Question

Consider an exothermic reaction:
2A(s) \(\longrightarrow\) B(s) + C(g) + D(g)
The correct statement about the reaction is

• A. spontaneous at all temperatures.
• B. spontaneous only at very high temperatures.
• C. spontaneous only at very low temperatures.
• D. non-spontaneous at all temperatures.

Hint:

A reaction that is exothermic (\(\Delta H < 0\)) and increases entropy (\(\Delta S > 0\)) is thermodynamically favored in both driving forces.
Such reactions are always spontaneous, regardless of the temperature.

Answer 1

The Correct Option is A

To determine the spontaneity of the given reaction, we need to consider the thermodynamic concepts related to exothermic reactions, entropy changes, and the Gibbs free energy change (\(\Delta G\)).

The reaction given is:

\(2A(s) \longrightarrow B(s) + C(g) + D(g)\)

1. First, analyze whether the reaction is exothermic or endothermic. The problem states that the reaction is exothermic. In thermodynamics, an exothermic reaction means that the enthalpy change (\(\Delta H\)) is negative.
2. To assess spontaneity, we use the Gibbs free energy change equation:
3. For a reaction to be spontaneous, \(\Delta G\) must be negative. Hence, a negative \(\Delta G\) is required for spontaneity.
4. In the given reaction, there is a change from 1 mole of solid on the reactant side to 2 moles of gas (C and D) on the product side. This indicates an increase in randomness or entropy (\(\Delta S\)), meaning that \(\Delta S\) is positive.
5. Therefore, \(\Delta H\) is negative, and \(\Delta S\) is positive. The Gibbs free energy change equation becomes:
6. Because \(\Delta H\) is negative and \(T\Delta S\) is positive, \(-\Delta H\) ensures that \(\Delta G\) remains negative at all temperatures.
7. Thus, the reaction is spontaneous at all temperatures.

Hence, the correct statement about the reaction is:

Spontaneous at all temperatures.

This is because both the exothermic nature and the increase in entropy contribute to making the Gibbs free energy negative at all temperatures, ensuring the spontaneity of the reaction.