Problem 18 - Chemistry: An Atoms-Focused Approach

Question

If we plot the concentration of reactants and products as a function of time for any sequence of two spontaneous chemical reactions, such as $$A \rightarrow B \rightarrow C$$ will the maximum concentration of final product C always appear after the maximum concentration of B?

Step-by-Step Solution

Answer

Answer: Yes, the maximum concentration of the final product (C) always appears after the maximum concentration of the intermediate product (B) in a series of two spontaneous chemical reactions. This is because the maximum concentration of B occurs at the transition point between the two reactions, while the maximum concentration of C occurs when the reaction B -> C is at its maximum.

Step 1: The given chemical reactions are A -> B -> C, where A is converted into B, and B is subsequently converted into C. Since these are spontaneous reactions, they occur naturally and progress with time. #Step 2: Identify variables involved and their relationships#

We need to focus on the concentrations of A, B, and C as a function of time. As the reaction progresses, the concentration of A decreases while B and C increase. Initially, the reaction A -> B will be more dominant as A decreases and B increases. Afterward, the reaction B -> C takes over and B starts to decline while C increases further. #Step 3: Examine the conditions for maximum concentrations#

Step 2: Maximum concentration of B occurs when the rate of change of B is zero over time, which happens at the transition point between reaction A -> B and B -> C. In comparison, the maximum concentration of C occurs when the reaction B -> C is complete or is at its maximum. #Step 4: Determine the relationship between maximum concentrations of B and C#

Since the maximum concentration of B occurs at the transition point between the two reactions, and the maximum concentration of C occurs when the reaction B -> C is at its maximum, it indicates that the maximum concentration of C always appears after the maximum concentration of B.

Key Concepts

Understanding Reaction Kinetics

The study of reaction kinetics revolves around the speed at which chemical reactions occur and the factors affecting this speed. Reaction kinetics gives us valuable insight into the mechanisms involved and how different conditions, like temperature and concentration, can influence a reaction's rate. When examining the reaction sequence \(A \rightarrow B \rightarrow C\), it's vital to comprehend how each step progresses over time.

• The initial reaction \(A \rightarrow B\) begins with A's concentration being highest, and it gradually decreases as B forms. This step typically speeds up until A is mostly used up.
• The following step \(B \rightarrow C\) starts as B accumulates. B reaches a maximum concentration when it's produced at the same rate as it is consumed by being turned into C.

Understanding the transition points in these reactions is crucial for predicting the timing and concentration of reactants and products effectively.

Exploring Concentration Profiles

Concentration profiles provide important visual insight into the behavior of reactants and products over time during a chemical reaction. In spontaneous reactions like \(A \rightarrow B \rightarrow C\), concentration profiles help clarify how and when different substances peak in concentration.

• Initially, A's concentration is high, but it begins to drop as B forms. The graph of A would typically show a descending curve.
• B's concentration rises initially and reaches a peak when the reaction \(A \rightarrow B\) slows down, transitioning to more emphasis on \(B \rightarrow C\).
• Finally, C's concentration increases as it is formed directly from B. The peak of C occurs after B's maximum due to sequential reactions.

These profiles illustrate how the maximum concentration of C always follows that of B due to the linear nature of this reaction sequence.

Understanding Spontaneous Reactions

Spontaneous reactions are naturally occurring processes that proceed without any external force or influence once started. Such reactions depend on factors like energy changes and entropy.

• A classic example found in sequences such as \(A \rightarrow B \rightarrow C\) has each step occurring naturally, driven by itself once initiated.
• The reactions progress due to a favorable decrease in free energy, making them energetically advantageous and self-sustaining.
• In terms of timing, the sequence and sequential consumption mean that C will only start forming significantly after B has accumulated enough, as seen in the earlier reaction kinetics.

Understanding how spontaneous reactions handle energy and materials underscores why products like C appear later in the sequence, reflecting a reaction's natural course.