The reaction of fumarate with water to form L-malate is catalyzed by the enzyme fumarase; Kc = 3.3 at 37°C. When a reaction mixture with [fumarate] = 1.56 * 10-3 M and [l -malate] = 2.27 * 10-3 M comes to equilibrium in the presence of fumarase at 37 °C, what are the equilibrium concentrations of fumarate and L-malate? (Water can be omit- ted from the equilibrium equation because its concentration in dilute solutions is essentially the same as that in pure water.)

Verified step by step guidance

1. Step 1: Write down the equilibrium expression for the reaction. Since water is not included in the equilibrium expression, the equilibrium constant Kc for the reaction is given by [L-malate]/[fumarate].
2. Step 2: Set up the ICE (Initial, Change, Equilibrium) table. Initially, [fumarate] = 1.56 * 10^-3 M and [L-malate] = 2.27 * 10^-3 M. Let x be the change in concentration of fumarate and L-malate as the reaction proceeds to equilibrium.
3. Step 3: Write the equilibrium concentrations in terms of x. The equilibrium concentration of fumarate will be (1.56 * 10^-3 - x) M and the equilibrium concentration of L-malate will be (2.27 * 10^-3 + x) M.
4. Step 4: Substitute the equilibrium concentrations into the equilibrium expression and set it equal to the given Kc value of 3.3. Solve the resulting equation for x.
5. Step 5: Substitute the value of x back into the expressions for the equilibrium concentrations of fumarate and L-malate to find their values at equilibrium.

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. In this case, Kc = 3.3 indicates that at equilibrium, the concentration of L-malate is 3.3 times greater than that of fumarate. Understanding Kc is essential for calculating the equilibrium concentrations of reactants and products.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust to counteract the change and restore a new equilibrium. This principle helps predict how changes in concentration, temperature, or pressure will affect the position of equilibrium, which is crucial for understanding how the concentrations of fumarate and L-malate will shift in response to their initial concentrations.

Reaction Quotient (Q)

The reaction quotient (Q) is a measure of the relative concentrations of products and reactants at any point in time during a reaction. It is calculated using the same formula as Kc but with the current concentrations. By comparing Q to Kc, one can determine the direction in which the reaction will proceed to reach equilibrium, which is vital for solving the problem of finding the equilibrium concentrations of fumarate and L-malate.