The interconversion of l-___-lysine and l-b-lysine, for which Kc = 7.20 at 333 K, is catalyzed by the enzyme lysine 2,3-aminomutase. Lysine occurs in proteins while l-b-lysine is a precursor to certain antibiotics. At 333 K, a solution of l-___-lysine at a concentration of 3.00 * 10^-3 M is placed in contact with lysine 2,3-aminomutase. What are the equilibrium concentrations of l-___-lysine and l-b-lysine?

Verified step by step guidance

1. Identify the initial concentration of l-\_\_\_-lysine, which is given as 3.00 \times 10^{-3} \text{ M}.
2. Write the balanced chemical equation for the interconversion: l-\_\_\_-lysine \rightleftharpoons l-b-lysine.
3. Define the change in concentration for each species using an ICE (Initial, Change, Equilibrium) table. Let x be the change in concentration of l-b-lysine formed at equilibrium.
4. Express the equilibrium concentrations in terms of x: [l-\_\_\_-lysine] = 3.00 \times 10^{-3} - x \text{ M} and [l-b-lysine] = x \text{ M}.
5. Use the equilibrium constant expression K_c = \frac{[l-b-lysine]}{[l-\_\_\_-lysine]} = 7.20 to solve for x, which will give the equilibrium concentrations of both species.

Key Concepts

Equilibrium Constant (Kc)

The equilibrium constant (Kc) 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 provides insight into the extent of a reaction; a Kc greater than 1 indicates that products are favored, while a Kc less than 1 suggests that reactants are favored. In this case, Kc = 7.20 indicates that at equilibrium, l-b-lysine will be present in a higher concentration compared to l-___-lysine.

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 is crucial in predicting how changes in concentration, temperature, or pressure will affect the equilibrium position of the reaction between l-___-lysine and l-b-lysine when catalyzed by lysine 2,3-aminomutase.

Catalysis

Catalysis is the process by which the rate of a chemical reaction is increased by a substance called a catalyst, which is not consumed in the reaction. In this scenario, the enzyme lysine 2,3-aminomutase acts as a catalyst, facilitating the interconversion of l-___-lysine and l-b-lysine without altering the equilibrium concentrations. Understanding the role of the catalyst is essential for analyzing the kinetics and dynamics of the reaction.