Consider a reaction that occurs by the following mechanism:

A + BC → AC + B

AC + D → A + CD

The potential energy profile for this reaction is as follows:

(c) Which of the two steps in the mechanism is the rate-determining step? Write the rate law for the overall reaction.

Video transcript

Hello. In this problem, we are asked to identify the rate determining step for reaction with the following mechanism and potential energy profile. So we have a two step mechanism. We are then asked what is the rate law for the overall reaction? So let's begin by looking at our reaction. So we see that we have J. On the reacting side of the first step and on the product side of the second step, J then goes into the reaction and comes out unchanged. That is what we refer to as a catalyst and then we have J. K. On the product side of the first step and then it is consumed in the second step. This is what we refer to as an intermediate and then what remains is our overall reaction. So we have K. L plus M. Most form L plus km. So this is our overall reaction. When we look at our two step mechanism, then the first step corresponds to the line from 1 to 3 in our energy profile diagram. And so we have the transition state for the first step and then the activation energy which is the difference between the energy of our reactant and the transition state. For our first step in this mechanism. Looking at the second step of our mechanism. Then the energy profile diagram from 3 to represents energy associated with the second step. So we again have a transition state to the second step. And then the activation energy associated with the second step which is the difference between the energy of our intermediate and our second transition state. So we'll call this C. A. Two. So our rate determining step is the slow step. It is the one with the largest energy barrier is indicated by the activation energy. So in our case, then the first step is the rate determining step because it has the largest activation energy. If we then determine the rate law, so we're focusing on then the rate determining step, which is the first step. So since this is a elementary step in the mechanism, we can write the rate law based on our reaction. So we have the rate is equal to the reaction rate, constant times the concentration of J. Times concentration of K. L. And so if we look at our answers that were provided, we find then that this matches with answer. A. So a then is our correct answer for the rate law for the overall reaction. Thanks for watching. Hope this help.