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.
(b) What are the signs ( + , - , or 0) of ∆H, ∆S, and ∆G for this process? Explain.

Verified step by step guidance

1. Identify the nature of the process: When the stopcock between two bulbs containing different gases is opened, the gases mix. This is a spontaneous mixing process at constant temperature and pressure.
2. Analyze ∆H (Change in Enthalpy): Since there is no heat exchange with the surroundings (isolated system) and no work done other than expansion against constant pressure, ∆H for mixing ideal gases is zero.
3. Analyze ∆S (Change in Entropy): The entropy increases as the gases mix due to the increase in randomness and number of microstates available to the system. Therefore, ∆S is positive.
4. Analyze ∆G (Change in Gibbs Free Energy): Use the Gibbs free energy equation, ∆G = ∆H - T∆S. Since ∆H is zero and ∆S is positive, and assuming the temperature T is positive, ∆G will be negative, indicating a spontaneous process.
5. Summarize the signs: ∆H = 0 (no heat exchange and no work done other than against constant pressure), ∆S > 0 (increase in randomness and microstates), ∆G < 0 (spontaneous process).

Key Concepts

Enthalpy (∆H)

Enthalpy is a thermodynamic quantity that represents the total heat content of a system. In the context of gas expansion, when the stopcock is opened, the gases A and B mix without any heat exchange with the surroundings, leading to no change in enthalpy (∆H = 0). This is because the process is isothermal and occurs at constant temperature.

Entropy (∆S)

Entropy is a measure of the disorder or randomness in a system. When the stopcock is opened, the gases A and B will mix, resulting in an increase in disorder as the molecules spread out to occupy a larger volume. Therefore, the change in entropy (∆S) is positive, indicating that the system has become more disordered.

Gibbs Free Energy (∆G)

Gibbs Free Energy is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. The relationship ∆G = ∆H - T∆S helps determine spontaneity. Since ∆H = 0 and ∆S is positive, ∆G will also be negative, indicating that the process of mixing the gases is spontaneous.