IMAT Chemistry · Acids, Bases and pH

Weak Acids and Bases: Ka, pKa and Kb

A weak acid ionises only partly, so its strength is measured by an equilibrium constant, Ka, and its pH needs a square root rather than a straight logarithm.

All Acids, Bases and pH notes

Why this matters

The ministry papers asked for the pH of a weak acid from its Ka (2025) and for the weak diprotic acid among drawn structures (2023); an older paper asked which of three acids are weak. Kb and pKa have not been asked directly, but they are on the syllabus.

Concept 1 of 4: Common weak acids and bases, and how many protons they give

Most acids you meet, including all the organic acids, are weak: only a small fraction of their molecules give up a proton at any moment. Only hydrogen atoms bonded to a strongly electronegative atom, usually oxygen, are acidic. That is why ethanoic acid has four hydrogens but gives only one proton.

Definition

A weak acid ionises only partly; the equation uses $\rightleftharpoons$ , and most molecules stay whole.
Monoprotic, diprotic and triprotic acids can give 1, 2 or 3 protons per molecule.
Only an H on O (or on another very electronegative atom) is acidic. The H atoms on carbon in $\mathrm{CH_3COOH}$ are not.
A polyprotic acid gives its protons one at a time, each step weaker than the last, because a negative ion holds its next proton more tightly.
Ammonia and the amines are the common weak bases: they accept a proton with their nitrogen lone pair.

Name	Formula	Strength	Acidic protons
Ethanoic (acetic) acid	$\mathrm{CH_3COOH}$	Weak acid	1 (only the COOH hydrogen)
Methanoic (formic) acid	$\mathrm{HCOOH}$	Weak acid	1
Carbonic acid	$\mathrm{H_2CO_3}$	Weak acid	2
Ethanedioic (oxalic) acid	$\mathrm{HOOC{-}COOH}$	Weak acid	2 (one per COOH group)
Phosphoric acid	$\mathrm{H_3PO_4}$	Weak acid	3
Hydrofluoric acid	$\mathrm{HF}$	Weak acid	1
Ammonia	$\mathrm{NH_3}$	Weak base	Accepts 1 to form $\mathrm{NH_4^+}$

Compare: sulfuric acid is a STRONG diprotic acid. An alcohol OH (ethanol, ethane-1,2-diol) is far too weak to count as an acid in water.

Practice this conceptself-check · 3 quick reps

Counting every H atom gives the wrong number of protons

Ethanoic acid,

\mathrm{CH_3COOH}

, has four hydrogen atoms but only one is acidic: the one on the oxygen of the COOH group. A molecule with two COOH groups is diprotic. A compound with OH groups only on carbon chains (an alcohol or a diol) is not an acid in water at all.

Concept 2 of 4: Ka and pKa: measuring the strength of a weak acid

A weak acid sets up an equilibrium between whole molecules and ions. The equilibrium constant, Ka, says how far the acid has gone towards ions. A bigger Ka means more ionisation and a stronger acid. Because Ka values are tiny powers of ten, chemists use pKa, which works like pH: a smaller pKa means a stronger acid.

Definition

For $\mathrm{HA \rightleftharpoons H^+ + A^-}$ , the acid dissociation constant is $K_a = [\mathrm{H^+}][\mathrm{A^-}]/[\mathrm{HA}]$ .
$\text{p}K_a = -\log K_a$ . Larger Ka, smaller pKa, stronger acid.
Ka depends on temperature only, not on concentration.
Rough values at 25 °C: ethanoic acid $K_a \approx 1.8 \times 10^{-5}$ (pKa about 4.7); methanoic acid about $1.8 \times 10^{-4}$ (pKa about 3.7); the ammonium ion about $5.6 \times 10^{-10}$ (pKa about 9.3).

Acid dissociation constant

K_a = \frac{[\mathrm{H^+}][\mathrm{A^-}]}{[\mathrm{HA}]} \qquad \text{p}K_a = -\log_{10} K_a

$[\mathrm{HA}]$ concentration of the un-ionised acid at equilibrium
$[\mathrm{A^-}]$ concentration of the conjugate base at equilibrium

Worked example

Three acids are described as: X has pKa 3.2, Y has

K_a = 1.0 \times 10^{-5}

, Z has pKa 6.4. Put them in order from strongest to weakest.

Practice this conceptself-check · 3 quick reps

A larger pKa is a weaker acid

pKa runs the opposite way to Ka, just as pH runs the opposite way to

[\mathrm{H^+}]

. The acid with the biggest Ka, or the smallest pKa, is the strongest. When options mix Ka and pKa values, convert them all to one form before comparing.

Concept 3 of 4: pH of a weak acid solution

A weak acid releases only a little

\mathrm{H^+}

, so the amount ionised is small next to the amount dissolved. Each ionised molecule gives one

\mathrm{H^+}

and one

\mathrm{A^-}

, so

K_a \approx [\mathrm{H^+}]^2 / c

. That gives

[\mathrm{H^+}]

as a square root, and in pH terms it means halving.

Definition

Assume $[\mathrm{H^+}] = [\mathrm{A^-}]$ and that $[\mathrm{HA}]$ stays about equal to the starting concentration $c$ .
Then $[\mathrm{H^+}] \approx \sqrt{K_a\,c}$ , or $\text{pH} \approx \tfrac{1}{2}(\text{p}K_a - \log c)$ .
The approximation works when the acid is only a few per cent ionised, which is true for typical IMAT numbers.
Degree of ionisation: $[\mathrm{H^+}]/c$ . It rises as the acid is diluted.
Diluting a weak acid 100 times raises its pH by only 1, not 2, because of the square root.

Weak acid

[\mathrm{H^+}] \approx \sqrt{K_a\,c} \qquad \text{pH} \approx \tfrac{1}{2}\left(\text{p}K_a - \log_{10} c\right)

$K_a$ acid dissociation constant
$c$ concentration of acid dissolved, in mol/L

Worked example

Find the pH of a 0.040 mol/L solution of a weak acid with

K_a = 4.0 \times 10^{-6}

. Take

\log 4 = 0.60

Practice this conceptself-check · 3 quick reps

A weak acid's pH is not minus log of its concentration

-\log c

gives the pH only for a strong acid. For a weak acid of the same concentration the pH is higher, because only a small fraction ionises. Treating a weak acid as strong is the most common wrong option in these questions.

Concept 4 of 4: Weak bases, Kb, and Ka × Kb = Kw for a conjugate pair

A weak base pulls a proton off water and leaves

\mathrm{OH^-}

behind, setting up its own equilibrium with its own constant, Kb. An acid and its conjugate base are linked: if the acid holds its proton loosely, the conjugate base has little pull on protons. Multiplying their constants gives Kw exactly.

Definition

For $\mathrm{B + H_2O \rightleftharpoons BH^+ + OH^-}$ : $K_b = [\mathrm{BH^+}][\mathrm{OH^-}]/[\mathrm{B}]$ , and $\text{p}K_b = -\log K_b$ .
For a weak base, $[\mathrm{OH^-}] \approx \sqrt{K_b\,c}$ ; then find pOH and pH.
For a conjugate pair: $K_a \times K_b = K_w$ , so $\text{p}K_a + \text{p}K_b = 14$ at 25 °C.
The stronger the acid, the weaker its conjugate base. The conjugate base of a strong acid ( $\mathrm{Cl^-}$ , $\mathrm{NO_3^-}$ ) has no measurable basic strength in water.

Conjugate pair at 25 °C

K_a \times K_b = K_w = 1.0 \times 10^{-14} \qquad \text{p}K_a + \text{p}K_b = 14

$K_a$ constant for the acid of the pair
$K_b$ constant for its conjugate base

Worked example

A weak base has

K_b = 1.0 \times 10^{-4}

. Find the pH of its 0.010 mol/L solution at 25 °C, and the Ka of its conjugate acid.

Practice this conceptself-check · 3 quick reps

A strong acid has a weak conjugate base

Strength runs in opposite directions within a pair. A strong acid such as HCl has a conjugate base (

\mathrm{Cl^-}

) too weak to take protons from water. A very weak acid such as HCN has a fairly strong conjugate base. An option saying a strong acid has a strong conjugate base is wrong.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Ka and pKa: measuring the strength of a weak acid
Acid dissociation constant
$K_a = \frac{[\mathrm{H^+}][\mathrm{A^-}]}{[\mathrm{HA}]} \qquad \text{p}K_a = -\log_{10} K_a$
pH of a weak acid solution
Weak acid
$[\mathrm{H^+}] \approx \sqrt{K_a\,c} \qquad \text{pH} \approx \tfrac{1}{2}\left(\text{p}K_a - \log_{10} c\right)$
Weak bases, Kb, and Ka × Kb = Kw for a conjugate pair
Conjugate pair at 25 °C
$K_a \times K_b = K_w = 1.0 \times 10^{-14} \qquad \text{p}K_a + \text{p}K_b = 14$

Reference tables (1)

Common weak acids and bases, and how many protons they give7 rows

Name	Formula	Strength	Acidic protons
Ethanoic (acetic) acid	$\mathrm{CH_3COOH}$	Weak acid	1 (only the COOH hydrogen)
Methanoic (formic) acid	$\mathrm{HCOOH}$	Weak acid	1
Carbonic acid	$\mathrm{H_2CO_3}$	Weak acid	2
Ethanedioic (oxalic) acid	$\mathrm{HOOC{-}COOH}$	Weak acid	2 (one per COOH group)
Phosphoric acid	$\mathrm{H_3PO_4}$	Weak acid	3
Hydrofluoric acid	$\mathrm{HF}$	Weak acid	1
Ammonia	$\mathrm{NH_3}$	Weak base	Accepts 1 to form $\mathrm{NH_4^+}$

Compare: sulfuric acid is a STRONG diprotic acid. An alcohol OH (ethanol, ethane-1,2-diol) is far too weak to count as an acid in water.

Watch out for (4)

Counting every H atom gives the wrong number of protons
→ Common weak acids and bases, and how many protons they give
A larger pKa is a weaker acid
→ Ka and pKa: measuring the strength of a weak acid
A weak acid's pH is not minus log of its concentration
→ pH of a weak acid solution
A strong acid has a weak conjugate base
→ Weak bases, Kb, and Ka × Kb = Kw for a conjugate pair

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