The following reaction of A3 molecules is spontaneous.
(b) What are the signs of ∆H, ∆S, and ∆G for the reaction? Explain.

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Step 1: Identify the initial and final states of the A3 molecules from the image. Initially, the molecules are in a compact state, and finally, they are in a dispersed state.

Step 2: Determine the sign of ∆S (entropy change). Since the molecules are moving from a compact to a more dispersed state, the entropy (∆S) increases, so ∆S is positive.

Step 3: Determine the sign of ∆H (enthalpy change). For a spontaneous reaction, if the process involves breaking bonds or increasing molecular motion, it is likely that the enthalpy change (∆H) is positive, indicating an endothermic process.

Step 4: Determine the sign of ∆G (Gibbs free energy change). For a reaction to be spontaneous, the Gibbs free energy change (∆G) must be negative.

Step 5: Summarize the signs of ∆H, ∆S, and ∆G. Based on the analysis, ∆H is positive, ∆S is positive, and ∆G is negative for the spontaneous reaction.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Enthalpy (∆H)

Enthalpy (∆H) is a measure of the total heat content of a system. In a spontaneous reaction, if the system releases heat to the surroundings, ∆H is negative, indicating an exothermic process. Conversely, if the system absorbs heat, ∆H is positive, indicating an endothermic process. Understanding the sign of ∆H helps determine whether the reaction is energetically favorable.

Entropy (∆S)

Entropy (∆S) is a measure of the disorder or randomness in a system. A positive ∆S indicates an increase in disorder, which is often the case when molecules transition from a more ordered state to a more dispersed state, as seen in the provided image. In spontaneous reactions, an increase in entropy is typically favorable, contributing to the overall spontaneity of the process.

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. For a reaction to be spontaneous, ∆G must be negative. Thus, understanding the signs of ∆H and ∆S is crucial for predicting the sign of ∆G and the spontaneity of the reaction.

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