Problem 9 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

For which of the following processes, \(\Delta \mathrm{S}\) is negative?(a) \(\mathrm{C}\) (diamond \() \rightarrow \mathrm{C}\) (graphite) (b) \(\mathrm{N}_{2}(\mathrm{~g}\), latm \() \rightarrow \mathrm{N}_{2}(\mathrm{~g}, 5 \mathrm{~atm})\) (c) \(\mathrm{N}_{2}(\mathrm{~g}, 273 \mathrm{~K}) \rightarrow \mathrm{N}_{2}(\mathrm{~g}, 300 \mathrm{~K})\) (d) \(\mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{H}(\mathrm{g})\)

Step-by-Step Solution

Answer

(b) \\( \mathrm{N}_2(g, 1\ atm) \rightarrow \mathrm{N}_2(g, 5\ atm) \\) has negative \\( \Delta S \\).

Step 1: Identifying Process States

Examine the given processes to understand the changes occurring: (a) Transition from diamond to graphite, (b) Pressure increase in nitrogen gas, (c) Temperature increase in nitrogen gas, and (d) Dissociation of hydrogen gas.

Step 2: Entropy Change in Phase Transition (Process a)

For (a), the transition from diamond to graphite, recall that graphite is a more stable form of carbon and usually has higher entropy due to increased disorder. Thus, \( \Delta S \) tends to be positive.

Step 3: Entropy Change with Pressure Change (Process b)

For (b), when the pressure of a gas increases from 1 atm to 5 atm, the volume decreases. Reduced volume leads to reduced disorder among gas molecules, hence \( \Delta S \) is negative.

Step 4: Entropy Change with Temperature Change (Process c)

For (c), raising the temperature from 273 K to 300 K increases the kinetic energy of gas molecules, increasing their disorder. Therefore, \( \Delta S \) is positive.

Step 5: Entropy Change with Molecular Dissociation (Process d)

For (d), the dissociation of \( \mathrm{H}_2 \) into individual hydrogen atoms increases disorder. The number of particles increases, leading to a positive \( \Delta S \).

Key Concepts

Phase Transition

During a phase transition, a substance changes from one state of matter to another, such as from a solid to a liquid. An important example of this is the transition of diamond to graphite.
While both are forms of carbon, graphite is more stable in normal conditions. Stability here means that graphite has a structure allowing the carbon atoms to move more freely, resulting in slightly increased disorder.
Entropy, which is a measure of disorder, usually increases during phase transitions if the resultant phase is more disordered. In the case of diamond to graphite, \( \Delta S \) is typically positive, indicating that graphite's greater disorder compared to diamond results in more entropy.

Pressure Change

Gas molecules move freely and have higher entropy due to their random motion. However, when you increase pressure, it has a distinct effect on entropy.
Take nitrogen gas as an example, where an increase in pressure from 1 atm to 5 atm is observed. As pressure increases, the volume occupied by nitrogen gas molecules decreases, forcing them into a tighter space.
This reduction in volume leads to a decrease in the disorder of the system.
As a result, the entropy change \( \Delta S \) is negative, highlighting the reduced randomness in the molecules' movement as they are compressed closer together.

Temperature Change

Temperature is directly related to the energy of particles in a system. A rise in temperature increases the kinetic energy of gases like nitrogen.
For instance, when the temperature of nitrogen gas increases from 273 K to 300 K, its molecules move more rapidly.
This increase in speed leads to greater randomness or disorder within the gaseous system.
Hence, \( \Delta S \) becomes positive, indicating that the entropy of the system increases with temperature due to the heightened motion and energy at the molecular level.

Molecular Dissociation

Molecular dissociation involves breaking a molecule into two or more smaller species. In the case of hydrogen gas dissociating into hydrogen atoms, we observe an increase in particle count.
Original hydrogen gas, \( \mathrm{H}_2 \), is made of paired molecules. When these dissociate into individual hydrogen atoms, the system experiences greater disorder due to more particles being present.
More particles mean more possible arrangements and states, indicating an increase in entropy.
As such, \( \Delta S \) is positive, reflecting how the dissociation process significantly enhances the randomness and disorder of the system.