The Acid Dissociation Constant, Ka
Simple Explanation
Ka is the equilibrium constant for a weak acid's ionisation — it quantifies exactly how far a weak acid ionises. A larger Ka means a stronger weak acid (more ionised); a smaller Ka means a weaker one (less ionised).
Why Do We Need It?
Ka lets chemists precisely rank and compare the strength of different weak acids, and — crucially — calculate the actual pH of a weak acid solution, which cannot be found just from its concentration the way a strong acid's pH can.
Formula
Acid Dissociation Constant, Ka
For HA ⇌ H⁺ + A⁻: Ka = [H⁺][A⁻] / [HA]
Quantifies how much a weak acid ionises in water — a larger Ka means a stronger (more ionised) weak acid.
- Ka
- — the acid dissociation constant, in mol/L
- [H⁺]
- — hydrogen ion concentration at equilibrium, in mol/L
- [A⁻]
- — concentration of the conjugate base at equilibrium, in mol/L
- [HA]
- — concentration of the undissociated weak acid at equilibrium, in mol/L
When to use it: Whenever you need to quantify or compare the strength of weak acids, or calculate the pH of a weak acid solution.
Worked Example
Calculate the pH of a weak acid solution
Acetic acid (Ka = 1.8 × 10⁻⁵) is dissolved to make a 0.10 mol/L solution. Find [H⁺] and the pH (assume the amount ionised is small compared to 0.10 mol/L).
Why Does This Work?
The Ka expression is simply the equilibrium constant expression (from chemical equilibrium) applied to a weak acid's ionisation reaction — assuming the ionised amount is small compared to the starting concentration simplifies the algebra dramatically, and works well whenever Ka is small relative to the initial concentration.
Real-Life Example
Ranking the strength of household weak acids
Citric acid, acetic acid, and carbonic acid are all weak acids found in food and drinks.
Comparing their Ka values directly ranks their strength — citric acid (Ka₁ ≈ 7.4 × 10⁻⁴) is noticeably stronger than acetic acid (Ka ≈ 1.8 × 10⁻⁵), which is in turn stronger than carbonic acid (Ka₁ ≈ 4.3 × 10⁻⁷), explaining why lemon juice tastes more sour than vinegar at similar concentrations.
Practice
A weak acid has Ka = 4.0 × 10⁻⁶ and a starting concentration of 0.25 mol/L. Estimate [H⁺] (in mol/L), assuming the ionised amount is small compared to 0.25.
HardCommon mistake
Forgetting that the simplifying assumption (ionised amount is negligible compared to starting concentration) only works well when Ka is small and concentration is not too dilute — for very dilute weak acid solutions or relatively larger Ka values, the full quadratic equation is needed for an accurate answer.
Quick Review
- Ka = [H⁺][A⁻] / [HA] — a larger Ka means a stronger weak acid.
- Ka lets you calculate a weak acid solution's actual pH.
- The simplifying assumption (x small vs. starting concentration) works when Ka is small.