Draw a reaction coordinate diagram for the following reaction ...

Question

Draw a reaction coordinate diagram for the following reaction in which C is the most stable and B the least stable of the three species and the transition state going from A to B is more stable than the transition state going from B to C:

Reaction coordinate diagram showing species A, B, and C with transition states and rate constants labeled.

a. How many intermediates are there?

b. How many transition states are there?

c. Which step has the greater rate constant in the forward direction?

d. Which step has the greater rate constant in the reverse direction?

Accepted Answer

Hello everyone. Let's do this problem together. It says the reaction of X in equilibrium with Y in equilibrium with Z follows the reaction coordinate diagram shown below. And we are shown the energy on the Y axis reaction progress on the X axis starting with point X going up to reach a peak, then drop down to a valley point Y. Then we have another peak that leads us down to point Z. We are asked four questions about this reaction. So let's start with part A count the number of intermediate and transition states present. So how do we identify intermediates and transition states on a reaction coordinate diagram? Well, intermediates have lower energy and are more stable than the transition states. So those are going to appear as valleys while a transition state requires more energy. So that will be shown as the peaks in the diagram. So we have one valley point Y and we have two peaks, one between X and Y and one between Y and Z. So that is the answer for part A one intermediate in two transition states. All right. Question B asks us to arrange the reaction species in order of increasing stability. So how can we determine stability from our reaction coordinate diagram? We can look at energy, right? Because we know that energy has an inverse relationship to stability. So the more stable a species will be the less energy it has. So we wanna start with the species that has the most energy and go to the species with the least energy. So which species has the most energy species? Y? So that will be the least stable. Then species Z has the next highest energy and species X has the lowest amount of energy. So that is increasing stability from Y to Z to X. All right, question C which is more stable, the transition state between X and Y or the transition state between Y and Z. So the transition state between X and Y, I'll label this T S one in between Y and Z, I'll label this T S two. So just like part B we're looking for which transition state is more stable. So again, that relates to energy. So the lower the energy, the more stable the transition state will be. So which transition state has a lower energy transition state? One or two transition state two. So the transition state between Y and Z transition state between Y and Z and we're just looking at simply the value based off its position against the Y axis, right. So looking at which one is higher or lower on this Y axis All right. Last question part D asks which step has a higher rate constant in the forward direction. How about in the reverse direction? So in the reaction given above, we have in the forward reaction X to Y has a rate constant of K one, Y to Z has a rate constant of K two. And in the reverse reaction, Z to Y has a rate constant K minus two Y to X has the reaction. Sorry, the rate constant K minus one. So how can we relate the rate constant to our energy diagram? Well, the higher the reaction rate that will require a lower activation energy, right? So the less amount of energy that is required to overcome that transition state, the faster it will occur, right? So we also can look at the energy state of the product versus energy state of the reaction. So if the energy state of the product is less than the energy state of the reactant, it will be easier to perform that reaction and it will happen at a higher reaction rate. So let's look at the activation energy and the energy state of the reactants and products for the two reactions mentioned the forward direction and the reverse direction. So in the forward direction going from X to Y, we can draw our activation energy on the diagram by starting with point X drawing a horizontal dotted line to the right and drawing an arrow between that dotted line. And the peak of the transition state and then repeat the same between Y and Z. So start at point Y draw a horizontal line to the right, draw a line between that dotted line and the peak of the transition state too. So which one has a lower or smaller activation energy transition state? Two right, or the reaction from Y to Z. So for the forward reaction, this reaction is going to have the higher rate constant. And as we said, that rate constant is represented as K two. All right, what about for the reverse reaction, we need to redraw our activation energies from right to left. So we start with point Z now draw our dotted line horizontal to the left moving in the direction of the reaction and redraw that same arrow from the dotted line to the peak of the transition state. Then from point Y to the left, draw our arrow from that dotted line to the transition state. Well, these activation energies look almost exactly the same right. We can't really quantify which one is larger based on this drawing because the difference is not significant enough. So how about we look at our second rule that we mentioned, which talked about the energy state of the products. So from Z to Y, the product Y is at a higher energy than the reactant Z. But from Y to X, that product X is at a lower energy than the reactant Y So that's going to make that second reaction more easy to achieve, right? We are decreasing energy from Y to X. So it's going to have a higher reaction rate and the rate constant for the reverse reaction Y two X is K minus one. So that is it for this problem? I hope this video is helpful and thanks for watching.

Key Concepts

Reaction Coordinate Diagram

Transition States and Intermediates

Rate Constants and Reaction Rates

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