Problem 33 - Chemistry: An Atoms-Focused Approach

Question

If the value of \(\Delta S_{\text {rxn }}\) of the non spontaneous reaction \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}\) is \(-66.0 \mathrm{J} / \mathrm{K},\) what is the maximum entropy change in the reaction's surroundings?

Step-by-Step Solution

Answer

Answer: The maximum entropy change in the reaction's surroundings is 66.0 J/K.

Step 1: Recall the formula for total entropy change

For any process, the total entropy change (∆S_total) is the sum of the entropy change in the system (∆S_sys or ∆S_rxn in our case) and the entropy change in the surroundings (∆S_surr): ∆S_total = ∆S_sys + ∆S_surr Since the reaction is non-spontaneous, the total entropy change for the reaction as it is given would be negative. We are interested in finding the maximum entropy change in the surroundings that would make the total entropy change equal to zero. In other words, we want to make the reaction on the verge of becoming spontaneous.

Step 2: Set the total entropy change to zero

To find the maximum entropy change in the surroundings that makes the reaction on the verge of becoming spontaneous, set ∆S_total equal to zero and solve for ∆S_surr: 0 = ∆S_sys + ∆S_surr

Step 3: Substitute the given entropy change of the reaction

We are given the entropy change of the reaction as ∆S_rxn = -66.0 J/K. Substitute this into our equation and solve for ∆S_surr: 0 = -66.0 J/K + ∆S_surr

Step 4: Solve for the maximum entropy change of the surroundings

Now, solve this equation for ∆S_surr: ∆S_surr = 66.0 J/K The maximum entropy change in the reaction's surroundings is 66.0 J/K.

Key Concepts

Non-Spontaneous Reactions

In chemistry, reactions are labeled as non-spontaneous when they don't occur on their own under given conditions. For a reaction to be non-spontaneous, it requires the input of energy to proceed. In the context of entropy, a non-spontaneous reaction typically means that the total entropy change for the system is negative. This is because such reactions naturally move towards lower disorder or higher order, which is less likely to occur without external energy assistance.

Non-spontaneous reactions can turn spontaneous if the conditions are changed. By altering temperature, pressure, or concentrations, you can potentially influence the direction of the reaction. It's this interplay of conditions and energy that adds depth to the study of chemical reactions.

Entropy of System and Surroundings

Entropy, which measures disorder or randomness, is a crucial concept in determining the spontaneity of a reaction. It is split between the system in question, such as reacting chemicals, and its surroundings. In a reaction, we label the system's change in entropy as \(\Delta S_{\text{sys}}\), while the change in the surroundings is \(\Delta S_{\text{surr}}\).

It's key to understand that entropy can be transferred between a system and its surroundings. This means even if a system's entropy decreases (becomes more ordered), the surrounding's entropy might increase to compensate. When calculating these changes, always remember:

• The total entropy change \(\Delta S_{\text{total}}\) is the sum of \(\Delta S_{\text{sys}}\) and \(\Delta S_{\text{surr}}\).
• Positive \(\Delta S_{\text{total}}\) indicates a spontaneous reaction.
• Negative \(\Delta S_{\text{total}}\) suggests non-spontaneity, unless driven by other factors.

Understanding these relations helps predict if a reaction will occur as intended.

Total Entropy Change

Total entropy change is a powerful predictor of a reaction’s direction and feasibility. Defined as the sum of entropy changes in the system and its surroundings, \(\Delta S_{\text{total}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}}\), it determines if processes are spontaneous.

In practical terms, if the total entropy change is positive, the reaction should happen without additional energy. However, when \(\Delta S_{\text{total}}\) is zero, the reaction is at an equilibrium, balancing the disorder of the system with its surroundings.

When analyzing chemical processes, looking at entropy changes can be an intuitive method to predict advances or reversals in reactions. Take, for example, the given reaction where \(\Delta S_{\text{rxn}} = -66.0 \, \text{J/K}\). For this non-spontaneous reaction to achieve an equilibrium state where \(\Delta S_{\text{total}} \, = \, 0\), the surroundings must compensate with an equal and opposite entropy change.