The acid dissociation constant, Ka, measures the strength of an acid. It indicates the extent to which an acid ionizes. Understanding Ka provides insights into how acids behave. This constant helps predict an acid’s reactivity and its impact on the pH of a solution.
What Ka Represents
Ka quantifies acid dissociation in water. When a weak acid, represented as HA, dissolves in water, it establishes an equilibrium where it partially dissociates into a hydrogen ion (H⁺) and its conjugate base (A⁻). This reversible reaction is written as HA ⇌ H⁺ + A⁻. The Ka value is derived from the equilibrium expression: Ka = [H⁺][A⁻]/[HA], where brackets denote molar concentrations at equilibrium.
The magnitude of the Ka value directly correlates with the extent of this dissociation. A higher Ka indicates that the acid dissociates more readily, producing a greater concentration of hydrogen ions, signifying a stronger acid. Conversely, a lower Ka value suggests that the acid dissociates less, characteristic of a weaker acid. This constant helps differentiate between strong acids, which dissociate almost completely, and weak acids, which only partially dissociate.
Calculating Ka Using pH
Calculating Ka from an acid’s initial concentration and solution pH. First, convert pH to hydrogen ion concentration, [H⁺], using [H⁺] = 10⁻ᵖᴴ. This gives the [H⁺] at equilibrium.
An ICE (Initial, Change, Equilibrium) table tracks the concentrations of the acid, hydrogen ions, and conjugate base during dissociation. The initial concentration of the weak acid is known, while initial concentrations of H⁺ and the conjugate base are assumed to be zero.
As the acid dissociates, the change in concentration of the acid is represented by ‘-x’, and the corresponding increase in H⁺ and conjugate base concentrations is ‘+x’. At equilibrium, the concentrations become the initial acid concentration minus ‘x’, and ‘x’ for both H⁺ and the conjugate base. Since the pH allows calculation of [H⁺] at equilibrium, this ‘x’ value is determined directly from the pH.
These equilibrium concentrations are substituted into the Ka expression: Ka = [H⁺][A⁻]/[HA]. For example, consider a 0.10 M solution of a weak acid (HA) with a measured pH of 2.89. First, calculate [H⁺] = 10⁻²·⁸⁹ ≈ 0.00129 M. This value represents ‘x’. In the ICE table, if the initial [HA] was 0.10 M, then at equilibrium, [HA] = 0.10 – 0.00129 = 0.09871 M, and [H⁺] = [A⁻] = 0.00129 M. Substituting these into the Ka expression yields Ka = (0.00129)(0.00129) / (0.09871) ≈ 1.68 × 10⁻⁵. This step-by-step calculation provides the Ka value, reflecting the acid’s dissociation in that specific solution.
Calculating Ka from pKa
The relationship between Ka and pKa offers a straightforward method for converting between these two values. The pKa is defined as the negative logarithm (base 10) of the Ka value, expressed by the equation: pKa = -log Ka. This logarithmic scale simplifies the comparison of acid strengths, especially when Ka values span many orders of magnitude. A lower pKa value corresponds to a higher Ka value, indicating a stronger acid.
Conversely, if the pKa value is known, the Ka value can be calculated by performing the inverse operation, which is raising 10 to the power of the negative pKa. The formula for this conversion is Ka = 10⁻ᵖᴷᵃ. For instance, if an acid has a pKa of 4.75, its Ka value would be calculated as 10⁻⁴·⁷⁵. Performing this calculation yields a Ka value of approximately 1.78 × 10⁻⁵. This direct mathematical relationship makes it convenient to determine Ka when pKa is readily available from reference tables.
Interpreting Your Ka Result
The calculated Ka value provides direct insight into the strength of an acid. A larger Ka value signifies a stronger acid because it indicates a greater extent of dissociation in solution, meaning more hydrogen ions are released. For example, acetic acid, a common weak acid found in vinegar, has a Ka value of approximately 1.8 × 10⁻⁵. This relatively small Ka value confirms that acetic acid is a weak acid, dissociating only partially in water.
In contrast, hydrofluoric acid (HF), though also considered a weak acid, has a larger Ka of about 6.3 × 10⁻⁴, indicating it is stronger than acetic acid as it dissociates to a greater extent. Strong acids, such as hydrochloric acid (HCl), have extremely large Ka values, often exceeding 10⁶, signifying near-complete dissociation in water. This quantitative measure allows chemists to compare the relative strengths of different acids and predict their behavior in chemical reactions, which is important for applications ranging from industrial processes to biological systems.