Assertion (A): A liquid crystallises into a solid and is accompanied by decrease in entropy. Reason (R): In cr

NCERT Exemplar · Q57

Q. Assertion (A): A liquid crystallises into a solid and is accompanied by decrease in entropy. Reason (R): In crystals, molecules organise in an ordered manner.

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

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

(iii) A is true but R is false.

(iv) A is false but R is true.

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Concept understanding — Entropy Change Prediction

Entropy Change Prediction

Imagine you have a box of marbles — all neatly arranged, reds on one side, blues on the other. Now shake the box. What happens? The colours mix. They never spontaneously unmix. That tendency — for things to go from ordered to disordered — is what entropy measures. Entropy is a measure of disorder or randomness in a system.

When you predict an entropy change, you're asking: Will this process make the system more disordered or less disordered? And by how much?

The Core Intuition

Entropy change ( $\Delta S$ ) is positive when disorder increases, negative when disorder decreases. Three things drive this:

Volume change — More space means more positions for particles → more disorder. A gas expanding into vacuum has $\Delta S > 0$ .
Temperature change — Higher temperature means particles move faster, explore more states → more disorder. Heating something increases entropy.
Phase change — Solid → liquid → gas is a ladder of increasing disorder. Melting ice increases entropy; freezing water decreases it.

Note

Entropy always increases for spontaneous processes in an isolated system (Second Law of Thermodynamics). But for a non-isolated system, entropy can decrease locally — as long as the surroundings' entropy increases enough to compensate.

The Precise Statement

For a reversible process at constant temperature, the entropy change is:

\Delta S = \frac{Q_{\text{rev}}}{T}

where $Q_{\text{rev}}$ is the heat transferred reversibly, and $T$ is the absolute temperature (in Kelvin).

For an irreversible process (which is what actually happens), you calculate $\Delta S$ by imagining a reversible path between the same initial and final states — because entropy is a state function. It depends only on where you start and end, not how you get there.

\Delta S = \int \frac{dQ_{\text{rev}}}{T}

For common cases, you use these:

Process	Formula	Sign intuition
Isothermal expansion/compression (ideal gas)	$\Delta S = nR \ln\frac{V_2}{V_1}$	Expanding → more volume → $\Delta S > 0$
Heating/cooling (constant pressure)	$\Delta S = nC_p \ln\frac{T_2}{T_1}$	Heating → higher T → $\Delta S > 0$
Phase change (melting, boiling)	$\Delta S = \frac{\Delta H_{\text{phase}}}{T_{\text{phase}}}$	Melting/boiling → more disorder → $\Delta S > 0$

How to Predict Without Calculation

You don't always need numbers. Ask these questions in order:

Is there a phase change? Solid → liquid or liquid → gas always increases entropy. Reverse decreases it.
Is the number of gas molecules changing? In a reaction, more gas molecules means more disorder. $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ (gas → liquid) has $\Delta S < 0$ because 3 gas molecules become 2 liquid molecules.
Is temperature increasing or decreasing? Higher temperature → higher entropy.
Is volume increasing? More space → more entropy. …

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Crystallisation reduces disorder as molecules move from random liquid motion to fixed lattice positions, so entropy decreases. Both statements are true, and the ordered arrangement in crystals directly explains the entropy drop.

Entropy measures the degree of disorder or randomness in a system. When we predict whether a process increases or decreases entropy, we look at how the freedom of molecular motion changes.

In a liquid, molecules slide past one another with considerable translational and rotational freedom. They occupy no fixed positions and their arrangement is constantly shifting. This high degree of randomness corresponds to high entropy.

When that liquid crystallises into a solid, the molecules lock into a rigid three-dimensional lattice. Each molecule now vibrates about a fixed equilibrium position. The translational and rotational freedoms are severely restricted. The system has moved from disorder to order, so entropy decreases.

Now let's examine both statements:

Assertion (A): "A liquid crystallises into a solid and is accompanied by decrease in entropy."

This is true. Crystallisation is an exothermic phase transition ( $\Delta H < 0$ ) that occurs spontaneously below the freezing point. Even though $\Delta S_{\text{system}} < 0$ , the heat released increases the entropy of the surroundings enough that $\Delta S_{\text{total}} > 0$ , satisfying the second law. The assertion correctly identifies that the system's entropy decreases.
Reason (R): "In crystals, molecules organise in an ordered manner."

This is also true. Crystals are defined by their long-range periodic order—atoms or molecules occupy specific lattice sites with translational symmetry. This ordered arrangement is the hallmark of the crystalline state.
Does R explain A? …

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Q.Assertion (A): A liquid crystallises into a solid and is accompanied by decrease in entropy. Reason (R): In crystals, molecules organise in an ordered manner.

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Q.Assertion (A): A liquid crystallises into a solid and is accompanied by decrease in entropy.
Reason (R): In crystals, molecules organise in an ordered manner.

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