Hi. It's Mr. Andersen and this chemistry essentials video 37. It's on the rate constant. Before
you watch this video make sure you've watched the video, it's 36 on the rate law. If you
don't know what a first, second, zero order reaction is, make sure you watch that video
so you know what I'm talking about. But here's our rate law right here. So in our rate law
the m and the n, and there can be more exponents than that, is going to tell us the reaction
order. In other words is A proceeding at a second-order reaction and B at a zeroth-order
reaction? So that's going to be in the exponent. In here we're going to get the concentration.
So this would be the concentration of reactant A and B. But remember if we have a really
big reaction we could have more of these reactants. And then finally we have reaction rate which
is going to be how fast this reaction is proceeding. So if we get rid of all of those things what
we're left with is k. And so what is k? It's going to be this rate constant. And so the
first thing you should understand about that rate constant is that it's not constant. It's
dependent upon things like temperature and the presence of a catalyst. But really you
want to understand what rate constant is. And how it can be calculated. And so if we
look at the rate law, the rate law is going to contain a constant. And we'll call that
k. And that k is measurable. In other words we can gather a bunch of experimental data.
We can look at it and we can work backwards to figure out what k is. A really easy way
to do that in AP chemistry is to measure the reaction rate over time. And then use that
to figure out k. There's going to be huge variability in k. In every reaction we're
going to have different k's. And you can't figure out what it is just looking at the
equation. So we have to measure that. Why is there so much variation? There's so much
variation in our chemical reactions, or the mechanisms of that. And we'll talk about that
in the next video. Also you should understand that k is not constant. It's going to be dependent
upon things like temperature and the presence of a catalyst. And then finally if we're looking
at the order of reaction, especially in a first-order reaction, there's a cool relationship
between the half-life and k. In other words they're going to be both independent of concentration.
So it's really easy to figure out once we have the rate we can figure out the half-life.
And so here's a simple relationship between the two. And a great example of half-life
then is going to be radioactive decay. I think visually when I show you it'll make sense.
And so the first thing you should understand is that k is going to have wide variability.
This is somebody's research paper. And before they get to the actual chemistry they had
to publish all of the rate constants that they'd figured out in all of their experiments.
And if you look at all of these numbers they're incredibly variable. And the reason we have
so much variation in k is that we have so much variation in reactions. We can't simply
look at the reaction itself and figure out what k is going to be. We have to experimentally
measure that in the laboratory. Also the rate constant is not constant. So temperature clearly
is going to affect the rate constant. And also things like catalysts. We'll talk more
about that in later videos. But catalysts can speed up a reaction. And so the catalyst
found in, this is a cut out of a catalytic convert in a car. And what those are really
doing are speeding up the reaction and getting rid of some of the really nasty stuff that
is produced in an internal combustion engine. And so if we look at the rate constant, and
now we're talking about a first-order reaction, right here we have radioactive decay. And
so let's look at this. On the left side we have fewer molecules than we do on the right
side. But let's just watch it occur in a first-order reaction. And so as this reaction goes, you
can see a lot of the reactants are being consumed right at the beginning but eventually it kind
of drops off. That rate at which their being consumed. And so let's watch that again. So
if we look at it again, a lot of reactants are being consumed at the beginning. But then
it's kind of falling off as we go. And so if we were to look at the ones over here on
the left, let's go back, how many did we have at the beginning? We have 16. And now let
me kind of move it forward. And let's try to find the half life. So we had 16 there.
And now we've got eight. And so we've got half of them during that given time. But now
if we watch during the next period of time, now we're going from 8 down to 4. And then
from 4 down to 2. And you can see that it's taking about 1 half-life each time. Now why
is it not exactly 1, 2 and 3 up here? It's because we have a very small sample size.
If we were to count all of these on the left it's being more specific. Okay. So let's get
to what that looks like graphically. And so what is half-life? Half-life is t sub one-half.
It's going to be the amount of time it takes for half of the reactants to be consumed.
And so this is what a curve of radioactive decay would look like. And so if I draw that
graphically, this box is showing that 50 percent of the reactants that we had right here are
being consumed. And if we look down on the bottom, let's say this takes one year. So
this doesn't always have to be one year. It could be, you know, thousands or millions
of years for the half-life. But if we look at that step, and then we look at the next
half life, now we're going from 50 down to 25. And so what we're doing is consuming half
of the reactants that we had left. You can see that as we do it again that each of these
half-lives is going to be constant. And so in a first order reaction all of the half-lives
are going to be constant. And so rate, or excuse me k and half-life have these cool
relationships. First thing is that both of them are independent of the concentration.
The k is going to remain constant and the half-life is going to remain constant. And
also we can use k, once we've calculated it to figure out half-life or vice verse. There's
a direct inversely proportional relationship between these two. And so it's easier to kind
of now look at zeroth-order and then a second-order reaction. So what would be the half-life of
this one? Well again we're going to consume half of it. And so this would be during a
given period of time in a zeroth-order reaction. Look how long the half-life is. But now were
going to go to a smaller half-life. And then even a smaller yet. And so in a zeroth-order
reaction you can see that the half-life of this is getting smaller. Or if we look at
a second-order reaction, let's look at that first half-life, it's really really short.
Next one is longer. Next one is even longer yet. And so you can tell, just looking at
a graph and figuring out the half-life, is this a zero-order, second-order. If it's exactly
the same in each one then it's going to be a half-life or a first order reaction. And
so can you connect the half-life of a reaction to the rate constant in a first-order reaction?
Again, they're both going to be constant. We can use this equation to figure it out.
And I hope that was helpful.