Question

Consider the simple one-step reaction: $$\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)$$ Since the reaction occurs in a single step, the forward reaction has a rate of \(k_{\text { fort }}[A]\) and the reverse reaction has a rate of \(k_{\text { rate }}[\mathrm{B}] .\) What happens to the rate of the forward reaction when we increase the concentration of A? How does this explain the reason behind Le Chatelier's principle?

Short answer

Increasing the concentration of A increases the rate of the forward reaction, which is consistent with the rate law. This increase in the forward reaction rate explains Le Chatelier's principle, as the system shifts to re-establish equilibrium by forming more B.

Step-by-step solution

Understand the Rate of Forward Reaction

The rate of the forward reaction, which is the conversion of A to B, is given by the expression \(k_{\text{fort}}[A]\), where \(k_{\text{fort}}\) is the rate constant for the forward reaction and \([A]\) is the concentration of reactant A. According to this rate law, the rate of the forward reaction is directly proportional to the concentration of A.

Analyze the Effect of Increasing Concentration of A

Increasing the concentration of A, denoted as \([A]\), leads to an increase in the rate of the forward reaction because the rate law \(k_{\text{fort}}[A]\) implies that the rate is directly proportional to \([A]\). Therefore, as the concentration of A increases, the forward reaction rate increases correspondingly.

Relate to Le Chatelier's Principle

Le Chatelier's principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. When the concentration of A is increased, the increase in the rate of the forward reaction leads to the formation of more B to counteract the change in concentration of A. This shift in the position of the equilibrium is in accordance with Le Chatelier's principle, as the system works to re-establish equilibrium after the concentration change.

Key concepts

Chemical Equilibrium

Chemical equilibrium occurs in a system when the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of the reactants and products over time. In the example given, reactant A converts to product B at the same rate B converts back to A. All closed systems will reach this balance point, though the time it takes to achieve equilibrium can vary. At equilibrium, the system's composition remains constant, although individual molecules continue to react.

When we examine a system at equilibrium, we are often looking at a delicate balance that can be disturbed by changes in conditions such as temperature, pressure, and concentration. Understanding how these changes can affect the equilibrium position is crucial in predicting the outcome of reactions in a variety of chemical processes.

Reaction Rate

The reaction rate indicates how quickly a chemical reaction proceeds. It's expressed as the rate of change in concentration of a reactant or product over time. For a simple reaction where A converts to B, the rate at which A disappears is given by the expression \(k_{\text{fort}}[A]\), with \(k_{\text{fort}}\) representing the rate constant for the forward reaction and \[A\] indicating the concentration of A.

Rate constants are determined experimentally and remain constant at a given temperature for a given reaction. The concentration of reactants, however, can be altered, and doing so will directly influence the reaction rate.

Equilibrium Constant

The equilibrium constant (\(K_{eq}\)) is a value that relates the concentrations of the reactants and products at chemical equilibrium. For the reaction \(A \rightleftharpoons B\), the equilibrium constant would be expressed as \(K_{eq} = \frac{[B]}{[A]}\), where \[B\] and \[A\] are the equilibrium concentrations of B and A, respectively.

The magnitude of \(K_{eq}\) indicates the position of the equilibrium. A large value implies that, at equilibrium, products are favored; a small value indicates that reactants are preferred. Importantly, \(K_{eq}\) is not affected by changes in concentration but is sensitive to temperature changes.

Concentration Effects

Concentration effects refer to the impact that changing the concentration of reactants or products has on the reaction rate and the position of equilibrium. According to Le Chatelier’s principle, increasing the concentration of a reactant will typically result in an increased rate of the forward reaction. This can temporarily disturb the equilibrium, causing the system to adjust by forming more product until equilibrium is re-established.

Conversely, adding more product or removing some reactant will typically cause the reverse reaction to proceed at a faster rate until equilibrium is once again reached. This interplay between concentration and reaction rate is fundamental to understanding chemical reactions and is utilized in various industrial and laboratory processes to control outcomes.