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Foundations: Chemistry

pH of a weak acid

Estimates the pH of a weak acid from its K_a and concentration.

Ref: FCH-24
Rev: v1
Field: Foundations: Chemistry
Result: pH

K_{a} = \frac{[H^{+}] [A^{-}]}{[HA]} \approx \frac{{[H^{+}]}^{2}}{[HA]}

For HA ⇌ H⁺ + A⁻ with [H⁺] = [A⁻] and [HA] ≈ initial concentration c₀ (valid when the acid is only slightly dissociated): [H⁺] = √(K_a c₀). Then pH = −log₁₀[H⁺].

A weak acid only partly splits into ions, so it makes far fewer hydrogen ions than a strong acid of the same concentration.

Calculator

Solve for

pHpHComputed

K_aAcid dissociation constant

mol/dm³

1e-120.01

c₀Initial concentration

mol/dm³

1e-45

[H⁺]0.001342 mol/dm³
Fraction dissociated1.342 %

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

pH () current value 2.872

K_aAcid dissociation constantKey driver

1.56.5

c₀Initial concentration

2.024.37

Ethanoic acid at 0.100 mol/dm³ has a pH of about 2.87, compared with 1.00 for the same concentration of hydrochloric acid.
The approximation fails when K_a is large or the acid very dilute.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing ()	Local step	Change in result
K_a Acid dissociation constant	1e-12 to 0.01 mol/dm³	1.5	6.5	5	+10%	−0.0207
c₀ Initial concentration	1e-4 to 5 mol/dm³	2.023	4.372	2.349	+10%	−0.0207

Sweep of Initial concentration

Initial concentration (mol/dm³)	pH
1e-4	4.372
3.867e-4	4.079
0.001495	3.785
0.005782	3.491
0.02236	3.198
0.08647	2.904
0.3344	2.61
1.293	2.317
5	2.023

Sweep one variable

Vary

pH ()Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

pH

Result ·

What the equation gives you. Everything else feeds it.

K_a

Acid dissociation constant

mol/dm³ · typical 1e-12 to 0.01

Ka of the acid (ethanoic acid 1.8×10⁻⁵). A larger K_a means a stronger acid and a lower pH.

c₀

Initial concentration

mol/dm³ · typical 1e-4 to 5

Concentration of the acid before dissociation. More concentrated acid has a lower pH.

Worked example with the values above

[H⁺] = √(K_a c₀) = √(1.8×10⁻⁵ × 0.1) = 0.001342 mol/dm³.
Take −log₁₀.
pH = 2.872.

Assumptions and limits

Dissociation is small compared with c₀.
Water’s own H⁺ is negligible.

Common mistakes

Using c₀ as [H⁺].
Forgetting the square root.

Statistics and uncertainty

Ka is typically known to two significant figures, which affects pH in the second decimal place.

Where it is used

Predicting acidity of weak acids.
Buffer and cleaning solution formulation.

Maths you need

Equilibrium constants: K_c
pH: −log[H⁺]

Related formulas

Practise this formula