Question

The reaction, \(\mathrm{A}+2 \mathrm{~B} \rightleftharpoons \mathrm{C}\), has an equilibrium constant of 2000 . During a reaction, the concentration of \(\mathrm{A}\) is \(0.01\) \(\mathrm{M}\), of \(\mathrm{B}\) is \(0.2 \mathrm{M}\), and of \(\mathrm{C}\) is \(0.5 \mathrm{M}\). a. What is the reaction quotient \((Q)\) ? b. In what direction will the reaction proceed?

Short answer

a. \( Q = 1250 \); b. Reaction proceeds forward.

Step-by-step solution

Write the Expression for Reaction Quotient (Q)

For the reaction \( \mathrm{A} + 2 \mathrm{B} \rightleftharpoons \mathrm{C} \), the reaction quotient \( Q \) is defined as the ratio of the products' concentrations to the reactants' concentrations at any point in time. The formula is \( Q = \frac{[\mathrm{C}]}{[\mathrm{A}][\mathrm{B}]^2} \).

Plug in the Concentration Values

Substitute the given concentrations into the equation for \( Q \): \( Q = \frac{0.5}{0.01 \times (0.2)^2} \).

Calculate the Reaction Quotient (Q)

Perform the arithmetic in the provided expression: \( Q = \frac{0.5}{0.01 \times 0.04} = \frac{0.5}{0.0004} = 1250 \). The reaction quotient \( Q \) is 1250.

Compare Q to the Equilibrium Constant (K)

The equilibrium constant \( K \) is given as 2000. Compare \( Q \) (1250) to \( K \) (2000). Since \( Q < K \), this indicates that the reaction will proceed in the forward direction to reach equilibrium.

Key concepts

Reaction Quotient

The reaction quotient, abbreviated as \( Q \), is a powerful tool in chemistry. It helps us understand the current state of a chemical reaction by examining the concentrations of reactants and products at any given moment. For any reaction such as \( \mathrm{A} + 2 \mathrm{~B} \rightleftharpoons \mathrm{C} \), the reaction quotient is calculated using the equation: \[ Q = \frac{[\mathrm{C}]}{[\mathrm{A}][\mathrm{B}]^2} \]. This formula takes into account the stoichiometry of the reaction, meaning it reflects the balanced equation. By substituting the concentrations of each species into this formula, we can calculate \( Q \). The value of \( Q \) provides insights into how the reaction compares to its equilibrium state. It tells us how far and in what direction a reaction must move to reach equilibrium.

Equilibrium Constant

The equilibrium constant, represented as \( K \), is an essential concept in chemical equilibrium. It is a fixed value for a given reaction at a particular temperature and provides a snapshot of where the reaction rests when it reaches equilibrium. For the synthesis reaction \( \mathrm{A} + 2 \mathrm{~B} \rightleftharpoons \mathrm{C} \), the equilibrium constant \( K \) is calculated using the same formula as \( Q \): \[ K = \frac{[\mathrm{C}]}{[\mathrm{A}][\mathrm{B}]^2} \]. However, unlike \( Q \), \( K \) only applies when the reaction has reached its equilibrium state.A large equilibrium constant, such as 2000 in our exercise, suggests that at equilibrium, the concentration of the products will be much higher than that of the reactants. This means the reaction strongly favors product formation when it reaches equilibrium, highlighting the stability of the products.

Reaction Direction

Understanding the direction in which a reaction will proceed is crucial when discussing equilibria. This direction is determined by comparing the reaction quotient \( Q \) with the equilibrium constant \( K \). - If \( Q < K \): The reaction proceeds in the forward direction, meaning more products will form. - If \( Q > K \): The reaction moves in the reverse direction, leading to the formation of more reactants. - If \( Q = K \): The system is at equilibrium; no net change occurs. In the original exercise, with \( Q = 1250 \) and \( K = 2000 \), the reaction will proceed in the forward direction. This indicates that the current concentrations of reactants and products will change until the ratio described by \( K \) is achieved, making more \( C \) and using up some \( A \) and \( B \).

Concentration

Concentration plays a pivotal role in determining the direction and position of chemical equilibria. It represents how much of a substance is present in a given volume. In our exercise, the concentrations were \([\mathrm{A}] = 0.01\; \mathrm{M}\), \([\mathrm{B}] = 0.2\; \mathrm{M}\), and \([\mathrm{C}] = 0.5\; \mathrm{M}\). These values are essential inputs into the equations for both \( Q \) and \( K \).Changes in concentration can shift the position of equilibrium. According to Le Chatelier's Principle, if the concentration of either reactants or products is modified, the equilibrium will shift to counteract that change. So, by adjusting concentrations, we can manipulate the point where equilibrium is established.Monitoring and calculating concentrations precisely are key to applications in chemical manufacturing and lab experiments, where achieving the desired amounts of products is critical.