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

Question

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

Step 1: Analyze Process I

Process I considers the evaporation of water from liquid to gas at 25°C with 50% relative humidity in an open vessel. In general, water tends to evaporate at any temperature due to the kinetic energy of the molecules. Even if relative humidity is at 50%, which means the air is not saturated, evaporation will still occur. Therefore, this process is spontaneous.

Step 2: Analyze Process II

Process II examines the melting of ice to liquid water at 25°C and 1 atm pressure. Since 25°C is above the melting point of ice (0°C), this process occurs without any external intervention under these conditions. Thus, this process is also spontaneous.

Step 3: Compare the Processes with Options

Given that both Process I and Process II are spontaneous under the described conditions, examine the provided options: (a) Both non-spontaneous — Incorrect (b) Both spontaneous — Correct (c) I is non-spontaneous and II is spontaneous — Incorrect (d) I is spontaneous and II is non-spontaneous — Incorrect

Step 4: Select the Correct Answer

Since both processes are spontaneous, the correct answer is option (b).

Key Concepts

Thermodynamics

Thermodynamics is the study of energy, heat transfer, and the work done by these interactions. In chemistry, it helps us understand why certain reactions or processes occur spontaneously.
A spontaneous process is one that occurs without the need for constant external energy. It tends towards thermodynamic equilibrium, often releasing free energy.
There are several factors affecting spontaneity:

• Temperature
• Pressure
• Entropy changes
• Enthalpy changes

For example, in Process I from the exercise, the conversion of liquid water to vapor occurs because of entropy. The system favors disordered states, like that of gases, over organized states, like liquids.

Phase Transitions

Phase transitions refer to changes in the state of matter—solid, liquid, and gas. They occur because of temperature and pressure changes. When ice melts at 25°C (Process II in our exercise), a solid turns into a liquid. This happens because the energy absorbed by the ice overcomes the lattice structure of the solid state.
During phase transitions:

• Temperature remains constant
• Energy is either absorbed or released
• There is a change in entropy

Thus, these changes often occur spontaneously when environmental conditions pass through critical points like the melting point or boiling point.

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases based on the idea that they are made of many small particles. These particles are in constant random motion.
This theory can be applied to understand evaporation, like in Process I, where:

• Molecules at the surface gain enough kinetic energy to break free into the vapor phase
• Evaporation increases with temperature
• Random molecular motion causes some molecules to escape even when the system isn't saturated

This theory helps explain why evaporation can be spontaneous even when relative humidity is not at 100%.

Relative Humidity

Relative humidity is a measure of how much moisture air contains compared to the maximum it can hold at that temperature.
In Process I of the exercise, the air has 50% relative humidity, meaning it is only halfway saturated.
This allows for continued evaporation:

• Relative humidity below 100% means there's room for more water vapor.
• Evaporation continues until air becomes saturated or equilibrium is reached.

Understanding relative humidity helps predict whether processes like drying or precipitation will occur, which are crucial for assessing the spontaneity of phase transitions.