Ideal gases A (red spheres) and B (blue spheres) occupy two...

Ideal gases A (red spheres) and B (blue spheres) occupy two separate bulbs. The contents of both bulbs constitute the initial state of an isolated system. Consider the process that occurs when the stopcock is opened. (a) Sketch the final (equilibrium) state of the system. (b) What are the signs $(+,-, \text { or } 0)$ of $\Delta H, \Delta S,$ and $\Delta G$ for this process? Explain. (c) How does this process illustrate the second law of thermodynamics? (d) Is the reverse process spontaneous or nonspontaneous? Explain.

Ideal gases A (red spheres) and B (blue spheres) occupy two separate bulbs. The contents of both bulbs constitute the initial state of an isolated system. Consider the process that occurs when the stopcock is opened.
(a) Sketch the final (equilibrium) state of the system.
(b) What are the signs $(+,-, \text { or } 0)$ of $\Delta H, \Delta S,$ and $\Delta G$ for this process? Explain.
(c) How does this process illustrate the second law of thermodynamics?
(d) Is the reverse process spontaneous or nonspontaneous? Explain.

Key Concepts

Gibbs Free Energy (?G) and Spontaneity

Gibbs free energy combines enthalpy, entropy, and temperature to predict whether a process will occur spontaneously at constant temperature and pressure. A negative change in Gibbs free energy (?G < 0) indicates a spontaneous process. In a gas mixing scenario with zero enthalpy change and increased entropy, the decrease in Gibbs free energy illustrates the spontaneous nature of the mixing process.

Second Law of Thermodynamics

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and processes occur in the direction of increasing entropy. In the case of mixing gases, the spontaneous drive towards a more disordered state (increased entropy) serves as a clear illustration of the second law, where the entropy increase underpins the irreversible nature of the process.

Entropy (?S)

Entropy is a measure of the number of possible microscopic configurations corresponding to the macroscopic state of a system, often interpreted as the degree of disorder. The mixing of gases increases the randomness or disorder of the system, leading to a positive change in entropy, which is a key factor driving the spontaneity of the process.

Enthalpy (?H)

Enthalpy is a thermodynamic quantity that represents the heat content of a system at constant pressure. In processes such as the mixing of ideal gases, if there are no significant interactions between the gas molecules, the net change in enthalpy is typically zero, reflecting that no heat is absorbed or released as a result of the mixing.

Isolated Systems

An isolated system is one that does not exchange heat, work, or matter with its surroundings, meaning that the total energy of the system remains constant. Processes occurring in isolated systems are driven solely by internal changes, such as the redistribution of particles, and the analysis of such systems emphasizes the increase in disorder or entropy without energy exchange with the environment.

Thermodynamic Equilibrium

Thermodynamic equilibrium is the state in which a system's macroscopic properties remain constant in time because there are no net flows of matter or energy. In the context of gas mixing, equilibrium is achieved when the gases are evenly distributed throughout the available volume, and no further spontaneous changes in concentration or energy distribution occur.

Mixing of Gases

When two or more ideal gases are allowed to mix, the system evolves toward a homogeneous state where the individual components are uniformly distributed. This mixing process is characterized by the absence of intermolecular forces between the separate species, meaning that the energetic interactions do not significantly change during the mixing, which has important consequences for the thermodynamic parameters of the system.

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