Let's say you're looking at a reaction coordinate diagram for an exothermic reaction. The reaction has two transition states, the first transition state having a lower hill than the second transition state. Also, the first transition state has the larger activation energy compared to the second transition state. The first transition state would be the slow step because it has the larger activation energy. The second transition step would be the rate determining step. This confuses me because I always thought that the slow step was the rate determining step. Can anyone explain this?
Graffiti,
I've seen the diagram you are explaining before in my studies that showed such results. What helped me to understand and retain the concept and it's reasoning is to just remember the following:
Highest Hill = Rate determining Step
and
Largest Energy of Activation (Ea) = Slow Step
Of course, the two are usually the same, being the highest hill with highest energy of activation, but remember this: "If the first hill goes downward after it's peak, dips and then goes up again to reach another transition state that will be higher than the second hill, the Energy of Activation for that second step will begin at the lowest point right after the first hill. This is what makes a higher energy transition state possible with a lower Ea. The Ea may actually be higher in the graph for the second hill, but it's length is not as long as the first hill, which required more energy."
So, in attempt to summarize, the first hill (reaction) took a much longer time to occur due to it's larger Ea, but since energy was already invested and did not decrease all the way back to the baseline where it began before starting another hill, it does not require a larger amount of additional energy then the first Ea amount to create a higher hill. The second hill's Ea is essentially being added onto a point of where it is already at. Since the second hill is the highest, it is the rate determining. This is because even though it did not take the longest to occur, it is the highest point in the graph and the completion of the reaction depends on getting to that highest point, since it is the "overall peak of energy".
The opposite of this would be a graph with a high hill, dipping about halfway, followed by a lower hill. Going from right to left, measure the hills' Ea's from where the hills begin to go upward until they reach their peaks. The first will have the largest Ea, which makes it the slow step for requiring the most energy in a single step, as well as the highest hill, which makes it the rate determining step since it is the point in the graph with the highest overall energy.
Let me note, when I originally wrote this, I said that the "highest" Ea = the slow step. And came back and edited it to say the "largest" Ea, only because this seems to create confusion for these types of problems. The largest is the the hill with the length from the starting point of the hill (not necessarily of the entire reaction) to the top of the hill. So the only things you need to pay attention to when asked to determine the rate determining step and slow step are: 1.) The highest hill and 2.) which hill has the largest Ea from the hill's low point, not the beginning of the overall reaction, to high point.
I sincerely hope this helps and apologize for writing you a short novel.