The Rate Constant Video Lecture | Science for ACT

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hi it's mr. Andersen and this is
chemistry essentials video 36 on the
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
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 be at a zero 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 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 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 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 knk in every reaction
we're going to have different KS 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 the half-life name is going
to be radioactive decay and I think
visually when I showed it to you it'll
make sense and so the first thing you
should understand is the 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 these numbers
they're incredibly variable and the
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
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 catalysts found in
this is a cutout of a catalytic
converter 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 we 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 that
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 kind of drops off that rate
at which they're 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 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 kind of find the half-life so
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
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 one 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 I were to count all of these on
the left
be more specific okay so let's get to
what that looks like graphically and so
what is half life half life is T sub 1/2
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% 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 now 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-life's 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 to figure out half-life or
vice-versa there's a direct inversely
proportional relationship between these
two and so it's easier to kind of now
look at a zero 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 zero order reaction look how
long the half-life is but now we're
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
reaction you can see that the half-life
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's longer next one's 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
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 a 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
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