Hi. It's Mr. Andersen and this is chemistry essentials video 36. It's on the Rate Law.
Now in the last video we talked about reactions and how the speed of reactions can vary. And
so if we look at this reaction right here, the breakdown of ammonia into hydrogen and
nitrogen gas, it's going to proceed along a straight line. In other words if we have
a high concentration of ammonia or a low concentration of ammonia the amount that's being consumed
is going to remain consistent. In other words the rate of this reaction is the same. But
if we look at something like this, nitrogen dioxide, and we look at it's rate as it's
broken down into nitric oxide and oxygen, it's going to follow a different curve. In
other words, when there's a lot of nitrogen dioxide, it's going to proceed really, really
quickly. And then when there's not much it's not going to proceed as quickly. And if we
look at those two equations, they almost look identical And so there's no way to tell just
looking at a balanced equation of a reaction how fast it's going to proceed. And that's
an important thing to understand as we move forward with the rate law. And so the rate
law really refers to the amount of reactants that are being consumed. And so we don't have
to concern ourselves with what products are being made. And here's the equation for the
rate law. And so if we break it down, rate, the speed of the reaction is equal to k, k
is going to be the rate constant. And we'll talk about that in the next video. And that's
going to be times the concentration of the reactant. How much A we have, raised to the
m power. And that power is going to tell us the reaction order. Now the three ones I'll
talk about are zero, first and second order reactions. And so what does that mean if we
have a zeroth-order? It means that we're putting a 0 right here. In other words it's the concentration
of A raised to the 0 power. In a first we're going to put a 1 there. And in a second-order
we're going to put a 2 there. And so what is a zeroth order look like? Well if you raise
anything to the 0 power it's simply 1. And so you can think of this turning into a 1.
And so rate is equal to k. In other words rate is going to be equal to that constant
or the rate constant. If we look at a first-order reaction then this is raised to the 1 power.
And so it's going to be the rate constant times the concentration of A. So what are
we going to get? We're going to get this curve where it's going really, really quickly at
the beginning and then slower as we get more. And then if it's raised to the second power,
it's going to be a second-order. So it's going to be k times the concentration of A raised
to the second power. And you can see that that reaction is actually going to go faster
the more we have. And so we'll go through each of those and I'll give you examples of
them as well. Now the thing that you have to remember is that we have to determine these
experimentally. We can't just look at the equation and figure out the rate law for that
reaction. What if we have more than one reactant? Then the rate law is still going to apply.
And so it's going to be simply this. Rate is equal to k, the rate constant, times the
concentration of A raised to the m power and B raised to the m power. And so each of these
can proceed along a different reaction order. And so if we want to figure out the overall
order we're simply going to add those values up. And so I'll show you how we can use data
to figure out what order it's going to be after we've calculated the data. And so in
a zeroth-order reaction, here's an example I gave you at the beginning. We're breaking
down ammonia into hydrogen gas and nitrogen gas. So rate is equal to k. In other words
it doesn't matter how much ammonia we have. It still is going to proceed at the same rate.
Now if we were to look at the data it would look like this. Imagine three experiments
where we vary the concentration of A. We would find that the rate is going to be identical.
And so if you have a rate that stays the same, if you're looking at simply data, you know
that's a zero order. How could we figure that out based on this graph? Well to figure out
the rate all you do is figure out the slope of that line. And so if we figure the slop
of the line here and then tangent here, we would find that those triangles are exactly
the same. And so if we were to graph the rate over time relationship, we'd find it's simply
going to be a straight line. It stays the same. If we look at a first-order reaction,
this is the breakdown of hydrogen peroxide. Remember rate is equal to k, that constant
times the concentration of A. And so this is what our graph is going to look like. If
we look at a couple of experiments where we have varying again the concentration of A,
what we'll find is that there's a direct relationship between these two. As we double the concentration,
we're doubling the rate. And you can see here that we're doubling the concentration. We're
doubling the rate as well. So a great example of a first-order is radioactive decay. Now
if we were to calculate the slope, we're going to have a steep slope at the beginning. And
a not so steep slope as we move farther out. So if I were actually to graph the rate over
time, it's going to be a straight line, but it's going to be a straight line that's descending
over time. Now another way to figure this out is simply to take the data and then take
the natural log of the concentration. And we're also going to get a straight line. What's
cool about that is the slope of that line is going to tell us k or that constant. If
we look at a second-order reaction it's going to go even faster. So rate is the concentration
raised to the second power. And so if we were to look at a graph, what does that look like?
Well in this first experiment from 0.100 to 0.200 you'll see that it looks like it's doubling.
And so don't be tricked by that. What we're really doing is squaring it. So 2 squared
is 4. 4 squared now is 16. So if we double it again from 0.200 to 0.400 we see that we're
squaring that rate. And so what would that look like if we were to graph it? You actually
get a curved line of the rate. And so you're taking the slope of a curved line. Getting
another curved line. What does that imply? That it's going really, really fast. The faster
we have that rate. And so that doesn't, wait, how do we find a slope of this curved line
without using a lot of calculus? It doesn't work. And so what we'll do is if we take over
time the inverse of the concentration of that, we'll actually get a straight line which is
related to k. Now let's say we're looking at overall reaction order. Like I had said,
if we have more than one reactant each of those may proceed along a different order.
And so let's look at this data. This is a real common question in AP Chem. So if we
look at the concentration of A, you can see right here it's held steady. And since we're
holding it steady, we can just look at B and see what's happening to B. Well you can see
that we're increasing the concentration of B, but the rate is not changing. And so I
know that B is going to proceed along a zeroth-order reaction. Now let's see where we're keeping
B the same. So B is the same here and here. And so if we look then at A from here to here,
A we're doubling the concentration in experiment 1 to experiment 3. Let's look at what's happening
to the rate. The rate is proceeding as a square. And so rate is equal to k times A raised to
the 2 power. So that's a second-order. B is a zeroth-order reaction. Since this is essentially
1, this would be our overall order. And so all we're doing is simply adding those reactions
orders and we're getting the overall reaction order. Now let me give you a problem. Say
this is the problem you have to figure out. Could you figure out the overall reaction
order? Pause the video. Give it a try. And then you could put your answer down below
in the video description. Let's say we gather a bunch of data. And we don't want to look
at specific points. We want to actually calculate which order it is really, really quickly.
A super simple way to do that is let's say this is the concentration of our reactants.
What we could do is simply graph the concentration versus time. In other words this would be
on the x-axis. This would be on the y. We could then graph the natural log of the concentration
versus time. And then we could do the inverse of the concentration versus time. Now it's
really easy to calculate this using a spreadsheet. We graph them, which ever one give us a straight
line. That's going to tell us what order it is. Either a zero, a first or a second. An
example of that in the chemistry lab, you could do the breakdown of crystal violet.
Crystal violet is going to be purple but when we mix it with hydroxide it's going to make
a clear form of a chemical. And so what we could do is use a spectrophotometer. A spectrophotometer
measures the amount of absorbance. In other words how much of that light is being absorbed
by the material. And we can simply graph it. We could graph the absorbance versus time.
Then the natural log of the absorbance versus time. And then the inverse of absorbance versus
time. And what that absorbance is really telling is that how much of that crystal violet is
here. The more that's there the more it's being absorbed. And so we could figure out
which of these lines is going to be a straight line. And that's going to actually tell us
k. And so did you learn to analyze concentration versus time data to figure out is this a zeroth
first of second order? Now we can go much high than that. We can have fractional orders.
But we're just getting started on Rate Law and I hope that was helpful.