Enzymes are often described as following the two-step mechanism:
E + S ⇌ ES (fast)
ES → E + P (slow)
where E = enzyme, S = substrate, ES = enzyme9substrate complex, and P = product.
(a) If an enzyme follows this mechanism, what rate law is expected for the reaction?

Verified step by step guidance

1. Identify the two steps in the mechanism: the first step is the formation of the enzyme-substrate complex (E + S ⇌ ES), which is fast and reversible, and the second step is the conversion of the enzyme-substrate complex to the product (ES → E + P), which is slow and rate-determining.
2. Recognize that the rate law for the overall reaction is determined by the slowest step, which is the second step (ES → E + P). This step is the rate-determining step.
3. Write the rate law for the rate-determining step. Since the slow step involves the conversion of ES to E and P, the rate law can be expressed as: rate = k[ES], where k is the rate constant for the slow step.
4. Consider the steady-state approximation for the intermediate ES. In the steady-state approximation, the formation and breakdown of the intermediate ES are balanced, so the concentration of ES remains relatively constant over time.
5. Express the concentration of the intermediate [ES] in terms of the concentrations of E and S using the equilibrium expression for the fast step: K_eq = [ES]/([E][S]), where K_eq is the equilibrium constant for the fast step. Substitute this expression into the rate law to obtain the overall rate law in terms of the initial reactants E and S.

Key Concepts

Enzyme Kinetics

Enzyme kinetics is the study of the rates of enzyme-catalyzed reactions. It involves understanding how various factors, such as substrate concentration and enzyme concentration, affect the speed of the reaction. The Michaelis-Menten model is a fundamental framework in this area, describing how the rate of reaction depends on the concentration of the substrate and the maximum rate achievable by the enzyme.

Rate Law

A rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as a mathematical equation, where the rate is proportional to the concentrations raised to a power, which reflects the reaction order. For enzyme-catalyzed reactions, the rate law can vary depending on whether the substrate is in excess or limiting.

Steady-State Assumption

The steady-state assumption is a key concept in enzyme kinetics, suggesting that the concentration of the enzyme-substrate complex (ES) remains relatively constant over the course of the reaction. This means that the rate of formation of ES is equal to the rate of its breakdown into product and free enzyme. This assumption simplifies the derivation of the rate law for enzyme-catalyzed reactions.