Problem 33 - A Complete Resource Book in Chemistry for JEE Main

Question

Classify each of the following processes as spontaneous or non-spontaneous. I. \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g}), \mathrm{T}=25^{\circ} \mathrm{C}\) vessel open to atomsphere with \(50 \%\) relative humidity. II. \(\mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l}), \mathrm{T}=25^{\circ} \mathrm{C}, \mathrm{P}=1 \mathrm{~atm}\) (a) I and II are both non-spontaneous (b) I and II are both spontaneous (c) I is non-spontaneous and II is spontaneous (d) I is spontaneous and II is non-spontaneous

Step-by-Step Solution

Answer

Both I and II are spontaneous (option b).

Step 1: Identify the Process of Part I

The first process is the evaporation of liquid water into water vapor. Since the temperature given is 25°C and the vessel is open to the atmosphere with 50% relative humidity, we need to determine if evaporation is spontaneous under these conditions.

Step 2: Analyze Spontaneity of Part I

At 25°C with 50% relative humidity, the air still has capacity to hold more water vapor. Evaporation is favored as it increases entropy and continues until the air is saturated (100% humidity), making this process spontaneous.

Step 3: Identify the Process of Part II

The second process is the melting of ice to liquid water at 25°C and 1 atm pressure.

Step 4: Analyze Spontaneity of Part II

Since ice melts naturally when the temperature is above 0°C at 1 atm (25°C is well above 0°C), this process is spontaneous.

Step 5: Conclusion Based on Analysis

Both processes are determined to be spontaneous based on the analysis of the conditions provided.

Key Concepts

Evaporation

Evaporation is the process where liquid turns into gas. In the context of water, it refers to the transition of water molecules from liquid to vapor. This process is influenced by factors like temperature and humidity. At 25°C, which is room temperature, water molecules have enough energy to escape from the liquid phase. The presence of 50% relative humidity means that the air can still accommodate more water vapor.

• Heat and Energy: Evaporation involves the absorption of heat by water molecules, which increases their kinetic energy. The movement and energy allow water molecules at the surface to break free into the air as vapor.
• Humidity's Role: Relative humidity is the amount of moisture in the air compared to what the air can hold at that temperature. When the air is not saturated (less than 100% humidity), evaporation is favored.

Thus, with a relative humidity of 50%, the air still has room for more moisture, making the evaporation process spontaneous under these conditions.

Melting

Melting is the process by which a solid turns into a liquid when its temperature is increased to its melting point. For ice, this transition happens at 0°C. At 25°C, well above the melting point of ice, the process is spontaneous.

• Heat Absorption: During melting, heat causes the molecules in a solid to vibrate more. Eventually, they gain enough energy to break the rigid structure, transitioning to a liquid state.
• Temperature Influence: The concept of melting is directly linked to the heat being higher than the solid's melting point. Ice melts spontaneously at any temperature above 0°C at standard atmospheric pressure.

So, with the conditions set at 25°C and 1 atm pressure, the melting of ice to water is a spontaneous process.

Entropy

Entropy is a measure of disorder or randomness in a system. In thermodynamics, it is said to always increase in a spontaneous process.

• Evaporation and Entropy: When water evaporates, the molecules move from a structured liquid state to a more random gaseous state. This increase in randomness leads to an increase in entropy.
• Melting and Entropy: Similarly, melting transitions molecules from the ordered structure of a solid to the less ordered arrangement in a liquid, thereby increasing entropy.

Thus, both evaporation and melting are examples of processes that lead to an increase in entropy, which aligns with the criteria for spontaneity.

Relative Humidity

Relative humidity is a climatic measure that expresses how much moisture is in the air relative to the maximum amount it can hold at a given temperature. It plays a pivotal role in evaporation.

• Understanding Humidity Levels: If the air is at 50% relative humidity, it contains half the moisture it is able to hold at that temperature. This means there is potential for more moisture to be absorbed from evaporation.
• Impact on Spontaneity: When humidity is below 100%, as in our scenario, the process of evaporation can continue because the air isn't saturated, allowing more water molecules to escape into the vapor phase.

Therefore, at 50% relative humidity, evaporation is encouraged and deemed spontaneous as there is ample capacity for the air to intake additional moisture.