Question

Consider the reversible reaction \(\mathrm{A} \rightleftarrows \mathrm{B}\). Explain how equilibrium can be reached by starting with only A, only \(\mathrm{B}\), or a mixture of \(\mathrm{A}\) and \(\mathrm{B}\).

Short answer

Equilibrium is achieved when rates of forward and reverse reactions equalize, no matter the starting concentrations of A and B.

Step-by-step solution

Understanding Equilibrium

Chemical equilibrium is a state in a reversible reaction where the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations of reactants and products remain constant over time, though they are not necessarily equal.

Scenario 1 - Starting with Only A

If we start with only reactant A, the forward reaction A -> B dominates initially. Over time, as B is produced, the rate of the forward reaction decreases and the rate of the reverse reaction B -> A increases until equilibrium is reached, with both A and B present.

Scenario 2 - Starting with Only B

Starting with only product B initiates the reverse reaction B -> A initially. A begins to form, increasing the forward reaction rate. Eventually, the rates of the forward and reverse reactions balance, reaching equilibrium with both A and B.

Scenario 3 - Starting with a Mixture of A and B

When starting with a mixture of both A and B, both forward and reverse reactions occur from the start. The system dynamically adjusts the reaction rates until equilibrium is achieved, where neither the concentrations of A nor B change, but they are in a particular ratio that maintains equilibrium.

Key concepts

Reversible Reaction

A reversible reaction is a type of chemical reaction where the reactants convert into products, and these products can also revert back to the original reactants. This means that the reaction can proceed in both the forward and reverse directions.
Reversible reactions are represented using a double arrow, such as in the reaction: \( \text{A} \rightleftarrows \text{B} \). This indicates that the reaction between A and B can move in either direction depending on the conditions and concentrations of each substance.
These reactions are dynamic and do not proceed to completion. Instead, they reach a state known as equilibrium, where the rates of the forward and reverse reactions are equal. This balance maintains constant concentrations of both products and reactants over time.

Forward Reaction

The forward reaction in a reversible chemical process is the pathway where the reactants transform into products. In the given reaction \( \text{A} \rightarrow \text{B} \), A is the reactant that changes into product B.
Initially, when starting with pure reactant A, the forward reaction rate is at its highest. As more product B forms, this rate begins to decrease because there is less A available. The system adjusts dynamically with the changing concentrations.
Ultimately, the rate of the forward reaction decreases until it equals the rate of the reverse reaction. At this point, a dynamic balance is achieved, and the reaction is at equilibrium.

Reverse Reaction

The reverse reaction is the process where products revert back into reactants. In the reaction \( \text{B} \rightarrow \text{A} \), B is the product converting back into reactant A.
Starting with only B initiates the reverse reaction. As A forms, the reverse reaction initially dominates. However, as A accumulates, it begins to balance the forward reaction \( \text{A} \rightarrow \text{B} \).
This dynamic adjustment continues until the rates of both the forward and reverse reactions become equal, and equilibrium is established. At equilibrium, although the reactions continue to occur, the concentrations of A and B remain constant.

Equilibrium Constant

The equilibrium constant, denoted as \( K \), is a numerical value that represents the ratio of the concentrations of products to reactants at equilibrium. For the reaction \( \text{A} \rightleftarrows \text{B} \), the equilibrium constant \( K \) would be expressed as:
\[ K = \frac{[B]}{[A]} \]
where \([B]\) and \([A]\) are the molar concentrations of B and A, respectively, at equilibrium.
The magnitude of \( K \) indicates the position of the equilibrium. A large \( K \) value means that, at equilibrium, the concentration of products is much greater than that of reactants, suggesting that the forward reaction is favored. Conversely, a small \( K \) value indicates a higher concentration of reactants compared to products, favoring the reverse reaction.
Understanding the equilibrium constant helps in predicting the outcome and extent of a reversible reaction.