Acid Dissociation Constant (Ka)
The acid dissociation constant (Ka) is the equilibrium constant for the ionisation of an acid in water, quantifying the extent to which an acid donates its proton to water at a given temperature. A large Ka (> 1) indicates a strong acid that dissociates almost completely, while a small Ka (< 10⁻³) indicates a weak acid with limited dissociation. Ka values are fundamental in predicting reaction directions, calculating pH of weak acid solutions, and designing buffer systems.
Key Formula
Ka = [H⁺][A⁻] / [HA]
LaTeX: K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}
| Symbol | Meaning | Unit |
|---|---|---|
| Ka | Acid dissociation constant | mol/L |
| [H⁺] | Equilibrium concentration of hydrogen ions | mol/L |
| [A⁻] | Equilibrium concentration of conjugate base | mol/L |
| [HA] | Equilibrium concentration of undissociated acid | mol/L |
Worked Example
Problem
Acetic acid (CH₃COOH) has Ka = 1.8 × 10⁻⁵. Calculate the pH of a 0.1 mol/L acetic acid solution.
Solution
Step 1: Write equilibrium: CH₃COOH ⇌ H⁺ + CH₃COO⁻ Step 2: Let x = [H⁺] = [CH₃COO⁻] at equilibrium; [CH₃COOH] ≈ 0.1 - x ≈ 0.1 (x is small) Step 3: Ka = x² / 0.1 → x² = 1.8 × 10⁻⁵ × 0.1 = 1.8 × 10⁻⁶ Step 4: x = √(1.8 × 10⁻⁶) = 1.34 × 10⁻³ mol/L Step 5: pH = -log(1.34 × 10⁻³) = 2.87
Answer
pH = 2.87
Ka Values of Common Weak Acids at 25 °C
| Acid | Formula | Ka | pKa |
|---|---|---|---|
| Acetic acid | CH₃COOH | 1.8 × 10⁻⁵ | 4.74 |
| Carbonic acid (1st) | H₂CO₃ | 4.3 × 10⁻⁷ | 6.37 |
| Hydrofluoric acid | HF | 6.8 × 10⁻⁴ | 3.17 |
| Ammonium ion | NH₄⁺ | 5.6 × 10⁻¹⁰ | 9.25 |
| Hydrocyanic acid | HCN | 6.2 × 10⁻¹⁰ | 9.21 |
| Phenol | C₆H₅OH | 1.0 × 10⁻¹⁰ | 9.99 |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Water Ionization Constant (Kw)
The water ionization constant (Kw) is the equilibrium constant for the self-ionisation of water, defined as the product of the molar concentrations of hydrogen ions and hydroxide ions in pure water at a given temperature. At 25 °C, Kw = 1.0 × 10⁻¹⁴ mol²/L², which establishes the fundamental link between pH and pOH. Kw increases with temperature (water ionises more at higher temperatures), so the neutral pH shifts below 7 at elevated temperatures.
Buffer Solution
A buffer solution is an aqueous system that resists significant changes in pH when small amounts of acid or base are added, typically composed of a weak acid and its conjugate base (or a weak base and its conjugate acid) in similar concentrations. Buffers operate by consuming added H⁺ or OH⁻ through equilibrium reactions, maintaining the pH within a narrow range. Buffer systems are critical in biological organisms (blood pH 7.35–7.45 maintained by carbonate/bicarbonate), pharmaceuticals, laboratory experiments, and industrial fermentation.
pH Scale
The pH scale is a logarithmic measure of the hydrogen ion concentration [H⁺] in a solution, ranging from 0 to 14 at 25 °C, where values below 7 indicate acidic conditions, 7 is neutral, and above 7 is basic or alkaline. Introduced by Danish chemist Søren Peder Lauritz Sørensen in 1909, the scale compresses a trillion-fold range of H⁺ concentrations into a convenient 0–14 range. pH measurement is critical in agriculture, biology, medicine, food science, and environmental monitoring.
Ka uses "K" from the German "Gleichgewichtskonstante" (equilibrium constant), introduced by Carl Guldberg and Peter Waage in 1864 via the Law of Mass Action. The subscript "a" specifically denotes acid dissociation, distinguishing it from Kb (base) and Kw (water).