The Rate Law Video Lecture | Science for ACT

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 its 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 so if we break it down
rate the speed of the reaction is equal
to K K is going to be the rate constant
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 all talked
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 zero right here in other
words it's the concentration of a raised
to the zero power in a first we're going
to put a 1 there and in the second order
we're going to put a 2 there and so what
does a zeroth order look like well if
you raise anything to the zero 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
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 N power and so each of these can
proceed along a different reaction order
and 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 and so rate is equal to K in other
words it doesn't matter how much ammonia
we have it's still 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 always 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 bit 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
slope 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
will get 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 very and 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've moved
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 point one
to point two 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 two squared is four
four squared now is 16 so if we double
it again from point 2 to point four we
see that were 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 how do we find a slope of this
curved line without using a lot of
calculus it doesn't right work and so
what we'll do is if we take over time
the inverse of the concentration of that
will actually get a straight line which
related to K now let's say we're looking
at overall reaction order like I'd 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 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 zero order reaction now let's see
where we're keeping be 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 and
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 zero
order
since this is essentially one this would
be our overall order and so all we're
doing is simply adding those reaction
orders and 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 we
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 whichever one
gives 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 that's going to
make a clear form of a chemical and so
what we could you is use a
spectrophotometer spectrophotometer
measures the amount of absorbance in
other words how much of that light is
being absorbed by the material and we
could 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 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 zero
first or second order now we can go much
higher than that we can have fractional
orders but we're just getting started on
rate law and I hope that was helpful