The ionisation constant of an acid, Ka, is the measure of strength of an acid. The Ka values of acetic acid, h

NCERT Exemplar · Q8

Q. The ionisation constant of an acid, Ka, is the measure of strength of an acid. The Ka values of acetic acid, hypochlorous acid and formic acid are 1.74 \times 10^-5, 3.0 \times 10^-8 and 1.8 \times 10^-4 respectively. Which of the following orders of pH of 0.1 mol dm^-3 solutions of these acids is correct?

(i) acetic acid > hypochlorous acid > formic acid

(ii) hypochlorous acid > acetic acid > formic acid

(iii) formic acid > hypochlorous acid > acetic acid

(iv) formic acid > acetic acid > hypochlorous acid

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Concept understanding — Weak Acid Ionization

Weak Acid Ionization: From Intuition to Precision

Imagine you drop a spoonful of sugar into a glass of water. Some sugar dissolves, but a lot just sits at the bottom. Now imagine you drop a spoonful of salt — it all dissolves completely. Acids behave the same way. Some acids, like hydrochloric acid (HCl), dissolve completely in water — every single molecule breaks apart. Others, like acetic acid (vinegar), only partially break apart. Most of the acid molecules stay intact, and only a few actually ionize.

That's the core idea: weak acids are shy about giving away their hydrogen ion. They don't fully commit.

The Precise Statement

A weak acid ( $HA$ ) in water establishes an equilibrium between the intact acid molecule and its ions:

HA_{(aq)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + A^-_{(aq)}

The double arrow ( $\rightleftharpoons$ ) is the key. It tells you the reaction happens in both directions simultaneously. Some $HA$ molecules break apart to form $H_3O^+$ and $A^-$ , while some $H_3O^+$ and $A^-$ recombine back into $HA$ . At equilibrium, both processes happen at the same rate — so the concentrations stop changing.

Important

For a weak acid, most of the acid remains as $HA$ at equilibrium. Only a tiny fraction exists as ions. This is the opposite of a strong acid, where the forward reaction goes to completion (single arrow: $\rightarrow$ ).

The Quantitative Measure: $K_a$

Every weak acid has a number that tells you exactly how "shy" it is — the acid dissociation constant, $K_a$ :

K_a = \frac{[H_3O^+][A^-]}{[HA]}

K_a = \frac{[H_3O^+][A^-]}{[HA]}

The smaller the $K_a$ , the weaker the acid. For acetic acid (vinegar), $K_a \approx 1.8 \times 10^{-5}$ . That tiny number means the numerator (ions) is very small compared to the denominator (intact acid). For a strong acid like HCl, $K_a$ is effectively infinite — the denominator is essentially zero because all the acid has ionized.

A Concrete Example

Suppose you dissolve 0.10 mol of acetic acid ( $CH_3COOH$ ) in 1 L of water. At equilibrium, you'll find:

$[CH_3COOH] \approx 0.0998$ M (almost all of it is still intact)
$[H_3O^+] \approx 0.0013$ M (only about 1.3% has ionized)
$[CH_3COO^-] \approx 0.0013$ M

Note

|---------|-------------|------------|-----------------|

| $CH_3COOH$ | 0.10 | $-x$ | $0.10 - x$ |

| $H_3O^+$ | 0 | $+x$ | $x$ |

| $CH_3COO^-$ | 0 | $+x$ | $x$ |

Plugging into $K_a = \frac{x^2}{0.10 - x} = 1.8 \times 10^{-5}$ and solving gives $x \approx 0.0013$ M.

Why This Matters …

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For weak acids, pH is inversely related to $K_a$ : the smaller the $K_a$ , the higher the pH. Since $K_a$ values are $1.8 \times 10^{-4}$ (formic), $1.74 \times 10^{-5}$ (acetic), $3.0 \times 10^{-8}$ (hypochlorous), the pH order is hypochlorous acid > acetic acid > formic acid, which is option (ii).

The key idea is simple: a weak acid’s strength is measured by its ionization constant $K_a$ . A larger $K_a$ means more dissociation, more $H^+$ in solution, and therefore a lower pH. For a given concentration, the pH of a weak acid solution depends directly on $K_a$ .

Let’s see why this works.

The relationship between $K_a$ and $[H^+]$ For a weak acid $HA$ of initial concentration $c$ , the equilibrium is:

HA \rightleftharpoons H^+ + A^-

If the degree of ionization is $\alpha$ , then $[H^+] = c\alpha$ and $[A^-] = c\alpha$ , while $[HA] = c(1-\alpha)$ . The ionization constant is:

K_a = \frac{[H^+][A^-]}{[HA]} = \frac{(c\alpha)^2}{c(1-\alpha)}

For a weak acid, $\alpha$ is small, so $1-\alpha \approx 1$ . This gives the approximation:

K_a \approx c\alpha^2 \quad \Rightarrow \quad \alpha \approx \sqrt{\frac{K_a}{c}}

Hence:

[H^+] = c\alpha \approx \sqrt{K_a c}

And pH is:

\text{pH} = -\log[H^+] \approx -\log\sqrt{K_a c} = \frac{1}{2}(-\log K_a - \log c)

c

Since $c$ is the same for all three acids (0.1 mol dm $^{-3}$ ), the pH depends only on $K_a$ : larger $K_a$ → smaller pH.

Compare the $K_a$ values
- Formic acid: $K_a = 1.8 \times 10^{-4}$ (largest)
- Acetic acid: $K_a = 1.74 \times 10^{-5}$ (middle)
- Hypochlorous acid: $K_a = 3.0 \times 10^{-8}$ (smallest)
So formic acid is the strongest among the three, and hypochlorous acid is the weakest.
Translate to pH order

Stronger acid → lower pH. Therefore:
- Formic acid has the lowest pH. …

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Q.The ionisation constant of an acid, Ka, is the measure of strength of an acid. The Ka values of acetic acid, hypochlorous acid and formic acid are 1.74 × 10^-5, 3.0 × 10^-8 and 1.8 × 10^-4 respectively. Which of the following orders of pH of 0.1 mol dm^-3 solutions of these acids is correct?

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