Weak Acids and Bases – K_a for Weak Acids

Full Notes

K_a has been covered in more detail here.
This page is just what you need to know for AQA A-level Chemistry :)

Weak Acids and Their Partial Dissociation

A weak acid (HA) only partially dissociates in water:

Unlike strong acids (which fully dissociate), weak acids establish an equilibrium in solution between HA, H⁺ and A^-.

The position of this equilibrium is based on the strength of the acid - the stronger the acid, the more the position lies to the right (more dissociation), meaning a higher concentration of H⁺ and A⁻ ions in the mixture.

Example ethanoic acid (CH₃COOH):

CH₃COOH ⇌ H⁺ + CH₃COO⁻
where HA = CH₃COOH and A⁻ = CH₃COO⁻

Acid Dissociation Constant (K_a)

Like with any equilibrium system, the position of equilibrium for the dissociation of a weak acid can be described using an equilibrium constant.

K_a is the equilibrium constant for acid dissociation.

Expression for K_a:

• Larger K_a = Stronger weak acid (more dissociation)
• Smaller K_a = Weaker acid (less dissociation)

Example For ethanoic acid (CH₃COOH): CH₃COOH ⇌ CH₃COO⁻ + H⁺
K_a = 1.75 × 10⁻⁵ mol dm⁻³ (shows weak dissociation).

Relationship Between K_a and pK_a

pK_a is a logarithmic measure of K_a:

• Lower pK_a = Stronger weak acid (more dissociation)
• Higher pK_a = Weaker acid (less dissociation)

To convert pK_a to K_a, use K_a = 10^−pK_a

Example
Ethanoic acid: K_a = 1.75 × 10⁻⁵, so pK_a = 4.76.
Carbonic acid: K_a = 4.3 × 10⁻⁷, so pK_a = 6.37.
Since pK_a of ethanoic acid is lower, it is stronger than carbonic acid.

Calculating pH of a Weak Acid

Since weak acids partially dissociate with H⁺ and A⁻ in a 1:1 ratio, we assume:

• [H⁺] ≈ [A⁻] (from dissociation).
• [HA] remains nearly unchanged.

This means we can assume that [H⁺] × [A⁻] = [H⁺]²

Steps to Calculate pH of a Weak Acid:

• Use K_a expression: K_a = ([H⁺]²) / [HA]
• Rearrange to find [H⁺]: [H⁺] = √(K_a × [HA])
• Find pH: pH = -log[H⁺]

Matt’s exam tip

Don’t forget that when using K_a to find the pH of a weak acid, we are assuming two things - that [H+] = [A-] and that the [HA] at the start is the same as the [HA] at equilibrium. These are assumptions - for example the [HA] at equilibrium won’t be exactly the same as the initial [HA] as some will have dissociated however the amount of dissociation is very small compared to the concentration meaning mathematically it isn’t significant enough for us to worry about.

Summary

• Weak acids partially dissociate; their strength is quantified by K_a and pK_a.
• Larger K_a (smaller pK_a) means a stronger weak acid; smaller K_a (larger pK_a) means a weaker acid.
• For a weak acid HA, assuming [H⁺] ≈ [A⁻] and [HA] ≈ initial, use [H⁺] = √(K_a × [HA]) and pH = -log[H⁺].