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- [Instructor] Let's consider a reaction

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with the following multi-step mechanism.

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In step one, A reacts
with BC to form AC plus B.

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And in step two, AC reacts
with D to form A plus CD.

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If we add the two steps
of our mechanism together

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we can find the balanced equation

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for this hypothetical reaction.

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So we're gonna put all of our reactants

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on the left side here,
and we're gonna have

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all of our products on the right side.

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And we can see that AC is on the left

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and it's on the right side,
so we can cancel that out.

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A is also in the left and the right side,

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so we can cancel that out.

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So the overall equation would be BC plus D

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goes to B plus CD.

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We've just seen that BC
and D are our reactants

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and B and CD are the products

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for this hypothetical reaction.

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If we look at the mechanism,
A is there in the beginning

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and A is there in the end.

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But A is not a reactant or a product,

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therefore A must be a catalyst.

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Something else that's not a
reactant or a product is AC.

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You notice how AC was generated

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in the first step of our mechanism,

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and then AC is used up in the
second step of the mechanism.

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Therefore AC must be the
intermediate for this reaction.

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Next, let's look at the energy profile

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for this multi-step reaction.

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Energy profiles usually have
potential energy in the y-axis

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and then reaction progress on the x-axis.

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So as we move to the right on the x-axis,

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the reaction is occurring.

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This first line on our energy profile

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represents the energy
level of our reactants,

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which are BC and D.

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So let's go ahead and show
the bond between B and C.

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And then we also have D present.

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Our catalyst is also present

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at the very beginning of our reactions.

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So I'll go ahead and draw in
A above our two reactants.

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We can see in our energy
profile that we have two hills.

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The first Hill corresponds
to the first step

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of the mechanism and the second hill

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corresponds to the second step.

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So the peak of the first
hill is the transition state

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for the first step of the mechanism.

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And we can see in the first
step that the catalyst A,

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is colliding with BC or reacting with BC

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to form our intermediate AC.

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So A must collide with BC
and at the transition state,

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the bond between B and C is breaking,

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and at the same time, the bond
between A and C is forming.

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We would still have reactant D present

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at the top of this hill too.

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So I'll go ahead and draw in D here.

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When a collides with BC,
the collision has to have

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enough kinetic energy to
overcome the activation energy

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necessary for this reaction to occur.

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And on this energy profile,

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the activation energy is
the difference in energy

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between the reactants
and the transition state,

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so the very peak of the hill.

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So this difference in energy,

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corresponds to the activation energy

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for the first step of the
mechanism which we will call Ea1.

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If we assume that the collision
has enough kinetic energy

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to overcome the activation energy,

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we'll form our intermediate
AC, and we'd also form B.

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So let's go ahead and show the bond

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between A and C has now been formed.

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So this valley here between our two hills

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represents the energy
level of the intermediate.

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We would also have be present,

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so I can go ahead and
I'll just write in B here.

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And then we still have some D present,

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D still hasn't reacted yet.

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So I'll go ahead and draw in D as well.

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Next we're ready for the second hill

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or the second step of our mechanism.

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In the second step, AC the
intermediate AC reacts with D

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to form A and CD.

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So the top of this second hill
would be the transition state

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for this second step.

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So we can show the bond
between A and C braking,

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and at the same time the bond
between C and D is forming.

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The difference in energy
between the energy

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of the intermediate and the
energy of the transition state

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represents the activation energy

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for the second step of the mechanism,

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which we will call Ea2.

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So AC and D must collide
with enough kinetic energy

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to overcome the activation
energy for this second step.

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If AC and D collide with
enough kinetic energy,

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we would produce A and CD.

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So this line at the end here
represents the energy level

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of our products.

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So CD is one of our products,
so we'll write that in here.

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And remember B is our other products,

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which we formed from the
first step of the mechanisms.

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So let's go ahead and
write in here B plus CD.

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And we also reformed our catalyst,

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so A would be present here as well.

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Next let's compare the
first activation energy Ea1

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with the second activation energy Ea2.

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Looking at the energy
profile we can see that Ea1

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has a much greater
activation energy than Ea2.

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So let's go ahead and write
Ea1 is greater than Ea2.

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The smaller the activation
energy, the faster the reaction,

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and since there's a
smaller activation energy

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for the second step,

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the second step must be
the faster of the two.

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Since the first step has the
higher activation energy,

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the first step must be slow
compared to the second step.

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Since the first step of the
mechanism is the slow step,

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the first step is the
rate determining step.

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Finally, let's Find the
overall change in energy

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for our reaction.

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So to find the overall change
in energy, that's Delta E,

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which is final minus initial.

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So that would be the
energy of the products

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minus the energy of the reactants.

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So the energy level of
the products is right here

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and then the energy level of the reactants

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is at the beginning.

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So let me just extend
this dashed line here

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so we can better compare the two.

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Representing Delta E on a graph,

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it would be the difference in energy

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between these two lines.

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And since the energy of the products

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is greater than the
energy of the reactants,

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we would be subtracting a smaller number

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from a larger number

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and therefore Delta E would be positive

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for this hypothetical reaction.

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And since Delta E is positive,

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we know that this reaction
is an endothermic reaction.