The Arrhenius Equation Video Lecture | Science for ACT

all right so this video is going to be
about the Arrhenius equation and in
using the Arrhenius equation the main
question that we're trying to figure out
is how does the temperature affect the
rate of a chemical reaction so if we
turn our attention to a general rate law
suppose we have one reactant the rate
law says that the rate is equal to the
rate constant times the concentration of
the reactant raised to a power and the
power is called the order of the
reaction with respect to this reactant
now when it comes to the temperature
dependence on a reaction rate well the
temperature dependence can't really lie
in the concentration in other words if I
have six molar that six molar is going
to be it's still going to be six molar
whether I had it at 20 Kelvin or you
know two thousand kelvins so that means
that the temperature dependence of the
rate of a chemical reaction must somehow
lie in the rate constant K and in
general the way that we quantify the
temperature dependence on the rate
constant and thus the the temperature
dependence on the overall rate of the
chemical reaction is by this equation K
equals a times e to the negative EA over
RT
okay as we know is the rate constant the
parameter a this is called the frequency
factor
lowercase e that's just a mathematical
constant and keep in mind we are raising
this whole thing this whole division
problem here is being we're raising e to
the power of this whole thing a sub a is
what we call the activation energy and
that's typically presented in kilojoules
per mole and R is the gas constant so
when you see the equation for instance
PV equals NRT for gas laws we're talking
about the same R and this R just happens
to be 8.314 joules over moles times
kelvins and T is the absolute
temperature in Kelvin
so given any three of these terms the
frequency factor the activation energy
or the absolute temperature we can solve
for whichever one
excuse me given two of these terms we
can solve for the unknown term remember
R is always going to be the same it's
simply a constant so it doesn't change
at all the only things that change are
the temperature the activation energy
and the frequency factor so let's get
into what the activation energy is well
a little bit more
so suppose we have the following graph
see if we can fit that in here on our
x-axis we have reaction progress
there we go and then on the y-axis we
have energy and for any chemical
reaction the energy versus reaction
progress diagram looks sort of like this
so over on the Left we have the energy
of the reactants and over on the right
here we have the energy of the products
now in general if we want to get any
chemical reactions started if we if we
want it to occur at all we must input a
certain value of energy and that is what
we call the activation energy so this
hump for instance we have to get over
that hump when it comes to energy for in
order to get the reaction to occur at
all so this energy between this hump and
the energy of the reactants that is
actually the activation energy that
we've just termed a Yi sub a
and the frequency factor a you can sort
of think as the of the frequency factor
as just sort of a you know a number that
represents the approaches that the
reaction that the reactants take towards
reaching this activation energy barrier
so just because we approach the
activation energy barrier doesn't mean
that we have surmounted it and basically
that's that's what this parameter a is
meant to measure so hopefully this helps
out and actually one more thing let's go
over a couple of tips as to how to solve
problems using the Arrhenius equation
notice that the activation energy is
given in kilojoules per mole and
generally and the gas constant is in
joules over moles times kelvins so one
of these has joules and the other has
kilo joules so when you want to solve a
problem you have to make sure your units
cancel always right so if this happens
to you if you ever have joules in one
thing and kilo joules in another what
you need to do is convert from one of
these to the other so we're going to
either convert the gas constant into
kilo joules or we're going to convert
the activation energy into joules also
note that the temperature is in kelvins
so if you're given a Celsius temperature
you must convert that Celsius
temperature into kelvins and I believe I
do have a video on how to do that it's
pretty straightforward so that is an
introduction on how to use the Arrhenius
equation