Question

For the process \(\mathrm{H}_{2} \mathrm{O}(l)(1\) bar, \(373 \mathrm{~K}) \rightarrow \mathrm{H}_{2} \mathrm{O}(g)\) ( 1 bar, \(373 \mathrm{~K}\) ), the correct set of thermodynamic parameters is (A) \(\Delta G=0, \Delta S=+v e\) (B) \(\Delta \mathrm{G}=0, \Delta \mathrm{S}=-\mathrm{ve}\) (C) \(\Delta \mathrm{G}=+\mathrm{ve}, \Delta \mathrm{S}=0\) (D) \(\Delta \mathrm{G}=-\) ve, \(\Delta \mathrm{S}=+\mathrm{ve}\)

Short answer

\( \Delta G = 0 \) and \( \Delta S \text{ is positive} \) for the boiling process of water at its boiling point under standard conditions.

Step-by-step solution

Understand the Phase Transition

The given process describes the phase transition of water from liquid to gas at its boiling point (373 K) under standard pressure (1 bar). This is an example of a phase change at equilibrium.

Relate to Gibbs Free Energy

At equilibrium in a phase transition, the Gibbs free energy change \( \Delta G \) is zero because the system is at its maximum entropy and no non-PV work is being done.

Analyze Entropy Change

When water boils, its entropy increases because the gas phase is more disordered than the liquid phase. This means that \( \Delta S \) is positive.

Select the Correct Option

Based on Steps 2 and 3, the correct set of thermodynamic parameters is where \( \Delta G = 0 \) and \( \Delta S \) is positive. Therefore, the correct answer is option (A) \( \Delta G = 0, \Delta S = +ve \).

Key concepts

Gibbs Free Energy

The concept of Gibbs free energy, denoted as \( G \), is crucial in the field of thermodynamics, particularly when we talk about chemical reactions and phase transitions. It combines the system's enthalpy (\( H \)), temperature (\( T \)), and entropy (\( S \)) in the formula \( G = H - TS \). In lay terms, Gibbs free energy measures the maximum reversible work that can be performed by a thermodynamic system at a constant temperature and pressure.

When the change in Gibbs free energy \( \Delta G \) for a process is negative, the process can occur spontaneously. Conversely, if \( \Delta G \) is positive, the process is non-spontaneous and requires energy input. A system is in equilibrium when \( \Delta G \) equals zero, which implies that no net change can occur; this is the case in a phase transition at equilibrium, such as when water boils at its boiling point.

To better understand this concept, let us consider a visual analogy: imagine Gibbs free energy as the fuel in a car's tank. A negative value would mean the car can drive forward under its own power, while a positive value would be like needing a push to move the car. When the fuel gauge reads 'empty', or \( \Delta G = 0 \), the car is at a rest stop. In the context of the textbook exercise, during the phase transition of water from liquid to gas at its boiling point, \( \Delta G \) is zero, indicating equilibrium.

Phase Transition

A phase transition is a transformation of a substance from one state of matter—solid, liquid, or gas—to another. Each state has unique properties and the transitions between these states occur at specific temperature and pressure conditions, often referred to as the phase boundaries.

During a phase transition, the substance absorbs or releases energy, typically as heat, without changing temperature. This energy change is associated with the breaking or forming of intermolecular bonds. The boiling of water (liquid to gas) and the melting of ice (solid to liquid) are typical examples of phase transitions.

Phase transitions are classified into first-order transitions, which involve a latent heat and discontinuity in the first derivative of free energy (like melting or boiling), and second-order transitions, which do not involve latent heat but exhibit discontinuity in the second derivative of free energy (like the superconducting transition).

Understanding Equilibrium in Phase Transitions

At equilibrium, during a phase transition, the system's temperature and pressure are constant, and the Gibbs free energy does not change, as reflected by \( \Delta G = 0 \). Applying this knowledge to our exercise, as water turns into vapor at its boiling point under a constant pressure of 1 bar, energy in the form of heat is being used to facilitate this transition without a change in temperature, symbolizing a typical phase transition.

Entropy Change

Entropy, symbolized by \( S \), is a measure of the disorder or randomness in a thermodynamic system. It is a fundamental concept in explaining the direction of processes and the efficiency of energy conversion. Entropy change, \( \Delta S \), during a process, indicates how the disorder of a system changes.

An increase in entropy (\( \Delta S > 0 \)) suggests a transition towards more disorder. For example, when ice melts to water or water evaporates to steam, the molecules move from a more structured state to a less structured, more random state. Conversely, a decrease in entropy (\( \Delta S < 0 \)) indicates a transition towards order.

In a closed system, the second law of thermodynamics proclaims that the entropy of the system and its surroundings cannot decrease overall. This implies that processes naturally progress in the direction that increases the total entropy of the universe.

Connecting Entropy to the Phase Change of Water

In our textbook exercise regarding the boiling of water at a constant temperature and pressure, the entropy of the water increases as it changes from liquid to gas. This is because the gas phase has more disorder due to the greater freedom of movement for the molecules compared to the liquid phase. Consequently, this increase in entropy is quantitatively represented by a positive value for \( \Delta S \) in the provided options of the exercise, reinforcing the principle that the randomness of the system increases during the phase transition from liquid to gas.