An increase in entropy can best be illustrated by

1. Analyze the Question

The question asks for an example of an increase in entropy. In chemistry, entropy is a measure of the degree of disorder, randomness, or chaos in a system. An increase in entropy means the system is moving from a more ordered state to a more disordered state.

2. Explain the Concept

• Entropy ($\Delta S$): Think of entropy as the "messiness" of particles. • Solids have low entropy because particles are fixed in a rigid structure (highly ordered). • Liquids have higher entropy because particles can move past each other. • Gases have the highest entropy because particles move randomly at high speeds and occupy all available space (highly disordered).
• The Rule: Processes that increase the freedom of movement or the volume available to particles result in an increase in entropy. Conversely, processes like freezing or condensation (moving from gas/liquid to solid) decrease entropy because they increase order.

3. Show the Solution

Let's evaluate the options:

• A. Mixing of gases: When two different gases are mixed, the particles of each gas spread out into a larger volume and become more randomly distributed. This increase in spatial randomness represents a significant increase in entropy.
• B. Freezing of water: Water molecules move from a liquid state (more random) to a solid ice state (ordered crystal lattice). This is a decrease in entropy.
• C. The condensation of vapour: Vapour (gas) molecules lose kinetic energy and come together to form a liquid. This transition from high disorder to lower disorder is a decrease in entropy.
• D. Solidifying candle wax: Similar to freezing, the wax molecules lose energy and settle into a more ordered solid structure. This is a decrease in entropy.

4. Identify the Answer

Since mixing gases increases the randomness and disorder of the system, it is the correct illustration of an increase in entropy.

5. Exam Tip

Remember the "Disorder Rule":

• Solid $\rightarrow$ Liquid $\rightarrow$ Gas = Entropy Increases ($\Delta S > 0$)
• Gas $\rightarrow$ Liquid $\rightarrow$ Solid = Entropy Decreases ($\Delta S < 0$)
• Mixing or Dissolving usually Increases entropy because the particles are spreading out!