Acid Dissociation Constant Ka-Ka Chemistry, Calculation and Examples

The acid dissociation constant (Ka) is a measure of the strength of an acid’s dissociation into its ions in solution. It is defined as the ratio of the concentrations of the free acid and its conjugate base in a solution at equilibrium. Ka is a measure of the acid’s strength and is important in understanding acid-base chemistry and reactions.

Calculate the acid dissociation(Ka)

The acid dissociation constant, Ka, is a quantitative measure of the strength of an acid in solution. It represents the extent to which an acid dissociates into its ions in water.

Let’s consider a generic acid HA that dissociates into H⁺ ions and A^– ions:

HA + H₂O ⇌ H₃O⁺ + A^–

The dissociation constant is defined as:

Ka = [H3O⁺][A^–] / [HA]

Where:

[H3O⁺] is the concentration of H3O⁺ ions [A^–] is the concentration of A^– ions [HA] is the concentration of undissociated HA molecules.

We can derive this expression mathematically starting from the equilibrium expression:

KA = [Products] / [Reactants]

For the dissociation of HA:

KA = [H3O⁺][A^–] / [HA]

We define Ka as the dissociation constant KA for the dissociation of an acid.

So the acid dissociation constant is a ratio of the product of the concentrations of the ions produced when the acid dissociates divided by the concentration of the undissociated acid. The larger the Ka is, the stronger the acid.

Acid Dissociation Constant Ka Example

Here is an example calculating the acid dissociation constant (Ka) for a weak acid:

Let’s say we have a 0.10 M solution of propanoic acid (CH3CH2COOH). When this weak acid dissociates slightly in water, the reaction is:

CH₃CH₂COOH ⇌ CH₃CH₂COO^– + H⁺

We are given the following information:

• Initial concentration of CH₃CH₂COOH (C0) = 0.10 M
• Measured pH of the solution = 4.57

To calculate Ka:

1. Write the Ka expression: Ka = [H⁺][CH₃CH₂COO^–] / [CH₃CH₂COOH]
2. Assume [H⁺] ≈ [CH₃CH₂COO^–] since this is a weak acid. We can calculate [H⁺] from the pH: [H⁺] = 10^-pH = 10^-4.57 = 2.69 x 10^-5 M
3. [CH₃CH₂COOH] ≈ C0 since only a small amount dissociated. So [CH₃CH₂COOH] = 0.10 M

Plugging these into the Ka expression: Ka = (2.69 x 10^-5)(2.69 x 10^-5) / (0.10) = 7.24 x 10^-10

So the Ka for propanoic acid is 7.24 x 10^-10, confirming it is a weak acid. This example demonstrates how Ka can be determined experimentally from the pH, initial concentration, and assumptions about a weak acid’s dissociation.

Predict the Equilibrium and Strength of Acids Using Ka

Here are some tips on how to predict the equilibrium and strength of acids using the acid dissociation constant (Ka):

• The larger the Ka value, the stronger the acid. Strong acids have large Ka values (>1), while weak acids have small Ka values (<1).
• You can compare Ka values to qualitatively assess acid strength. For example, HCl (Ka = 107) is stronger than acetic acid (Ka = 1.8 x 10^-5).
• For polyprotic acids (acids with multiple ionizable protons), the first Ka value is the largest, and subsequent values get smaller. E.g. for sulfuric acid: Ka1 > Ka2
• To predict the extent of dissociation, compare Ka to the initial acid concentration.
  • If Ka >> [A-], dissociation will be extensive.
  • If Ka << [A-], dissociation will be limited.
• For weak acids, you can generally assume that [H3O⁺] ≈ [A^–] since the undissociated acid concentration is much greater.
• The pH of a weak acid solution can be estimated using -log(Ka) as an approximate value.
• Le Chatelier’s principle applies – if [H3O⁺] increases, the equilibrium will shift left to produce more undissociated acid. If [H3O⁺] decreases, the opposite occurs.

Acid Dissociation Constant From pH

Here are the steps to determine an acid dissociation constant (Ka) from the pH of an acid solution:

1. Write out the dissociation equation for the acid. For example, with acetic acid: CH₃COOH ⇌ CH₃COO^– + H⁺
2. Set up the Ka expression: Ka = [CH₃COO^–][H⁺] / [CH₃COOH]
3. Make assumptions:
   • For a weak acid, assume the dissociation is small, so [CH3COOH] ≈ initial concentration
   • Assume [H⁺] ≈ [CH₃COO^–] since H⁺ and acetate are produced in equal amounts
4. Substitute [H⁺] = 10^-pH into the Ka expression: Ka = (10^-pH)2 / (initial [CH₃COOH])
5. Rearrange and take logarithms: pKa = pH + log(initial [CH₃COOH])

So if you know the pH and initial concentration of a weak acid solution, you can determine its pKa value.

For example, if 0.1 M acetic acid has a pH of 3.0: pKa = 3.0 + log(0.1) = 4.7

This allows you to calculate Ka values for weak acids from pH measurements. The assumption that [H⁺] ≈ [A^–] holds for acids with Ka < 10^-3.