The following set of data was obtained by the method of initial rates for the reaction: (H₃C) ₃CBr + OH^- → (H₃C) ₃COH + Br^-
What is the value of the rate constant,k?

Question

The following set of data was obtained by the method of initial rates for the reaction: (H₃C)₃CBr + OH^- → (H₃C)₃COH + Br^- What is the value of the rate constant,k?

Quizplus · Accepted Answer

The rate law for this reaction can be written as rate = k[H₃C] [OH^-]. Since the question states that this data was obtained by the method of initial rates, it means that the initial concentration of each reactant is different in each experiment, but the time taken for the reaction to reach a certain point is the same. Therefore, we can compare the initial rates of the reaction in different experiments and find the value of k. From the given data, it can be observed that when [H₃C] is kept constant and [OH^-] is doubled, the initial rate of the reaction is also doubled. Therefore, the order of the reaction with respect to [OH^-] is 1. Similarly, when [OH^-] is kept constant and [H₃C] is doubled, the initial rate of the reaction is quadrupled. Therefore, the order of the reaction with respect to [H₃C] is 2. Using these orders, we can calculate the value of k as 4.4 × 10^-4 s^-1. Hence, the correct answer is option B.

The Following Set of Data Was Obtained by the Method