Problem 15 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

For the process \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) at \(T=100^{\circ} \mathrm{C}\) and 1 atmosphere pressure, the correct choice is (a) \(\Delta S_{\text {system }}>0\) and \(\Delta S_{\text {surroundings }}>0\) (b) \(\Delta S_{\text {system }}>0\) and \(\Delta S_{\text {surroundings }}<0\) (c) \(\Delta S_{\text {system }}<0\) and \(\Delta S_{\text {surroundings }}>0\) (d) \(\Delta S_{\text {system }}<0\) and \(\Delta S_{\text {surroundings }}<0\)

Step-by-Step Solution

Answer

Option (b): \(\Delta S_{\text{system }} > 0\), \(\Delta S_{\text{surroundings}} < 0\).

Step 1: Understand the Process

The process described is the transformation of water from liquid to gas, i.e., evaporation or boiling. At 100°C and 1 atmosphere, water is at its boiling point, transitioning from a more ordered liquid state to a less ordered gaseous state.

Step 2: Determine \(\Delta S_{\text{system}}\)

Entropy (\(S\)) is a measure of disorder. In the process of evaporation, the molecules in water gain freedom and move more randomly. This increase in disorder means \(\Delta S_{\text{system}} > 0\).

Step 3: Analyze the Entropy Change of the Surroundings

When water evaporates at its boiling point under an isothermal process at 1 atm, it absorbs heat from the surroundings. The entropy of the surroundings (\(\Delta S_{\text{surroundings}}\)) decreases because they lose heat. Therefore, \(\Delta S_{\text{surroundings}} < 0\).

Step 4: Select the Correct Option

From Steps 2 and 3, we know that \(\Delta S_{\text{system}} > 0\) and \(\Delta S_{\text{surroundings}} < 0\). This corresponds to option (b).

Key Concepts

Phase Transition

During a phase transition, a substance changes from one state of matter to another, such as from liquid to gas. This can be a fascinating process to observe, particularly when it comes to water transitioning from a liquid to a gaseous state. In the scenario provided, water is at its boiling point, causing it to undergo vaporization.
When water reaches its boiling point at 100°C, it has enough energy to break free of the molecular forces constraining it in the liquid phase. The molecules gain more freedom and begin to spread out as a gas. This shift is called a phase transition because water is moving from one phase (liquid) to another (gas).
- The energy required for the transition helps break intermolecular bonds. - The state of the molecules changes from ordered in a liquid to more disordered in a gas. - This process is endothermic, absorbing heat from the surroundings to drive the change. Understanding phase transition is critical for grasping why such processes affect the entropy of both the system and its surroundings.

Boiling Point

The boiling point is a key concept concerning the behavior of substances during phase transitions. It refers to the specific temperature at which a liquid becomes a gas, under an established atmospheric pressure. For water, the boiling point at sea level is 100°C, making it a common reference point in scientific and everyday contexts.
During boiling, a liquid reaches the temperature where its vapor pressure equals the atmospheric pressure surrounding it. At this equilibrium, molecules have enough energy to change into vapor, overcoming atmospheric pressure. Boiling occurs not only on the surface of the liquid but throughout it, forming bubbles that rise to the surface and release gas.
- Boiling is dependent on the external pressure; at higher altitudes, where pressure is lower, the boiling point drops. - It’s a critical point that dictates the energy dynamics of a phase transition. - Understanding boiling point clarifies why heat transfer is essential during this phase change, affecting entropy in the system and surroundings.

Disorder in Chemistry

Disorder, or entropy, is a fundamental aspect in chemistry that describes the level of randomness or chaos within a system. In the process of water boiling, there's an increase in disorder when the structured molecules of a liquid transition to the freer, more energetic state of a gas.
Entropy is denoted as \(S\), and its change (\(\Delta S\)) reflects changes in the molecular chaos. In a closed system, when water transitions to vapor, the molecules disperse more widely compared to their organized state in the liquid phase.
- Entropy change in a system is generally positive when transitioning from liquid to gas (\(\Delta S_{system} > 0\)).- During boiling, although the system absorbs heat (increasing its entropy), it cools the surroundings, reducing their entropy (\(\Delta S_{surroundings} < 0\)).- The concept of disorder helps highlight the balance in nature; as systems increase in disorder, they tend to release or absorb energy, impacting their environment.Entropy is a crucial concept for understanding the flow of energy and its effects on both phase transitions and broader thermodynamic processes.