Dissociation constant – Definition, Explanation, Formula, Example, and Application

Definition:

The dissociation constant is the equilibrium constant for the reversible splitting of a compound into its ions or components. For a weak acid it is called the acid dissociation constant (Ka), and for a weak base the base dissociation constant (Kb). The larger the value, the more the compound dissociates. For example: Splitting up of common salt into its component ions. A dissociation constant depicts the concentration of conjugate bases and free hydrogen ions (Products) to that of the original acid compounds (reactant).

An Explanation for Dissociation Constant:

In terms of acids and bases, dissociation is a process where acids or base separates into ions in water. The strength of an acid is determined by the moles of H₃O⁺ ions produced from each mole of acid that dissociates. And the same goes with a base strength determined by the moles of OH^– produced from each mole of the base that dissolves in water. Higher the dissociation, the strong the acid or base is. Strong acid and base dissociate entirely in water, whereas weak acids and weak bases slightly dissociate, leaving most of the initial acid undissociated. Because weak acids in water dissociate only slightly, the ion products reach equilibrium with the undissociated weak acid molecules. For example, when a weak acid (HA) is added to water, an equilibrium is formed where HA protonate the H₂O to form Hydronium ion (H₃O⁺) and the conjugate base (A^–)

HA(aq) + H₂O(l) ⇋ H₃O⁺(aq) + A^– (aq)

In the case of a base a similar equilibrium exists. The base will accept a proton from water and form a conjugate acid, BH⁺:

HB(aq) + H₂O(l) ⇋ BH⁺(aq) + OH^–(aq)

Formula to find Dissociation Constant:

Typically, to determine the dissociation constant of an acid or base, we need to measure how much of a base or acid is dissociated when came in contact with water. As discussed above, a conjugate base of an acid and hydronium ions are formed when an acid protonates the water. During this protonation process, acid molecules donate H⁺ ions to H₂O to form Hydronium (H₃O⁺⁾ ions and conjugate base (A^–). The reverse reaction also occurs here, where hydronium ions release a proton (H⁺) and transfer it back to acid. This movement of hydrogen ions from acid to water and vice versa continues until an equilibrium is reached where the products and reactants are exchanged.

An acid dissociation expression, Ka, can be written for weak acids that give the ratio of the concentrations of products to the weak acid reactants. Water is the solvent and is present in large excess, so its concentration stays effectively constant and is not included in Ka. The concentration of water during the reaction is, therefore, a constant and can be excluded from the expression for K. This gives rise to a special equilibrium constant, Ka, known as the acid dissociation constant. For example, the acid dissociation expression for the equilibrium equation of acid shown in the explanation above is written.

K_a = [H3O+][A-] / [HA]

Similarly, the base dissociation constant expression for the equilibrium equation of base shown in the explanation above is written.

K_b = [BH⁺][OH^–] / [HB]

In the above equations of acid, the numerator denotes the concentration of free hydronium ions multiplied by the conjugate base concentration. At the same time, the denominator is the concentration of the initial acid substance. Most of the time, the concentration of the numerator values is unknown. Since the equilibrium dissociation constant requires these numbers, they must be calculated before proceeding. These can be calculated by testing the pH of the solution using pH meter. Once the pH is obtained, the number of free hydrogen ions can be calculated using the following equation:

[H] = 10^-pH

Remember that H⁺ can be used to replace H₃O⁺, thus simplifying the depiction of the reaction between a weak acid with water and its expression is written as

HA(aq) ⇋ H⁺(aq) + A^– (aq)

A logarithmic measure of K_a is the more common and convenient term used in practice. pKa is the negative logarithm of Ka (pKa = −log Ka). The lower the pKa, the stronger the acid.

Example:

Example: A 0.1 M solution of formic acid has a pH of 2.38. Calculate its Ka.

HCOOH ⇌ H⁺ + HCOO⁻

Step 1: [H⁺] = 10^(−pH) = 10^(−2.38) = 0.00417 mol/L

Step 2: Each HCOOH molecule that dissociates gives one H⁺ and one HCOO⁻, so [HCOO⁻] = [H⁺] = 0.00417 mol/L, and [HCOOH] = 0.1 − 0.00417 = 0.0958 mol/L

Step 3: Ka = [H⁺][HCOO⁻] / [HCOOH] = (0.00417 × 0.00417) / 0.0958 = 1.8 × 10⁻⁴

Step 4: pKa = −log Ka = −log (1.8 × 10⁻⁴) = 3.74

This matches the accepted value for formic acid (Ka ≈ 1.8 × 10⁻⁴).

Relationship between Ka, Kb and Kw

For a weak acid and its conjugate base:

Ka × Kb = Kw

where Kw is the ionic product of water, 1.0 × 10⁻¹⁴ at 25 °C. Taking logarithms gives:

pKa + pKb = 14 (at 25 °C)

So if you know the pKa of an acid, you can find the pKb of its conjugate base. A strong acid has a weak conjugate base, and vice versa.

Before Applications, a new H2. This connects the topic to what pharmacy students and freshers actually need:

Dissociation Constant in Pharmacy: pKa and Drug Absorption

The Henderson–Hasselbalch equation links pH, pKa and the degree of ionisation of a drug:

• For a weak acid: pH = pKa + log ([A⁻] / [HA])
• For a weak base: pH = pKa + log ([B] / [BH⁺])

When pH equals pKa, the drug is exactly 50% ionised. Only the un-ionised form crosses cell membranes easily, so pKa strongly affects where a drug is absorbed.

Example: aspirin (a weak acid, pKa about 3.5)

• In the stomach (pH about 1.5): log ([A⁻]/[HA]) = 1.5 − 3.5 = −2, so the ratio is 1 : 100. About 99% of the aspirin is un-ionised and can be absorbed.
• In the small intestine (pH about 6.5): log ([A⁻]/[HA]) = 6.5 − 3.5 = 3, so the ratio is 1000 : 1. Almost all the aspirin is ionised.

This is the pH-partition hypothesis. In practice, most drugs are still absorbed mainly in the small intestine because of its very large surface area, but pKa explains why the degree of ionisation changes along the gut. It also guides the choice of salt forms, solubility and buffer systems in formulation.

Applications of Dissociation Constant:

1. The concept is applied in the fields of Pharmacology and Chemistry. It determines the affinity between protein and a ligand in protein-ligand binding. A higher dissociation constant indicates a less tightly bound ligand. In binding studies, the dissociation constant is written Kd. A lower Kd means the drug binds more tightly to its target.
2. pKa values of proteins and amino acid side chains are of significant importance to finding the activity of enzymes and the stability of proteins
3. Frequently applied in environmental science to find out the acid-base equilibria of lakes and rivers.
4. Ka of a drug can be helpful to determine its solubility, side of protein binding and rate of absorption in the gastrointestinal tract. Weakly acidic drugs are less ionized, readily available in the stomach and hence have a higher absorption rate. In the same way, drugs which are weak bases are readily absorbed in the intestines.