An isolated system comprises the liquid in equilibrium with vapours. At this stage, the molar entropy of the vapour is (a) less than that of liquid (b) more than that of liquid (c) equal to zero (d) equal to that of liquid

Exploring the relationship between entropy and phases of matter reveals some fundamental properties regarding the disorder within different states. Entropy, a concept often discussed in thermodynamics, measures the randomness or disorder within a system. As a substance changes phases, such as transitioning from a solid to a liquid or a liquid to a gas, its entropy changes as a direct result of molecular behavior.

For example, in the liquid phase, molecules are relatively close to each other but move more freely than in a solid phase. However, when the phase shifts from liquid to gas, also known as vaporization, molecules are far apart and move with high degrees of freedom. This increased molecular freedom leads to higher entropy because there is a greater number of possible positions and energies the molecules can have.

In the context of the exercise, as the liquid and vapour are in equilibrium within an isolated system, the vapour phase possesses a higher level of disorder compared to the liquid phase. Therefore, its entropy is greater, as confirmed in the step-by-step solution provided.

An isolated system is one that does not exchange matter or energy with its surroundings. In terms of thermodynamics, an equilibrium within such a system means that macroscopic properties like temperature, pressure, and, notably, entropy, remain constant over time.

When a liquid is in equilibrium with its vapour in an isolated system, it signifies that the rates of evaporation and condensation are equal, resulting in no net change in the quantities of the respective phases. At this equilibrium point, entropy reaches a maximum value under the given constraints because there are no external influences to cause further changes in entropy.

Even though individual molecules may be exchanging between the liquid and vapour phases, the system as a whole does not evolve further; it has reached a state referred to as thermodynamic equilibrium. This balance captures the essence of equilibrium in isolated systems and is a crucial concept when analyzing changes in entropy during phase transitions.

Phase transitions are transformations from one state of matter to another, such as from solid to liquid (melting), liquid to gas (vaporization), or solid to gas (sublimation). During a phase transition, the energy of the system changes, often in the form of heat exchange, without a change in temperature until the transition is complete.

During phase transitions, entropy plays a significant role. For a phase change to occur, such as liquid to vapour, energy is added to the system to overcome intermolecular forces. As heat is absorbed during vaporization, for example, the molar entropy increases because the gaseous molecules can occupy a much larger volume and exhibit a greater range of kinetic energies.

The exercise highlights a key point about phase transitions: the entropy change that accompanies them is integral to understanding the behavior of substances. By recognizing that the entropy of a vapor is higher than that of its corresponding liquid, one gains insight into the nature of molecular disorder and the direction of phase changes in systems seeking equilibrium.