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. \(\mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(1), \mathrm{T}=25^{\circ} \mathrm{C}, \mathrm{P}=1 \mathrm{~atm}\) (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

The correct answer is (b) I and II are both spontaneous.

Step 1: Understanding Spontaneity

Spontaneous processes occur without any energy input from outside the system. Non-spontaneous processes require energy to occur.

Step 2: Evaluating Process I

Process I is the evaporation of liquid water into water vapor at 25°C with 50% relative humidity. Evaporation is a spontaneous process at room temperature when the humidity is less than 100%, as the air can absorb more water vapor.

Step 3: Evaluating Process II

Process II is the melting of ice at 25°C and 1 atm. Since the temperature is above the melting point of ice (0°C), the process is spontaneous under these conditions.

Step 4: Conclusion

Both processes occur spontaneously at 25°C under the given conditions.

Key Concepts

Spontaneity

In thermodynamics, a process is said to be spontaneous if it occurs without needing any input of external energy. Spontaneity is an essential concept because it indicates the natural direction of a process. A simple way to think about it is that spontaneous processes are those that tend to occur under their own energy. For example, water flows downhill spontaneously because it moves towards a state of lower energy. In the context of the given exercise, spontaneity helps us understand whether water will evaporate or freeze under certain conditions. A process like evaporation, where liquid water turns into vapor, happens spontaneously at 25°C in an environment with less than 100% humidity. This is because the atmosphere can absorb more water vapor, allowing the process to occur naturally. Another key example from the exercise is the melting of ice. Since the temperature is above 0°C, ice molecules have enough energy to break free from their solid-state and transition into a liquid state without needing additional energy. This indicates the spontaneous nature of melting ice at 25°C.

Phase Transitions

Phase transitions are changes between different states of matter, such as solid, liquid, and gas. These transitions occur when energy (usually in the form of heat) flows into or out of a substance. Understanding phase transitions is crucial to thermodynamics, as it allows us to predict how a substance behaves under varying temperature and pressure conditions. There are several common phase transitions:

• Melting: solid to liquid.
• Freezing: liquid to solid.
• Evaporation: liquid to gas.
• Condensation: gas to liquid.
• Sublimation: solid to gas without becoming a liquid.
• Deposition: gas to solid without becoming a liquid.

In the exercise, we observe two phase transitions: evaporation of water into vapor and melting of ice into liquid water. Evaporation at 25°C occurs spontaneously because the air, having 50% relative humidity, can still absorb more moisture. Melting is also spontaneous since the temperature is above ice's freezing point, causing the solid to convert to a liquid naturally as heat energy is absorbed.

Free Energy Change

Free energy change, often expressed by the Gibbs Free Energy (9G), is a measure used to predict the spontaneity of a process. It considers both enthalpy (heat content) and entropy (disorder) changes in a system, providing a clearer picture of a process's potential to occur spontaneously.The formula for Gibbs Free Energy is:\[9G = 9H - T9S\]where:

• \(9G\) is the change in free energy.
• \(9H\) is the change in enthalpy.
• \(T\) is the temperature in Kelvin.
• \(9S\) is the change in entropy.

For a process to be spontaneous, the change in free energy must be negative (\(9G < 0\)). This means the energy available from the system's own resources is sufficient to drive the process.In the provided exercise, evaluating the free energy change helps in determining spontaneous behavior for both evaporation and melting. At 25°C, both processes have negative free energy changes, thus confirming their spontaneous nature. The loss of order when water evaporates increases entropy, which coupled with adequate enthalpy, ensures that \(9G\) for both phase transitions is negative.