Both the forward reaction and the reverse reaction in the following equilibrium are believed to be elementary steps: CO(g) + Cl2(g) Δ COCl(g) + Cl(g). At 25 _x001F_C, the rate constants for the forward and reverse reactions are 1.4 * 10^-28 M^-1 s^-1 and 9.3 * 10^10 M^-1 s^-1, respectively. (a) What is the value for the equilibrium constant at 25 _x001F_C? (b) Are reactants or products more plentiful at equilibrium?

Verified step by step guidance

1. Step 1: Understand the relationship between the rate constants and the equilibrium constant. The equilibrium constant (K) for a reaction is the ratio of the rate constant of the forward reaction (k_f) to the rate constant of the reverse reaction (k_r). This can be expressed as K = k_f / k_r.
2. Step 2: Identify the given rate constants. From the problem, the rate constant for the forward reaction (k_f) is 1.4 \times 10^{-28} \text{ M}^{-1} \text{s}^{-1}, and the rate constant for the reverse reaction (k_r) is 9.3 \times 10^{10} \text{ M}^{-1} \text{s}^{-1}.
3. Step 3: Substitute the given rate constants into the equilibrium constant expression. Use the formula K = k_f / k_r to find the equilibrium constant.
4. Step 4: Analyze the equilibrium constant value. If K > 1, products are more plentiful at equilibrium. If K < 1, reactants are more plentiful at equilibrium.
5. Step 5: Conclude based on the calculated equilibrium constant whether reactants or products are more plentiful at equilibrium.

Key Concepts

Equilibrium Constant (K)

The equilibrium constant (K) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is calculated using the formula K = [products]/[reactants], where the concentrations are raised to the power of their coefficients in the balanced equation. A large K value indicates that products are favored at equilibrium, while a small K value suggests that reactants are favored.

Rate Constants (k)

Rate constants (k) are specific values that indicate the speed of a reaction under given conditions. For elementary reactions, the rate constant is directly related to the reaction's mechanism and temperature. In the context of equilibrium, the forward and reverse rate constants can be used to determine the equilibrium constant, as K = k_forward / k_reverse, highlighting the relationship between reaction rates and equilibrium position.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to counteract the change and restore a new equilibrium. This principle helps predict how changes in concentration, pressure, or temperature will affect the position of equilibrium, indicating whether reactants or products will be more plentiful based on the equilibrium constant and the initial concentrations.