Question

Write the rate law for the first-order reaction. Justify the statement that the half-life for the first-order reaction:

A. Rate=k[A]; The half-life is constant.
B. Rate=k[A]²; The half-life depends on the initial concentration.
C. Rate=k√[A]​; The half-life decreases as the reaction progresses.
D. Rate=kln([A]); The half-life increases as the reaction progresses.

Answer 1

The correct rate law for a first-order reaction is Rate = k[A], where k is the rate constant. The half-life of a first-order reaction is constant and is given by t1/2 = 0.693/k, which is explained by option A. Thus, the correct option is A.

Step-by-step explanation:

The rate law for a first-order reaction is given by the equation: Rate = k[A]. A first-order reaction is characterized by the property that its rate is directly proportional to the concentration of one reactant. First-order reactions have a unique feature in that the half-life of the reaction is constant and is given by the equation t1/2 = 0.693/k, where k is the rate constant. This is because the time it takes for the reactant concentration to decrease to half its initial value does not depend on the starting concentration of the reactant.

Unlike first-order reactions, the half-life for a second-order reaction does depend on the initial concentration, which is not what we're discussing here. Likewise, zero-order reactions have a half-life that changes as the reaction proceeds. Looking back at the question, option A is the correct answer since it correctly represents the rate law for a first-order reaction and notes that the half-life is constant.