Question

For the idealized reaction \(a \mathrm{A}+b \mathrm{B} \rightleftharpoons \mathrm{c} \mathrm{C}+d \mathrm{D},\) suppose that the equilibrium constant, \(K_{\text {eq }}\), is \(0.01 .\) If the starting concentrations for A. \(\mathbf{B}, \mathbf{C},\) and \(\mathbf{D}\) are \(1 \mathbf{M}\) each, what would you predict based on the value of \(K_{e q} ?\) a. The forward reaction is favored. b. The reverse reaction is favored. c. The forward reaction is fast. d. The reverse reaction is fast. e. both b and d.

Short answer

The correct answer is option b. The reverse reaction is favored.

Step-by-step solution

Establish the reaction

The given reaction is \( aA + bB \leftrightharpoons cC + dD \) and the equilibrium constant \(K_{eq}\) provided is 0.01.

Evaluate the equilibrium constant

The equilibrium constant \( K_{eq} \) is less than 1 (0.01) which indicates that the reactants A and B are more favored than the products C and D at equilibrium. Therefore, the reaction will tend to move in the reverse direction.

Interpret the results

Based on the value of the equilibrium constant, it can be predicted that the reverse reaction is favored, but not necessarily that the reverse reaction is fast.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in which the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentrations of reactants and products over time. It's a balance, not an end to the chemical activity. The reactions continue to occur, but because they are happening at an equal rate, the system appears to be static. For example, when we have an idealized reaction such as \( aA + bB \rightleftharpoons cC + dD \), the concentrations of \( A, B, C, \) and \( D \) eventually reach a point where they no longer change.

This point is described by the equilibrium constant \( K_{eq} \), which provides a ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients. A small \( K_{eq} \) value, like 0.01, suggests that the concentrations of reactants, \( A \) and \( B \), will be larger than the concentrations of the products, \( C \) and \( D \), when the system reaches equilibrium.

Le Chatelier's Principle

Le Chatelier's principle is named after the French chemist who proposed it. This principle predicts how a system at equilibrium will respond to disturbances. It states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. Basically, it's the chemical equivalent of a system trying to maintain stability.

In the context of our example, if we were to add more of reactant \( A \) or \( B \) to the system, according to Le Chatelier's principle, the equilibrium would shift to favor the formation of more products, \( C \) and \( D \), to reduce the stress of the added reactants. Similarly, if product \( C \) or \( D \) were to be added, the equilibrium would shift towards the reactants to balance it out.

Reaction Quotient

The reaction quotient, \( Q \), is a measure used to determine the direction in which a reaction mixture will move in order to reach equilibrium. It is calculated by the same formula as the equilibrium constant \( K_{eq} \), but for \( Q \), you use the concentrations of reactants and products at any point in time, not necessarily at equilibrium.

Comparing \( Q \) to \( K_{eq} \) gives us an idea of which way the reaction will proceed. If \( Q > K_{eq} \), the reaction will proceed in the reverse direction to reach equilibrium. If \( Q < K_{eq} \), the reaction will proceed in the forward direction. And if \( Q = K_{eq} \), the reaction is already at equilibrium. For the given problem, since our \( K_{eq} \) is 0.01 and the initial concentrations of reactants and products are the same, \( Q \) is initially 1, which is greater than \( K_{eq} \). This suggests the reaction will proceed in the reverse direction to reach equilibrium.

Equilibrium Concentration

Equilibrium concentration pertains to the amounts of reactants and products present when a reaction has reached equilibrium. These concentrations are constant over time as long as external conditions remain unchanged. In our reaction of \( aA + bB \rightleftharpoons cC + dD \), the equilibrium concentrations will reflect the favor towards reactants or products as dictated by the value of the equilibrium constant \( K_{eq} \).

Given the initial conditions in our problem—concentrations of 1M for each reactant and product and a \( K_{eq} \) value of 0.01—you can predict that, at equilibrium, the concentrations of \( C \) and \( D \) will be less than those of \( A \) and \( B \). In other words, the system will have relatively higher concentrations of reactants than products, which aligns with the provided solution indicating that the reverse reaction is favored.