A beaker contains a solution of substance 'A'. Precipitation of substance 'A' takes place when small amount of

NCERT Exemplar · Q4

Q. A beaker contains a solution of substance 'A'. Precipitation of substance 'A' takes place when small amount of 'A' is added to the solution. The solution is _________.

(i) saturated

(ii) supersaturated

(iii) unsaturated

(iv) concentrated

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Concept understanding — Types Of Solutions

Types of Solutions: From Everyday Life to Chemistry

You already know what a solution is — sugar dissolved in water, salt in water, even the air you breathe. But not all solutions behave the same way. Some dissolve easily, some refuse to dissolve beyond a point, and some can hold more solute than they normally should. That difference is what we classify as types of solutions based on how much solute is dissolved.

The Intuition: A Cup of Tea

Imagine making a cup of tea. You add one spoon of sugar — it dissolves completely. You add a second spoon — still dissolves. A third spoon — maybe it dissolves, maybe it doesn't. At some point, no matter how much you stir, the sugar just sits at the bottom.

That moment — when no more sugar dissolves — is the saturation point. Before that, you have an unsaturated solution. At that exact point, you have a saturated solution. And if you carefully heat the tea, dissolve more sugar, then cool it down without disturbing it — you might get a supersaturated solution, where more sugar stays dissolved than should be possible at that temperature.

That's the entire idea. Three types, defined by how much solute is dissolved relative to the maximum possible.

The Precise Statement

A solution is a homogeneous mixture of a solute (the substance being dissolved) and a solvent (the substance doing the dissolving). Based on the amount of solute dissolved relative to its solubility at a given temperature, solutions are classified into three types:

Types of Solutions (by saturation) Unsaturated solution — contains less solute than the maximum that can be dissolved at that temperature. Saturated solution — contains exactly the maximum amount of solute that can be dissolved at that temperature. Supersaturated solution — contains more solute than the maximum normally possible at that temperature (a metastable state).

Breaking Down Each Type

Unsaturated solution — the most common type. You can still add more solute and it will dissolve. The concentration is below the solubility limit. If you have a glass of water at room temperature and add a pinch of salt, you get an unsaturated solution. Add more salt — still unsaturated, until you hit the limit.

Saturated solution — the solute and undissolved solute are in dynamic equilibrium. At the molecular level, the rate at which solute particles dissolve equals the rate at which they crystallize out. No net change. If you keep adding salt to water and it stops dissolving, the liquid above the undissolved salt is a saturated solution. The concentration is fixed at the solubility value for that temperature.

Watch out

A common mistake: thinking a saturated solution is always "thick" or "concentrated." Not true. Saturation depends on the solute's solubility. Lead(II) chloride saturates at about 0.45 g per 100 mL water — that's a very dilute saturated solution. Saturation ≠ high concentration.

Supersaturated solution — this is a tricky one. You create it by heating the solvent, dissolving more solute than normally possible, then carefully cooling it. The excess solute stays dissolved because there's no nucleation site (no scratch, no dust particle) to trigger crystallization. It's unstable — the slightest disturbance (a dust speck, a scratch on the glass, even a sudden jolt) causes the excess solute to crystallize out instantly. …

Why this formula?

Types of Solutions: Why the Key Formulae Hold

Understanding why the formulae work is essential for Indian exams (JEE, NEET, CBSE). Let's break down the reasoning behind the most important relationships.

1. The Basic Classification: What Makes a Solution?

A solution is a homogeneous mixture of two or more substances. The key idea is intermolecular forces between solute and solvent particles.

Ideal Solution: Solute-solvent interactions are identical to solute-solute and solvent-solvent interactions. Why? No net energy change on mixing — the molecules "fit" perfectly.
Non-Ideal Solution: Interactions differ, leading to deviation from Raoult's law.

2. Raoult's Law: The Foundation

Formula:

P_{\text{solution}} = x_{\text{solvent}} \cdot P_{\text{solvent}}^0

Why does this hold?

Imagine a pure solvent surface. The vapour pressure $P^0$ comes from molecules escaping the liquid. When you add a non-volatile solute, solute molecules occupy some surface area, blocking solvent molecules from escaping.

The fraction of surface available to solvent = mole fraction of solvent ( $x_{\text{solvent}}$ ).
Therefore, the rate of escape (vapour pressure) is proportional to that fraction:

P_{\text{solution}} \propto x_{\text{solvent}}

At the limit $x_{\text{solvent}} = 1$ , $P_{\text{solution}} = P^0$ , so the constant is $P^0$ .

Key insight: Raoult's law is a surface-area argument, not a volume argument.

3. Relative Lowering of Vapour Pressure

Formula:

\frac{P^0 - P}{P^0} = x_{\text{solute}}

Derivation in one line:

From Raoult's law:

P = x_{\text{solvent}} \cdot P^0

Since $x_{\text{solvent}} + x_{\text{solute}} = 1$ ,

P = (1 - x_{\text{solute}}) P^0

\Rightarrow P^0 - P = x_{\text{solute}} \cdot P^0

\Rightarrow \frac{P^0 - P}{P^0} = x_{\text{solute}}

Why is this useful?

It depends only on the mole fraction of solute, not on its identity — making it a colligative property.

4. Elevation of Boiling Point

Formula:

\Delta T_b = K_b \cdot m

Why does boiling point rise?

Boiling occurs when vapour pressure = atmospheric pressure.
Adding a non-volatile solute lowers vapour pressure (Raoult's law).
To reach atmospheric pressure again, you must raise the temperature.
The shift $\Delta T_b$ $Δ T_{b}$ is proportional to the molality $m$ $m$ (moles of solute per kg of solvent), because:
- More solute → greater vapour pressure lowering → more temperature needed.
- $K_b$ (ebullioscopic constant) is a property of the solvent only.

5. Depression of Freezing Point

Formula:

\Delta T_f = K_f \cdot m

Why does freezing point drop?

At the freezing point, solid and liquid solvent are in equilibrium.
Adding solute disrupts this equilibrium — solute molecules interfere with the orderly crystal formation of the solvent.
To re-establish equilibrium, you must lower the temperature.
Again, $\Delta T_f \propto m$ , and $K_f$ depends only on the solvent.

Common exam trap: Both $\Delta T_b$ and $\Delta T_f$ are colligative — they depend on number of solute particles, not their nature.

6. Osmotic Pressure

Formula:

\Pi = i \cdot C \cdot R \cdot T

Why does this hold?

Osmosis is the net movement of solvent from low solute concentration to high solute concentration across a semipermeable membrane.
The solvent moves to dilute the higher concentration — this is a entropy-driven process (mixing increases disorder). …

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The key idea is that precipitation upon adding a small amount of solute indicates the solution is holding more dissolved solute than its equilibrium solubility - it is supersaturated. The correct option is (ii).

Why this works: The concept of saturation

Unsaturated: More solute can still dissolve. Adding a little more simply dissolves it - no precipitation.
Saturated: The solution holds exactly the maximum solute. Adding extra remains undissolved, but the existing dissolved amount stays unchanged.
Supersaturated: The solution holds more solute than the equilibrium solubility - a metastable state. The slightest disturbance (adding a seed crystal or a tiny amount of solute) triggers rapid precipitation until the concentration drops to the saturation level.

The question says precipitation occurs when a small amount of 'A' is added - the classic behaviour of a supersaturated solution.

Step-by-step reasoning

Rule out unsaturated (iii). Added solute would simply dissolve - no precipitation. …

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Here’s a breakdown of the common mistakes students make on this question, along with how to avoid each.

Mistake 1: Confusing "adding solute" with "adding a seed crystal"

The error: Many students think that if you add more solute and it dissolves, the solution must be unsaturated. Here, the question says precipitation takes place when a small amount of 'A' is added. Students often miss the key trigger: the added solid acts as a seed or nucleation site.
Why it’s wrong: In a supersaturated solution, the solute is already present in an amount greater than its solubility at that temperature. It is metastable. Adding even a tiny crystal of the solute provides a surface for the excess solute to crystallize out immediately.
How to avoid: Always read the action carefully. If adding a small amount of the solid causes precipitation, the solution was holding more solute than it normally can — that’s the definition of supersaturated.

Mistake 2: Choosing "saturated" because precipitation occurs

The error: Students recall that in a saturated solution, adding more solute causes it to settle at the bottom. They think this matches the description.
Why it’s wrong: In a saturated solution, adding more solute does not cause precipitation of the original solute — the added solid simply does not dissolve and remains as a separate solid. The question says "precipitation of substance 'A' takes place," meaning the existing dissolved solute comes out of solution. That only happens in a supersaturated solution.
How to avoid: Distinguish between:
- Saturated: Added solid stays undissolved (no change in dissolved amount).
- Supersaturated: Added solid triggers crystallization of dissolved solute.

Mistake 3: Thinking "concentrated" means the same as "supersaturated"

The error: Students pick "concentrated" because they think a lot of solute is present.
Why it’s wrong: "Concentrated" is a relative term (compared to a dilute solution) and does not imply that the solution is unstable or that precipitation will occur upon seeding. A concentrated solution can be unsaturated, saturated, or supersaturated. The key property here is metastability, not just concentration. …

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Q.A beaker contains a solution of substance 'A'. Precipitation of substance 'A' takes place when small amount of 'A' is added to the solution. The solution is _________.

Concept understanding — Types Of Solutions

Types of Solutions: From Everyday Life to Chemistry

The Intuition: A Cup of Tea

The Precise Statement

Breaking Down Each Type

Why this formula?

Types of Solutions: Why the Key Formulae Hold

1. The Basic Classification: What Makes a Solution?

2. Raoult's Law: The Foundation

Why does this hold?

3. Relative Lowering of Vapour Pressure

Derivation in one line:

4. Elevation of Boiling Point

Why does boiling point rise?

5. Depression of Freezing Point

Why does freezing point drop?

6. Osmotic Pressure

Why does this hold?

Why this works: The concept of saturation

Step-by-step reasoning

Concept: Saturation and Supersaturation

Method: Observation of Solute Addition

Steps:

Mistake 1: Confusing "adding solute" with "adding a seed crystal"

Mistake 2: Choosing "saturated" because precipitation occurs

Mistake 3: Thinking "concentrated" means the same as "supersaturated"

Q.A beaker contains a solution of substance 'A'. Precipitation of substance 'A' takes place when small amount of 'A' is added to the solution. The solution is _________.

Why this works: The concept of saturation

Step-by-step reasoning

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