Question

Consider the reaction \(\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D} .\) Assume that both the forward reaction and the reverse reaction are elementary processes and that the value of the equilibrium constant is very large. (a) Which species predominate at equilibrium, reactants or products? (b) Which reaction has the larger rate constant, the forward or the reverse? Explain.

Short answer

(a) At equilibrium, products (C and D) predominate due to the very large value of the equilibrium constant. (b) The forward reaction (A + B -> C + D) has the larger rate constant, as K = k_forward / k_reverse, and a large K indicates a larger k_forward compared to k_reverse.

Step-by-step solution

(a) Identifying the predominant species at equilibrium

The equilibrium constant (K) for a given reaction is defined as the ratio of the concentrations of products to reactants at equilibrium. Since we are given that the equilibrium constant is very large, it means that the concentration of products (C and D) is much higher than the concentration of reactants (A and B) at equilibrium. Therefore, the products (C and D) predominate at equilibrium.

(b) Understanding the relationship between equilibrium constant and rate constants

The equilibrium constant (K) is related to the rate constants of the forward (k_forward) and reverse (k_reverse) reactions by the following equation: K = k_forward / k_reverse. This equation tells us that if the equilibrium constant is very large, the forward rate constant must be much larger than the reverse rate constant since K is the ratio of k_forward to k_reverse.

(b) Determining which reaction has the larger rate constant

Based on our understanding of the relationship between the equilibrium constant and the rate constants, we can conclude that the forward reaction (A + B -> C + D) has the larger rate constant since K is very large. This means that the forward reaction is faster than the reverse reaction, ultimately leading to a higher concentration of products (C and D) at equilibrium.

Key concepts

Rate Constants

The rate constants of a reaction are critical in understanding how quickly a reaction proceeds. Rate constants, denoted by the symbols \(k_{\text{forward}}\) and \(k_{\text{reverse}}\), represent the speed at which the forward and reverse reactions occur, respectively. These constants depend on various factors including temperature and the nature of the reactants involved.

In the context of equilibrium, the relationship between the rate constants and the equilibrium constant (\(K\)) is crucial. The equilibrium constant is given by the ratio of the forward and reverse rate constants:

• \(K = \frac{k_{\text{forward}}}{k_{\text{reverse}}}\)

This equation shows that if the equilibrium constant is large, the forward rate constant is significantly larger than the reverse rate constant. This indicates a faster forward reaction, leading to a predominance of products at equilibrium. Understanding the size of these constants allows chemists to predict and manipulate reaction conditions for desired outcomes.

Reaction Rates

Reaction rates dictate how fast a reaction proceeds toward equilibrium. They are influenced by the concentration of reactants and the temperature at which the reaction occurs. For elementary reactions, the rate is directly proportional to the concentration of the reactants raised to the power of their stoichiometric coefficients.

The rate of reaction can be described by the rate law, which for a generic reaction \(A + B \rightarrow C + D\) is expressed as:

• Rate = \(k \cdot [A][B]\)

The rate law shows that increasing the concentration of reactants will generally lead to an increase in the reaction rate. The temperature dependence of the rate is described by the Arrhenius equation, which states that the rate constant increases with temperature, thereby increasing the reaction rate. In equilibrium, the forward and reverse reactions occur at the same rate, maintaining a constant concentration of reactants and products. This dynamic state means that while the compositions remain constant, the individual molecules are continuously reacting.

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions in a closed system are equal, resulting in constant concentrations of reactants and products. It is a dynamic state where the reactions occur continuously but there is no net change in the concentration of species in the system.

The position of equilibrium is represented by the equilibrium constant \(K\), which quantitatively expresses the ratio of product to reactant concentrations. For a general reaction \(aA + bB \rightleftharpoons cC + dD\), the equilibrium constant expression is:

• \(K = \frac{[C]^c[D]^d}{[A]^a[B]^b}\)

A large \(K\) value indicates that products are favored at equilibrium, whereas a small \(K\) suggests reactants are favored.
Factors such as concentration, pressure, and temperature can shift the equilibrium position, a concept described by Le Chatelier's Principle. This principle states that if an external change is applied to a system at equilibrium, the system adjusts to counteract the effect and re-establish equilibrium. Understanding chemical equilibrium helps in predicting the concentrations of reactants and products at any given time, thus aiding in the control and optimization of industrial chemical processes.