so for this practice problem we're gonna be looking at energy diagrams. energy
diagrams are very important for understanding the thermodynamics and
kinetics of a reaction so what we want to be able to do is write, we're gonna draw an energy
diagram for a two-step reaction that is exothermic overall and has a first step
that is a rate determining step. so see if you can draw an energy diagram that fulfills those criteria
i've gone ahead and drawn an energy diagram that does fit these
criteria so let's remind ourselves a couple of things about energy and energy
diagrams. number one on the y axis here we have potential energy so potential
energy increases going up and then we're always moving forwards in time this way
so this is the reaction coordinate, we're going forwards in time, so we have our
reactants and we have our products and then we must have an intermediate
because this is a two-step reaction so this is two discrete steps which means
we need two slopes like that. now first of all we said it's exothermic so what that
means is that the delta H must be negative
that means that from reactants to products it must release energy and must
go lower in energy so the first thing that must be true about your energy
diagram is that the products must sit lower than the reactants on the energy
diagram, that is how we make sure that it is exothermic overall. now the second thing
that we have to understand is that this is a two-step reaction so there has to
be two discrete steps and each step has its own activation energy so right here
we have the activation energy Ea1 and that is the activation energy required
to get to transition state one, so for any reaction
we're gonna have an activation barrier that has to be overcome to reach the
transition state after which point it certainly will continue to completion so
there's transition state one, so we're starting with the reactants, transition state
activation energy, and then we get to this intermediate and then right here
this is going to be activation energy two, and transition state two, and now when we
say that the first step has to be the rate-determining step what has to be
true about your energy diagram must therefore then be that Ea1 must be
greater than Ea2, because in solution things are swimming around in terms of
kinetics a larger activation barrier means that molecules must collide with a
greater amount of kinetic energy so the bigger than the bigger the activation
energy is the more often that collisions will not result in a reaction, you
can have them collide with this much kinetic energy they don't go, a little
more they don't go, a little more they don't go, only when they
collide with enough kinetic energy to get over that very
large barrier do they go ahead and generate the intermediate and so the larger the
activation energy, the slower its gonna go because it's going to take
longer for enough collisions to occur for all the molecules to react so on the
macroscopic scale what that ends up meaning is that the reaction with the
largest activation energy is going to be the slowest step and therefore the rate
determining step, once we reach this intermediate right there
this relatively much much smaller activation energy two is going to mean
that so many more collisions will result in a reaction so once they get finally above
this one they are very quickly gonna go ahead and undergo the second reaction to
generate products, so a two-step reaction means we need two like that
exothermic means the products must sit lower than the reactants, and then the
first step being the rate determining step means that Ea1 must be greater
than Ea2
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