Question

For which of the following process entropy change ($\Delta S$) is negative ?
I) Sublimation of dry ice
II) Freezing of water
III) Crystallisation of the dissolved substance
IV) Burning of rocket fuel

• A. I, II only
• B. II, III only
• C. III, IV only
• D. I, IV only

Hint:

To easily determine the sign of $\Delta S$, look at the physical states involved in the transition:
- Phase changes from more ordered to less ordered states (solid $\rightarrow$ liquid $\rightarrow$ gas) have $\Delta S > 0$.
- Phase changes from less ordered to more ordered states (gas $\rightarrow$ liquid $\rightarrow$ solid) have $\Delta S < 0$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to identify the processes among the given choices where the change in entropy ($\Delta S$) is negative, meaning the process leads to a decrease in randomness or disorder in the system.

Step 2: Detailed Explanation:

• Entropy ($S$) is a thermodynamic state function that measures the degree of randomness, molecular disorder, or chaos in a system. A positive change in entropy ($\Delta S > 0$) indicates an increase in disorder, while a negative change ($\Delta S < 0$) indicates an increase in order.

• Let us evaluate each process individually:

• I) Sublimation of dry ice: Sublimation is the direct transition of a substance from the solid phase to the gaseous phase. Dry ice is solid carbon dioxide ($\text{CO}_2$). When it sublimes, highly ordered solid molecules transition into highly disordered gaseous molecules. Thus, the randomness increases, leading to a positive entropy change ($\Delta S > 0$).

• II) Freezing of water: Freezing is the phase change from liquid water to solid ice. In the liquid state, water molecules move randomly and have high translational kinetic energy. Upon freezing, they lose kinetic energy and arrange themselves into a highly structured, rigid crystalline lattice. This transition from liquid to solid decreases the randomness, resulting in a negative entropy change ($\Delta S < 0$).

• III) Crystallisation of a dissolved substance: In a solution, solute particles are dissociated and randomly dispersed among solvent molecules, possessing high disorder. During crystallisation, these dissolved solute particles precipitate out of the solution to form a highly ordered solid crystal structure. The system moves from a state of higher dispersion to a highly ordered state, so the entropy decreases ($\Delta S < 0$).

• IV) Burning of rocket fuel: Combustion is a highly exothermic process that typically converts solid or liquid chemical propellants into a vast volume of hot, rapidly expanding gases (such as water vapor, $\text{CO}_2$, nitrogen, etc.). The conversion of a condensed phase into numerous gaseous molecules dramatically increases molecular chaos, meaning the entropy change is highly positive ($\Delta S > 0$).

• Combining these evaluations, we see that both freezing of water (II) and crystallisation of a dissolved substance (III) exhibit a negative entropy change ($\Delta S < 0$).

Step 3: Final Answer:
The processes with a negative entropy change are II and III.