The standard molar entropy of H2O(l) is 70 J K^-1 mol^-1. Will the standard molar entropy of H2O(s) be more, o

NCERT Exemplar · Q32

Q. The standard molar entropy of H2O(l) is 70 J K^-1 mol^-1. Will the standard molar entropy of H2O(s) be more, or less than 70 J K^-1 mol^-1?

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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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The standard molar entropy is a measure of molecular disorder. Since water molecules in the solid state (ice) are more ordered and have less freedom of movement than in the liquid state, the standard molar entropy of H2O(s) will be less than 70 J K $^{-1}$ mol $^{-1}$ .

The question asks us to compare the standard molar entropy of liquid water, H $_2$ O(l), with that of solid water, H $_2$ O(s). To understand this, we need to grasp the fundamental concept of entropy.

Entropy, denoted by $S$ , is a thermodynamic property that quantifies the degree of randomness or disorder in a system. It can also be thought of as a measure of the number of possible microscopic arrangements (microstates) that correspond to a given macroscopic state. A system with more microstates has higher entropy.

The key factors influencing entropy are:

Molecular motion: The more freedom molecules have to move (translate, rotate, vibrate), the higher the entropy.
Molecular arrangement: A more disordered or random arrangement of molecules corresponds to higher entropy.
Energy distribution: The more ways energy can be distributed among the molecules, the higher the entropy.

Let's apply this understanding to compare the entropy of liquid and solid water.

Understanding the States of Matter:
- Solid State (H $_2$ O(s) - Ice): In the solid state, water molecules are arranged in a highly ordered, rigid crystal lattice structure. Each molecule is held in a relatively fixed position by strong intermolecular forces (hydrogen bonds). Their primary motion is vibration about these fixed positions. There is very little translational or rotational freedom.
- Liquid State (H $_2$ O(l) - Liquid Water): In the liquid state, water molecules are still relatively close to each other, but the intermolecular forces are weaker and constantly breaking and reforming. This allows molecules to move past one another, translate, rotate, and vibrate. The arrangement is much less ordered than in a solid, though not as random as in a gas.
Comparing Disorder and Molecular Freedom:
- Because molecules in liquid water have greater freedom of movement (translational, rotational, and vibrational) and a less ordered arrangement compared to molecules in solid water (which are largely restricted to vibrational motion in fixed positions), the liquid state represents a higher degree of disorder. …

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Q.The standard molar entropy of H2O(l) is 70 J K^-1 mol^-1. Will the standard molar entropy of H2O(s) be more, or less than 70 J K^-1 mol^-1?

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