Question

Which of the following represents the integrated rate law for a first-order reaction?

-1/[A]o − 1/[A]t = −kt
-ln(k1/k2) = ln(Ea/R)(1T) + lnA
-k = Ae^(Ea/RT)
-[A]o − [A]t= −kt
-ln([A]t/[A]o) = −kt

Answer 1

The integrated rate law for a first-order reaction is represented by the equation: ln([A]t/[A]₀) = -kt.

Step-by-step explanation:

In the given options, the correct integrated rate law for a first-order reaction is expressed by the equation ln([A]t/[A]₀) = -kt. This equation is derived from the general form of the first-order integrated rate law, which is ln([A]t/[A]₀) = -kt. Here, [A]t represents the concentration of the reactant at time 't,' [A]₀ is the initial concentration, 'k' is the rate constant, and 't' is the reaction time. This equation indicates that the natural logarithm of the ratio of reactant concentrations is linearly related to time, with the negative slope equal to the rate constant 'k.' It is a characteristic feature of first-order reactions where the rate is proportional to the concentration of a single reactant.

The correct answer is distinguished from other options through a careful examination of the mathematical representation. The other equations provided do not precisely capture the behavior of a first-order reaction. The correct equation, ln([A]t/[A]₀) = -kt, is established through rigorous mathematical analysis of the reaction kinetics, emphasizing the logarithmic relationship between reactant concentrations and time. This logarithmic transformation simplifies the representation of the first-order reaction kinetics, making it a fundamental tool in understanding and predicting the behavior of such reactions in chemical kinetics studies.