) without making the approximation.
Worked example: starting from pKa
A 0.0500 mol dm⁻³ solution of a weak monoprotic acid has pKa = 4.76. Calculate its pH using the weak-acid approximation.
First convert pKa to Ka:
Then:
pH = 3.03
Finding Ka from pH data
The calculation can also run in the opposite direction. If the initial concentration and pH of a weak monoprotic acid are given, we can use the pH to determine the equilibrium concentrations and hence Ka.
First convert pH to [H⁺]:
If the acid is the only significant source of H⁺:
and:
Therefore:
Worked example: calculating Ka from pH
A 0.200 mol dm⁻³ solution of a weak monoprotic acid has pH 2.72. Calculate Ka.
Therefore:
Substituting into the equilibrium expression:
Ka = 1.84 × 10⁻⁵ mol dm⁻³
Ka given, pH required: use the equilibrium expression to find [H⁺], then calculate pH.
pH given, Ka required: convert pH into [H⁺] first, build the equilibrium concentrations, then calculate Ka.
Connecting acid and base strength: KaKb = Kw
Every Brønsted–Lowry acid has a conjugate base. If HA is an acid, then A⁻ is the conjugate base produced when HA donates H⁺.
For the acid:
The conjugate base A⁻ can accept a proton from water:
Its base dissociation constant is:
Multiplying the two expressions gives:
Since:
we obtain:
At 25°C:
At a fixed temperature, KaKb is fixed at Kw. If Ka is large, the corresponding Kb must therefore be small.
The corresponding pK relationship
Taking negative logarithms gives:
At 25°C:
Therefore:
Worked example: finding pKb
An acid has pKa = 4.76 at 25°C. Find the pKb of its conjugate base.
pKb = 9.24
Comparing acids using Ka and pKa
When several acids are given, Ka or pKa provides a direct way to rank their strengths.
| Acid | Ka | pKa | Relative strength |
|---|---|---|---|
| Acid P | 3.2 × 10⁻³ | 2.49 | Strongest |
| Acid Q | 6.3 × 10⁻⁵ | 4.20 | Intermediate |
| Acid R | 2.0 × 10⁻⁷ | 6.70 | Weakest |
Acid P has the largest Ka and the smallest pKa, so its dissociation equilibrium lies furthest towards the ions.
Why pH alone does not measure intrinsic acid strength
The pH of a solution depends on both the strength of the acid and the concentration of the solution. It is therefore unsafe to compare the inherent strengths of acids simply by comparing the pH values of solutions that have different concentrations.
pH describes a particular solution. It depends on the actual [H⁺] in that solution.
Ka and pKa describe acid strength. At the same temperature, they allow different acids to be compared independently of the particular concentrations chosen for their solutions.
Common mistakes with Ka and pKa
| Common mistake | Why it is wrong | Correct approach |
|---|---|---|
| Using concentration to decide whether an acid is strong or weak | Strength and concentration describe different properties | Use extent of dissociation, Ka or pKa to compare acid strength |
| Saying that a smaller Ka means a stronger acid | A smaller Ka means less extensive dissociation | Larger Ka = stronger acid |
| Saying that a larger pKa means a stronger acid | The negative logarithm reverses the numerical trend | Smaller pKa = stronger acid |
| Including H₂O(l) in the Ka expression | The pure liquid solvent is incorporated into the equilibrium constant | For HA, write Ka = [H⁺][A⁻]/[HA] |
| Using initial concentrations directly in the Ka expression | Ka is defined using equilibrium quantities | Work out the equilibrium concentrations first |
| Assuming [H⁺] equals the initial concentration of a weak acid | A weak acid is only partially dissociated | Use its Ka equilibrium to determine [H⁺] |
| Writing [H⁺] = Kac | The simplified equilibrium relationship gives [H⁺]² ≈ Kac | Take the square root: [H⁺] ≈ √(Kac) |
| Using c − x ≈ c without checking whether x is small | The approximation may be inaccurate if a substantial fraction dissociates | Check the percentage dissociation and use the full equation if necessary |
| Thinking dilution changes Ka | The equilibrium composition changes, but Ka is constant at fixed temperature | Remember that equilibrium constants depend on temperature |
| Using KaKb = Kw for unrelated species | The relationship applies to a conjugate acid–base pair | Identify the conjugate pair before applying the relationship |
Ka and pKa checklist
Identify acid strength
- Strong acids are essentially completely dissociated.
- Weak acids establish a dissociation equilibrium.
- Larger Ka means a stronger acid.
- Smaller pKa means a stronger acid.
Write Ka correctly
- Start from HA ⇌ H⁺ + A⁻.
- Use equilibrium concentrations.
- Write Ka = [H⁺][A⁻]/[HA].
- Do not include liquid water.
Calculate weak-acid pH
- Let the amount dissociated be x.
- Use Ka = x²/(c − x).
- If justified, use [H⁺] ≈ √(Kac).
- Calculate pH using −log10[H⁺].
Connect conjugate pairs
- Identify HA and A⁻ as a conjugate pair.
- Use KaKb = Kw.
- At 25°C, pKa + pKb = 14.00.
- Stronger acid means weaker conjugate base.
Mastery Quiz
Now apply the chapter to unfamiliar acid-strength comparisons, logarithmic conversions, weak-acid equilibria and conjugate acid–base relationships.
- 10 application-focused questions
- Includes equilibrium and pH calculations
- Every answer option is explained
Frequently asked questions
Questions students often ask about Ka and pKa
These questions connect acid strength, equilibrium and pH calculations and clarify distinctions that become especially important in later acid–base topics.
Can a weak acid be more concentrated than a strong acid?
Yes. Strength and concentration are independent ideas. A weak acid can be concentrated if a large amount is present per unit volume, while a strong acid can be dilute if only a small amount is present.
Strong and weak describe the extent of dissociation rather than the concentration of the solution.
Why use pKa when Ka already measures acid strength?
Weak-acid Ka values often span many powers of ten. The logarithmic pKa scale converts them into numbers that are easier to compare and work with.
No acid-strength information is lost because Ka and pKa can be converted into each other.
Can a strong acid have a pKa value?
Yes. The pKa concept is not restricted mathematically to weak acids, and sufficiently strong acids can have very small or even negative pKa values.
In routine A-Level aqueous calculations, however, strong acids are usually treated as essentially completely dissociated rather than analysed using the weak-acid Ka method.
Does diluting a weak acid change its Ka?
No, provided the temperature remains unchanged. Dilution changes the equilibrium concentrations and generally increases the fraction of acid that dissociates, but the new concentrations still satisfy the same Ka value.
Why are [H⁺] and [A⁻] equal in the usual weak-acid calculation?
For HA ⇌ H⁺ + A⁻, every mole of HA that dissociates produces one mole of H⁺ and one mole of A⁻. If the contribution of H⁺ from water is negligible, the concentrations produced by the acid are therefore equal.
When can I use [H⁺] ≈ √(Kac)?
The shortcut can be used when the amount of acid that dissociates is small compared with its initial concentration. Under this condition, c − x can be approximated as c.
A useful practical check is that the calculated percentage dissociation should be only a few percent. The commonly used 5% guideline is a convenient test.
What should I do if the weak-acid approximation is not valid?
Return to the full expression Ka = x²/(c − x) and solve for x without replacing c − x by c. This normally gives a quadratic equation.
Is Ka just a special type of equilibrium constant?
Yes. Ka is an equilibrium constant specifically describing acid dissociation. It obeys the same central idea as other equilibrium constants: at a fixed temperature, its value is constant for the specified equilibrium.
Why does a stronger acid have a weaker conjugate base?
A stronger acid has a greater tendency to donate H⁺. The species left after that donation therefore has a smaller tendency to accept H⁺ again.
Quantitatively, KaKb = Kw. At fixed temperature, a larger Ka therefore corresponds to a smaller Kb.
Is a solution with the lower pH always made from the stronger acid?
No. pH depends on both acid strength and concentration. A sufficiently concentrated weak acid can have a lower pH than a very dilute strong acid.
To compare the inherent strengths of acids at the same temperature, compare their Ka or pKa values rather than pH alone.
Ka turns the qualitative idea of acid strength into a measurable equilibrium quantity, while pKa expresses the same information on a convenient logarithmic scale. Larger Ka and smaller pKa both indicate a stronger acid, and the Ka expression provides the link between acid strength and the pH of a weak-acid solution. The relationship KaKb = Kw then connects each acid to its conjugate base, providing the foundation for buffer solutions and more advanced acid–base equilibria.