Question

Consider the equilibrium system \(3 \mathrm{~A} \rightleftarrows \mathrm{B}\). Sketch the changes in the concentrations of \(\mathrm{A}\) and \(\mathrm{B}\) over time for the following situations: (a) initially only \(\mathrm{A}\) is present, (b) initially only B is present, (c) initially both A and \(B\) are present (with A in higher concentration). In each case, assume that the concentration of \(\mathrm{B}\) is higher than that of \(\mathrm{A}\) at equilibrium.

Short answer

In all scenarios, the system reaches equilibrium with \(\mathrm{B}\) having a higher concentration than \(\mathrm{A}\).

Step-by-step solution

Analyze System Dynamics

The equilibrium system is given by \(3\mathrm{~A} \rightleftarrows \mathrm{B}\). This implies that three molecules of \(\mathrm{A}\) convert into one molecule of \(\mathrm{B}\) and vice versa. At equilibrium, the rates of the forward and reverse reactions are equal.

Scenario (a) – Only \(\mathrm{A}\) Initially

Initially, only \(\mathrm{A}\) is present, so its concentration starts high, while \(\mathrm{B}\) is zero. As the system progresses towards equilibrium, \(\mathrm{A}\) will convert to \(\mathrm{B}\). The concentration of \(\mathrm{A}\) will decrease while the concentration of \(\mathrm{B}\) will increase until equilibrium is reached. At equilibrium, the concentration of \(\mathrm{B}\) is higher than that of \(\mathrm{A}\), indicating \(\mathrm{B}\) stabilizes at a higher concentration.

Scenario (b) – Only \(\mathrm{B}\) Initially

Initially, only \(\mathrm{B}\) is present, so its concentration starts high, while \(\mathrm{A}\) is zero. As the system approaches equilibrium, \(\mathrm{B}\) will convert back to \(\mathrm{A}\). The concentration of \(\mathrm{B}\) decreases while the concentration of \(\mathrm{A}\) increases until equilibrium is reached, where once again \(\mathrm{B}\) will be higher than \(\mathrm{A}\).

Scenario (c) – Both \(\mathrm{A}\) and \(\mathrm{B}\) Initially, \(\mathrm{A}\) Higher

For this scenario, both \(\mathrm{A}\) and \(\mathrm{B}\) are present with \(\mathrm{A}\)'s concentration initially higher. Since equilibrium has \(\mathrm{B}\) with a higher concentration, \(\mathrm{A}\) will decrease and \(\mathrm{B}\) will increase as the system approaches equilibrium. The transition continues until the equilibrium is reached with more \(\mathrm{B}\) than \(\mathrm{A}\).

Equilibrium Characteristics

For all scenarios, the system will always adjust until the concentration of \(\mathrm{B}\) is higher than that of \(\mathrm{A}\). The reaction naturally moves towards balancing out the two processes so that the forward and reverse reactions happen at equal rates with \(\mathrm{B}\) favored in concentration.

Key concepts

Reaction Dynamics

In a chemical equilibrium, such as the system involving 3A converting to B, reaction dynamics are crucial. Here, the reaction dynamics refer to the interplay of molecules and how they transform within the system. In this context, three molecules of A are involved in a reaction to form one molecule of B, and this process can reverse. This transformation works through a mechanism where A molecules collide and rearrange to form B, while B molecules can also decompose back into A. With these dynamics, the reaction at equilibrium stabilizes such that the forward reaction rate, creating B from A, equals the reverse reaction rate, converting B back to A. These dynamic transitions are subtle and continuous, underpinning the concept of a dynamic chemical equilibrium.

Concentration Changes

When dealing with chemical reactions, understanding concentration changes over time is essential. Consider a scenario where only A is initially present. As the reaction begins, the concentration of A starts high and decreases as it is converted into B. Conversely, the concentration of B, starting at zero, continuously increases until equilibrium is reached.
In another situation where only B is present initially, B's concentration begins high but decreases as it is partly converted back into A. Meanwhile, the concentration of A, initially zero, rises during this process. No matter the initial conditions, the concentration of both A and B will adjust until they achieve equilibrium, highlighting dynamic shifts in concentration levels.

Equilibrium Concentration

The concept of equilibrium concentration focuses on the specific levels of reactants and products when a chemical system achieves balance. In our system, at equilibrium, the concentration of B will be higher than that of A. This means that the reaction has adjusted so that the quantities of A and B stabilize in a way where the dynamic conversion rates are equal, even though the concentrations differ.

• Initially, regardless of whether A or B is more abundant, the system will rearrange itself until the equilibrium concentrations are reached.
• In every scenario of the exercise, the system naturally evolves so that B remains more concentrated than A.

This higher concentration of B signifies where the system has found its point of minimal energy exchange.

Forward and Reverse Reactions

In the equilibrium system of 3A rightleftharpoons B, forward and reverse reactions play a critical role. The forward reaction involves A converting into B, while the reverse reaction breaks down B back into A. At the outset, these reactions will not be at equilibrium. However, as time progresses, their rates will match, indicating equilibrium has been reached.
It is essential to understand that both reaction directions continue to occur even at equilibrium. They maintain a balance, meaning while molecules of A are continuously forming B, an equal number of B molecules decompose to reform A. This concept is paramount in chemical equilibria, emphasizing that even when balance is achieved, molecular transformations do not halt but occur at equal magnitudes in both directions.