- [Instructor] Let's consider a reaction
with the following multi-step mechanism.
In step one, A reacts with BC to form AC plus B.
And in step two, AC reacts with D to form A plus CD.
If we add the two steps of our mechanism together
we can find the balanced equation
for this hypothetical reaction.
So we're gonna put all of our reactants
on the left side here, and we're gonna have
all of our products on the right side.
And we can see that AC is on the left
and it's on the right side, so we can cancel that out.
A is also in the left and the right side,
so we can cancel that out.
So the overall equation would be BC plus D
goes to B plus CD.
We've just seen that BC and D are our reactants
and B and CD are the products
for this hypothetical reaction.
If we look at the mechanism, A is there in the beginning
and A is there in the end.
But A is not a reactant or a product,
therefore A must be a catalyst.
Something else that's not a reactant or a product is AC.
You notice how AC was generated
in the first step of our mechanism,
and then AC is used up in the second step of the mechanism.
Therefore AC must be the intermediate for this reaction.
Next, let's look at the energy profile
for this multi-step reaction.
Energy profiles usually have potential energy in the y-axis
and then reaction progress on the x-axis.
So as we move to the right on the x-axis,
the reaction is occurring.
This first line on our energy profile
represents the energy level of our reactants,
which are BC and D.
So let's go ahead and show the bond between B and C.
And then we also have D present.
Our catalyst is also present
at the very beginning of our reactions.
So I'll go ahead and draw in A above our two reactants.
We can see in our energy profile that we have two hills.
The first Hill corresponds to the first step
of the mechanism and the second hill
corresponds to the second step.
So the peak of the first hill is the transition state
for the first step of the mechanism.
And we can see in the first step that the catalyst A,
is colliding with BC or reacting with BC
to form our intermediate AC.
So A must collide with BC and at the transition state,
the bond between B and C is breaking,
and at the same time, the bond between A and C is forming.
We would still have reactant D present
at the top of this hill too.
So I'll go ahead and draw in D here.
When a collides with BC, the collision has to have
enough kinetic energy to overcome the activation energy
necessary for this reaction to occur.
And on this energy profile,
the activation energy is the difference in energy
between the reactants and the transition state,
so the very peak of the hill.
So this difference in energy,
corresponds to the activation energy
for the first step of the mechanism which we will call Ea1.
If we assume that the collision has enough kinetic energy
to overcome the activation energy,
we'll form our intermediate AC, and we'd also form B.
So let's go ahead and show the bond
between A and C has now been formed.
So this valley here between our two hills
represents the energy level of the intermediate.
We would also have be present,
so I can go ahead and I'll just write in B here.
And then we still have some D present,
D still hasn't reacted yet.
So I'll go ahead and draw in D as well.
Next we're ready for the second hill
or the second step of our mechanism.
In the second step, AC the intermediate AC reacts with D
to form A and CD.
So the top of this second hill would be the transition state
for this second step.
So we can show the bond between A and C braking,
and at the same time the bond between C and D is forming.
The difference in energy between the energy
of the intermediate and the energy of the transition state
represents the activation energy
for the second step of the mechanism,
which we will call Ea2.
So AC and D must collide with enough kinetic energy
to overcome the activation energy for this second step.
If AC and D collide with enough kinetic energy,
we would produce A and CD.
So this line at the end here represents the energy level
of our products.
So CD is one of our products, so we'll write that in here.
And remember B is our other products,
which we formed from the first step of the mechanisms.
So let's go ahead and write in here B plus CD.
And we also reformed our catalyst,
so A would be present here as well.
Next let's compare the first activation energy Ea1
with the second activation energy Ea2.
Looking at the energy profile we can see that Ea1
has a much greater activation energy than Ea2.
So let's go ahead and write Ea1 is greater than Ea2.
The smaller the activation energy, the faster the reaction,
and since there's a smaller activation energy
for the second step,
the second step must be the faster of the two.
Since the first step has the higher activation energy,
the first step must be slow compared to the second step.
Since the first step of the mechanism is the slow step,
the first step is the rate determining step.
Finally, let's Find the overall change in energy
for our reaction.
So to find the overall change in energy, that's Delta E,
which is final minus initial.
So that would be the energy of the products
minus the energy of the reactants.
So the energy level of the products is right here
and then the energy level of the reactants
is at the beginning.
So let me just extend this dashed line here
so we can better compare the two.
Representing Delta E on a graph,
it would be the difference in energy
between these two lines.
And since the energy of the products
is greater than the energy of the reactants,
we would be subtracting a smaller number
from a larger number
and therefore Delta E would be positive
for this hypothetical reaction.
And since Delta E is positive,
we know that this reaction is an endothermic reaction.