Assertion (A): Aqueous solution of ammonium carbonate is basic. Reason (R): Acidic/basic nature of a salt solu

NCERT Exemplar · Q48

Q. Assertion (A): Aqueous solution of ammonium carbonate is basic. Reason (R): Acidic/basic nature of a salt solution of a salt of weak acid and weak base depends on Ka and Kb value of the acid and the base forming it.

(i) Both A and R are true and R is correct explanation of A.

(ii) Both A and R are true but R is not correct explanation of A.

(iii) A is true but R is false.

(iv) Both A and R are false.

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Concept understanding — Buffer Solution pH

What is a Buffer Solution?

Imagine you're making lemonade. If you add a few drops of lemon juice to a glass of water, the pH drops sharply — it becomes very acidic. But if you add the same few drops to a glass of already acidic lemonade, the pH barely changes. Why? Because lemonade contains a buffer — a mixture that resists pH change when small amounts of acid or base are added.

A buffer solution is a mixture of a weak acid and its conjugate base (or a weak base and its conjugate acid). It "soaks up" added H⁺ or OH⁻ ions without letting the pH swing wildly.

Note

The key is that both components must be present in significant amounts. A weak acid alone won't buffer — you need its conjugate base partner too.

The Intuition: A Chemical Sponge

Think of a buffer as a two-way sponge:

If you add acid (H⁺): The conjugate base in the buffer grabs the extra H⁺, turning into the weak acid. The H⁺ is "absorbed" — pH barely drops.
If you add base (OH⁻): The weak acid donates an H⁺ to neutralise the OH⁻, turning into the conjugate base. The OH⁻ is "absorbed" — pH barely rises.

The buffer works best when the amounts of weak acid and conjugate base are roughly equal. That's when the sponge is most "spongy" — it can absorb shocks in either direction.

The Precise Statement: The Henderson–Hasselbalch Equation

For a buffer made from a weak acid $HA$ and its conjugate base $A^-$ , the pH is given by:

\text{pH} = \text{p}K_a + \log_{10} \left( \frac{[A^-]}{[HA]} \right)

Where:

$\text{p}K_a = -\log_{10} K_a$ (a measure of the weak acid's strength — lower pKa = stronger acid)
$[A^-]$ = concentration of the conjugate base
$[HA]$ = concentration of the weak acid

This equation tells you exactly how the pH depends on the ratio of base to acid, not their absolute amounts.

Tip

When $[A^-] = [HA]$ , the ratio is 1, $\log(1) = 0$ , so $\text{pH} = \text{p}K_a$ . This is the buffer's optimal pH — it resists change most strongly here.

Why This Works: A Quick Derivation

Start from the weak acid equilibrium:

HA \rightleftharpoons H^+ + A^-

The acid dissociation constant is:

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

Take negative logs of both sides:

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

Which gives:

\text{p}K_a = \text{pH} - \log \frac{[A^-]}{[HA]}

Rearrange:

\text{pH} = \text{p}K_a + \log \frac{[A^-]}{[HA]}

That's it. The derivation is just algebra on the definition of $K_a$ .

Watch out

The Henderson–Hasselbalch equation assumes that the concentrations $[HA]$ and $[A^-]$ are the initial concentrations you mixed. It works well when both are much larger than $[H^+]$ or $[OH^-]$ from dissociation — which is true for a properly made buffer.

Example: Making an Acetate Buffer

You mix 0.1 M acetic acid ( $\text{p}K_a = 4.76$ ) with 0.1 M sodium acetate. What's the pH?

$\text{pH} = 4.76 + \log \frac{0.1}{0.1} = 4.76 + \log 1 = 4.76$ …

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For a salt of a weak acid and a weak base, the pH is determined by comparing $K_a$ and $K_b$ — here, ammonium carbonate gives a basic solution because $K_b(\text{NH}_3) > K_a(\text{HCO}_3^-)$ , making both Assertion and Reason true, with Reason correctly explaining Assertion.

Identify the salt and its ions. Ammonium carbonate, $(NH_4)_2CO_3$ , dissociates in water into $NH_4^+$ (the conjugate acid of the weak base $NH_3$ ) and $CO_3^{2-}$ (the conjugate base of the weak acid $HCO_3^-$ ). Both ions come from weak parents, so the salt is of the weak acid–weak base type.
Recall the pH rule for such salts. For a salt of a weak acid and a weak base, the solution’s pH depends on the relative strengths of the parent acid and base. The key formula is:

[H^+] = \sqrt{\frac{K_w \cdot K_a}{K_b}}

where $K_a$ is the acid dissociation constant of the weak acid (here, $HCO_3^-$ ) and $K_b$ is the base dissociation constant of the weak base (here, $NH_3$ ).

[H^+] = \sqrt{\frac{K_w \cdot K_a}{K_b}} \quad \Rightarrow \quad \text{pH} = 7 + \frac{1}{2}(\text{p}K_a - \text{p}K_b)

If $K_a > K_b$ , the solution is acidic (pH < 7); if $K_a < K_b$ , it is basic (pH > 7); if equal, neutral.

Apply to ammonium carbonate. For the carbonic acid system, $K_{a2}$ of $H_2CO_3$ (the $K_a$ of $HCO_3^-$ ) is $4.7 \times 10^{-11}$ . For ammonia, $K_b = 1.8 \times 10^{-5}$ . Clearly:

K_a (4.7 \times 10^{-11}) \ll K_b (1.8 \times 10^{-5})

So $K_a < K_b$ , meaning the solution is basic. Hence Assertion (A) is true. …

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Q.Assertion (A): Aqueous solution of ammonium carbonate is basic. Reason (R): Acidic/basic nature of a salt solution of a salt of weak acid and weak base depends on Ka and Kb value of the acid and the base forming it.

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Q.Assertion (A): Aqueous solution of ammonium carbonate is basic.
Reason (R): Acidic/basic nature of a salt solution of a salt of weak acid and weak base depends on Ka and Kb value of the acid and the base forming it.

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