The Rate Constant Bozeman Science English (auto-generated) English

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[Music] hi it's mr. Andersen and this is

chemistry essentials video 36 on the

Hi. It's Mr. Andersen and this chemistry essentials video 37. It's on the rate constant. Before

rate constant before you watch this video make sure you've watched the video it's 37 on the rate law if you don't

you watch this video make sure you've watched the video, it's 36 on the rate law. If you

know what a first second zero order reaction is make sure you watch that

don't know what a first, second, zero order reaction is, make sure you watch that video

video so you know what I'm talking about but here's our rate law right here so in

so you know what I'm talking about. But here's our rate law right here. So in our rate law

our rate law the M and the N and there can be more exponents than that is going

the m and the n, and there can be more exponents than that, is going to tell us the reaction

to tell us the reaction order in other words is a proceeding at a second order reaction and be at a zero order reaction

order. In other words is A proceeding at a second-order reaction and B at a zeroth-order

so that's going to be in the exponent in here we're going to get the

reaction? So that's going to be in the exponent. In here we're going to get the concentration.

concentration so this would be the concentration of reactant a and B but remember if we have a really big

So this would be the concentration of reactant A and B. But remember if we have a really

reaction we could have more of these reactants and then finally we have

big reaction we could have more of these reactants. And then finally we have reaction rate which

reaction rate which is going to be how fast this reaction is proceeding so if

is going to be how fast this reaction is proceeding. So if we get rid of all of those things what

we get rid of all those things what we're left with is K and so what is K it's going to be this rate constant and

we're left with is k. And so what is k? It's going to be this rate constant. And so the

so the first thing you should understand about that rate constant is that it's

first thing you should understand about that rate constant is that it's not constant. It's

not constant it's dependent upon things like temperature and the presence of a catalyst but really want to understand

dependent upon things like temperature and the presence of a catalyst. But really you

what rate constant is and how it can be

want to understand what rate constant is. And how it can be calculated. And so if we

calculated and so if we look at the rate law the rate law is going to contain a

look at the rate law, the rate law is going to contain a constant. And we'll call that

constant we'll call that K and that K is measurable in other words we can gather a bunch of experimental data we can look

k. And that k is measurable. In other words we can gather a bunch of experimental data.

at it and we can work backwards to figure out what K is a really easy way

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

to do that in AP chemistry is to measure the reaction rate over time. And then use that

that to figure out K there's going to be huge variability knk in every reaction

to figure out k. There's going to be huge variability in k. In every reaction we're

we're going to have different KS and you can't figure out what it is just looking

going to have different k's. And you can't figure out what it is just looking at the

at the equation so we have to measure that why is there so much variation

equation. So we have to measure that. Why is there so much variation? There's so much

there's so much variation in our chemical reactions or the mechanisms of

variation in our chemical reactions, or the mechanisms of that. And we'll talk about that

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

in the next video. Also you should understand that k is not constant. It's going to be dependent

dependent upon things like temperature and the presence of a catalyst and then

upon things like temperature and the presence of a catalyst. And then finally if we're looking

finally if we're looking at the order of reaction especially in a first-order reaction there's a cool relationship

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

between the half-life and k. In other words they're going to be both independent of concentration.

really easy to figure out once we have the rate we can figure out

So it's really easy to figure out once we have the rate we can figure out the half-life.

the half-life and so here's a simple relationship between the two and a great

And so here's a simple relationship between the two. And a great example of half-life

example of the half-life name is going to be radioactive decay and I think visually when I showed it to you it'll

then is going to be radioactive decay. I think visually when I show you it'll make sense.

make sense and so the first thing you should understand is the K is going to have wide variability this is somebody's

And so the first thing you should understand is that k is going to have wide variability.

research paper and before they get to

This is somebody's research paper. And before they get to the actual chemistry they had

the actual chemistry they had to publish all of the rate constants that they'd figured out in all of their experiments

to publish all of the rate constants that they'd figured out in all of their experiments.

and if you look at all these numbers they're incredibly variable and the

And if you look at all of these numbers they're incredibly variable. And the reason we have

reason we have so much very variation in K is that we have so much variation in reactions we can't simply look at the

so much variation in k is that we have so much variation in reactions. We can't simply

reaction itself and figure out what K is going to be we have to experimentally

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

measure that in the laboratory. Also the rate constant is not constant. So temperature clearly

temperature clearly is going to affect the rate constant and also things like

is going to affect the rate constant. And also things like catalysts. We'll talk more

catalysts we'll talk more about that in later videos but catalysts can speed up a reaction and so the catalysts found in

about that in later videos. But catalysts can speed up a reaction. And so the catalyst

this is a cutout of a catalytic converter in a car and what those are

found in, this is a cut out of a catalytic convert in a car. And what those are really

really doing are speeding up the reaction and getting rid of some of the really nasty stuff that we is produced

doing are speeding up the reaction and getting rid of some of the really nasty stuff that

in an internal combustion engine and so if we look at the rate constant and now

is produced in an internal combustion engine. And so if we look at the rate constant, and

we're talking about a first-order reaction right here we have radioactive

now we're talking about a first-order reaction, right here we have radioactive decay. And

decay and so let's look at this on the left side we have fewer molecules that

so let's look at this. On the left side we have fewer molecules than we do on the right

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

side. But let's just watch it occur in a first-order reaction. And so as this reaction goes, you

a lot of the reactants are being consumed right at the beginning but

can see a lot of the reactants are being consumed right at the beginning but eventually it kind

eventually kind of drops off that rate at which they're being consumed and so

of drops off. That rate at which their being consumed. And so let's watch that again. 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

if we look at it again, a lot of reactants are being consumed at the beginning. But then

kind of falling off as we go and so if we were to look at the the ones over

it's kind of falling off as we go. And so if we were to look at the ones over here on

here on the Left let's go back how many did we have at the beginning we have 16

the left, let's go back, how many did we have at the beginning? We have 16. And now let

and now let me kind of move it forward and let's kind of find the half-life so

me kind of move it forward. And let's try to find the half life. So we had 16 there.

we had 16 there and now we've got 8 and so we've got half of them during that given period of time but now if we watch

And now we've got eight. And so we've got half of them during that given time. But now

during the next period of time now we're going from 8 down to 4 and then from 4

if we watch during the next period of time, now we're going from 8 down to 4. And then

down to 2 and you can see that it's taking about one half-life each time now

from 4 down to 2. And you can see that it's taking about 1 half-life each time. Now why

why is it not exactly 1 2 and 3 up here it's because we have a very small sample

is it not exactly 1, 2 and 3 up here? It's because we have a very small sample size.

size if I were to count all of these on the left be more specific okay so let's get to

If we were to count all of these on the left it's being more specific. Okay. So let's get

what that looks like graphically and so what is half life half life is T sub 1/2

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

It's going to be the amount of time it takes for half of the reactants to be consumed.

consumed and so this is what a curve of radioactive decay would look like and so

And so this is what a curve of radioactive decay would look like. And so if I draw that

if I draw that graphically this box is showing that 50% of the reactants that we had right here are being consumed and

graphically, this box is showing that 50 percent of the reactants that we had right here are

if we look down on the bottom let's say this takes one year now this doesn't

being consumed. And if we look down on the bottom, let's say this takes one year. So

always have to be one year it could be you know thousands or millions of years

this doesn't always have to be one year. It could be, you know, thousands or millions

for the half-life but if we look at that step and then we look at the next

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

half life, now we're going from 50 down to 25. And so what we're doing is consuming half

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

of the reactants that we had left. You can see that as we do it again that each of these

going to be constant and so in a first-order reaction all of the

half-lives is going to be constant. And so in a first order reaction all of the half-lives

half-life's are going to be constant and so rate or excuse me k and half-life

are going to be constant. And so rate, or excuse me k and half-life have these cool

have these cool relationships first thing is that both of them are independent of the concentration the K

relationships. First thing is that both of them are independent of the concentration.

is going to remain constant and the half-life is going to remain constant

The k is going to remain constant and the half-life is going to remain constant. And

and also we can use K once we've calculated to figure out half-life or

also we can use k, once we've calculated it to figure out half-life or vice verse. There's

vice-versa there's a direct inversely proportional relationship between these two and so it's easier to kind of now

a direct inversely proportional relationship between these two. And so it's easier to kind

look at a zero order and then a second-order reaction so what would be

of now look at zeroth-order and then a second-order reaction. So what would be the half-life of

the half-life of this one well again we're going to consume half of it and so

this one? Well again we're going to consume half of it. And so this would be during a

this would be during a given period of time in a zero order reaction look how long the half-life is but now we're

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 let and so even then a smaller yet and so in a zero order

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 is getting smaller or if we look at a

reaction you can see that the half-life of this is getting smaller. Or if we look at

second-order reaction let's look at that first half-life it's really really short

a second-order reaction, let's look at that first half-life, it's really really short.

next one's longer next one's even longer yet and so you can tell just looking at

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 or if

a graph and figuring out the half-life, is this a zero-order, second-order. If it's exactly

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

the same in each one then it's going to be a half-life or a first order reaction. And

connect a half-life of a reaction to the rate constant in a first-order reaction

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

Again, they're both going to be constant. We can use this equation to figure it out.

out and I hope that was helpful [Music]

And I hope that was helpful.