About first-order kinetics, the true statement is
**Core Concept:** First-order kinetics is a model used to describe the relationship between substrate concentration and reaction rate in chemical reactions or biological processes, where the reaction rate is directly proportional to the concentration of the substrate. It is often used to describe enzyme-catalyzed reactions.
**Why the Correct Answer is Right:** In first-order kinetics, the reaction rate (v) is directly proportional to the enzyme concentration (E): v = k[E]. In other words, the reaction rate increases linearly with increasing substrate concentration. This simplifies the rate equation to: v = k.
**Why Each Wrong Option is Incorrect:**
A. **False:** This option contradicts the definition of first-order kinetics where the reaction rate is directly proportional to the enzyme concentration (E). In reality, the reaction rate is directly proportional to the substrate concentration ([Et]).
B. **False:** The relationship between substrate concentration and reaction rate in first-order kinetics is described by the equation v = k[Et], where [Et] represents the enzyme concentration. This option is incorrect because it refers to the enzyme concentration ([E]) instead of the enzyme-substrate complex (Et).
C. **False:** This statement does not describe the relationship between substrate concentration and reaction rate in first-order kinetics, which is v = k[Et], where [Et] represents the enzyme-substrate complex concentration.
D. **False:** This option contradicts the definition of first-order kinetics where the reaction rate is directly proportional to the enzyme concentration ([Et]). In reality, the reaction rate is directly proportional to the substrate concentration ([Et]).
**Clinical Pearl:** Understanding first-order kinetics is crucial in pharmacokinetics, where it is used to describe the elimination rate of a drug in the body, and in pharmacodynamics, where it is used to describe the rate of drug action. By knowing the rate constants (k) and the initial substrate concentration ([Et]), you can accurately predict the reaction rate and optimize drug dosage regimens for effective treatment.