Consider the dissociation reaction A₂(g) ⇌ 2 A(g). The following pictures represent two possible initial states and the equilibrium state of the system:
(b) What are the signs ( + , - , or 0) of ∆H, ∆S, and ∆G when the system goes from initial state 1 to the equilibrium state? Explain. Is this a spontaneous process?

Verified step by step guidance

1. Identify the nature of the reaction: The dissociation of A₂(g) into 2 A(g) involves breaking bonds, which generally requires energy. Thus, the enthalpy change (∆H) for the reaction is likely positive (+), as energy is absorbed to break the bonds in A₂(g).
2. Consider the entropy change (∆S): The reaction results in the formation of more gas particles (from 1 molecule of A₂ to 2 molecules of A). Increasing the number of gas particles increases the randomness or disorder of the system, suggesting that the entropy change (∆S) is positive (+).
3. Determine the sign of the Gibbs free energy change (∆G) using the relationship ∆G = ∆H - T∆S. Since ∆H is positive and ∆S is also positive, the temperature (T) will play a crucial role. At high temperatures, the T∆S term may outweigh ∆H, leading to a negative (∆G), which indicates a spontaneous process.
4. Assess the spontaneity of the process: If ∆G is negative, the process is spontaneous. The temperature dependency must be considered to fully determine spontaneity across different temperatures.
5. Summarize the signs: ∆H is positive (+), ∆S is positive (+), and ∆G could be negative (-) depending on the temperature, indicating that the reaction could be spontaneous under certain conditions.

Key Concepts

Enthalpy (∆H)

Enthalpy (∆H) is a measure of the total heat content of a system. In a dissociation reaction like A₂(g) ⇌ 2 A(g), if the reaction absorbs heat, it is endothermic, resulting in a positive ∆H. Conversely, if it releases heat, it is exothermic, leading to a negative ∆H. Understanding the sign of ∆H helps determine whether the reaction requires or releases energy.

Entropy (∆S)

Entropy (∆S) is a measure of the disorder or randomness in a system. In the reaction A₂(g) ⇌ 2 A(g), the dissociation of one molecule into two increases the number of gas particles, leading to greater disorder. Therefore, this process typically has a positive ∆S, indicating an increase in entropy, which is a driving force for spontaneity in many reactions.

Gibbs Free Energy (∆G)

Gibbs Free Energy (∆G) combines enthalpy and entropy to determine the spontaneity of a reaction at constant temperature and pressure. The relationship is given by the equation ∆G = ∆H - T∆S. A negative ∆G indicates a spontaneous process, while a positive ∆G suggests non-spontaneity. Evaluating the signs of ∆H and ∆S is crucial for predicting the sign of ∆G and the spontaneity of the reaction.