Problem 11 - Chemistry: An Atoms-Focused Approach

Question

How is the entropy change that accompanies a reaction related to the entropy change that happens when the reaction runs in reverse?

Step-by-Step Solution

Answer

Answer: The entropy change of a reaction running in reverse is the negative of the entropy change that accompanies the forward reaction. The magnitudes of their entropy changes are the same, but with reversed signs.

Step 1: Understanding entropy as a state function

Entropy (S) is a state function, which implies that its value depends only on the initial and final states of a system, regardless of the path taken to go from the initial state to the final state. That means that if we reverse the direction of a reaction, the difference between final and initial states remains the same, just the signs will flip.

Step 2: Entropy change accompanying a forward reaction

In a forward reaction, we have an initial state and a final state. The entropy change for the forward reaction, ΔS_forward, can be calculated using the following formula: ΔS_forward = S_final - S_initial

Step 3: Entropy change accompanying a reverse reaction

If we reverse the direction of the reaction, then the initial and final states will also be reversed. In other words, the initial state of the reverse reaction is the final state of the forward reaction and the final state of the reverse reaction is the initial state of the forward reaction. Hence, the entropy change for the reverse reaction, ΔS_reverse, can be calculated using: ΔS_reverse = S_initial - S_final

Step 4: Relationship between forward and reverse entropy changes

Now that we have the expressions for the entropy change in both forward and reverse reactions, we can relate these two values: ΔS_forward = -(ΔS_reverse) This relationship means that the change in entropy of a reaction running in reverse is the negative of the entropy change that accompanies the forward reaction. It also highlights that the magnitudes of their entropy changes are the same but with reversed signs.