The reaction progress diagram for A plus B reacts to form C plus D with and without a catalyst is shown. Which of the following represents the activation energy of the enzyme-catalyzed version of the reaction?
In this problem, we’re given a reaction progress diagram with progress of the reaction on the 𝑥-axis and free energy on the 𝑦-axis. Our answer choices are different differences in energy that are marked on the diagram. Catalysts are substances that increase the rate of reaction without being consumed by the reaction. This question specifically mentions enzymes, which are proteins that act as biological catalysts. In the body, most processes are catalyzed by enzymes.
Catalysts increase the rate of reaction by providing an alternative pathway for the reaction to occur. Although how they do this is beyond the scope of this video. But the overall effect of catalysts is that they lower the activation energy for the reaction. The activation energy is the energy that’s needed for a reaction to begin to occur.
In our reaction progress diagram, this would be the difference in energy between our reactant state and the top of the hump on the diagram. There are two humps in this diagram. And we know that a catalyst has the effect of lowering the activation energy for the reaction. That means that the energy difference between the reactant state and the higher hump in the diagram indicated by the letter c must be the activation energy without a catalyst. And the energy difference between the reactant state and the top of the lower hump must be the activation energy when there is a catalyst present. Which is what we were trying to find to solve this question, the activation energy for the enzyme-catalyzed version of the reaction.
So, we found our answer. But while we’re here, let’s take a look at the other marked energy differences on this diagram and see if we can identify them. The energy difference marked by the letter d is between the reactant state and the product state of our reaction. And since the units on our 𝑦-axis is free energy, this would be the free energy change or Δ𝐺 for this reaction. As we can see from this diagram, the change in free energy would be less than zero for the forward reaction, that is, where A plus B reacts to form C plus D.
When Δ𝐺 is less than zero for a reaction, that means the reaction is spontaneous. So, we know that the forward direction of this reaction is spontaneous. If we look at the energy difference indicated by the letter a, we’ll see that this is the difference in energy between the product state and the top of the lower hump. So, this would be the activation energy when there’s a catalyst present for the reverse reaction, where C plus D react to form A plus B.
And the final energy difference in our diagram is between the product state and the top of the higher hump indicated by the letter e. So, this must be the activation energy for the reverse reaction when there’s no catalyst present. So, now, we’ve identified all of the energy differences that were marked on the diagram. But we were interested in the energy difference that represented the activation energy for the enzyme-catalyzed version of the reaction, which is letter b.