start today we will cover chapter 14
chemical kinetics now chemical kinetics
simply studies the speed of chemical
reactions
now some chemical reactions are very
very slow and some chemical reactions
are very very fast for example if you
simply consider the oxidation of ayran
with oxygen which we call it rust and in
fact in the presence of vapor water
particularly and we get iron 3 oxide and
this is simply rust and we can have
different number of water molecules
attached there so this reaction is very
very slow very slow and it takes years
actually to have a piece of iron
converted to what we call rust
actually simple oxidation actually says
oxidation of ayran metal to iron 3 oxide
with some water that's the frost we call
it now on the other side some reactions
if you simply take magnesium dust and in
the presence of oxygen gas and a little
bit heat some just heated you get
magnesium oxide like this this is a game
solids and Plus this gives actually
light in the visible region simply
visible white let's say some of the
energy is give given off in the form of
white and this light is so bright and
the reaction takes place in fractions of
seconds
and you all you probably don't remember
when we had cameras used to be
disposable flash cubes little flash
cubes actually or you can have a
permanent electrical flash flash
in fact with your camera or disposable
one and those disposable ones was like
like a cube little cube and you attach
it to your used to actually we use the
attach it to our camera and when we
simply take a picture press the shutter
release and that sends a little bit heat
electricity actually to the disposable
flash which contains oxygen and the
magnesium it dust separately and when
you just press the shutter release you
mix that heated up and you start that
reaction when that reaction starts it
finishes in fractions of a second and in
that time it gives light and that light
used to take the pictures in fact flash
you see again some reactions very very
slow some are very fast now the speed of
reactions are very important for
industrial chemistry particularly why
because when you produce an industrial
product by using a chemical reaction to
be economical to make it economical you
should be able to produce certain amount
of product in a given time so if the
reaction is fast then it will be a
profitable actually I should say work
and but if the reactions is very very
slow then it will not be economically
feasible actually right so in industry
particularly we try to increase the rate
of reaction this way you try to increase
the product per unit time and more
product product means more money and
more economical the business becomes
actually so chemical kinetics studies in
far
the rate of reactions that means speed
of reactions and it also tries to
determine what are the factors that
affect the speed of reaction so that by
changing those factors how can we
increase the rate of chemical reactions
now in addition to that chemical
kinetics also studies how reactants are
converted to the products what are the
steps between the reactant and a product
when we write down a chemical reaction
we write down the reactants and then on
the right hand side we write down the
products we usually think that it's a
one-step reaction you know but it's
never usually actually most cases
there's never be one-step reaction
there's always series of chemical
reaction steps between the reactant and
a product as the reactants are converted
to the product so those details how the
reactants are converted to the products
is called the mechanism of a chemical
reactions so the chemical kinetics also
studies the mechanism of the chemical
reactions to now this slide simply shows
you for example again this is excitation
of an electron in a molecule from one
level to another level takes about 10 to
the minus 15 seconds which is a
femtoseconds is called femtoseconds very
fast on the other side you have an
explosion for example that's all
chemical reactions and that takes about
one second
you know but on the other side this is
rustin and it takes years and this one
is whether an off a rock they call and
that takes millions of years and so on
and all of these are if you consider
those as a chemical reactions you see
again some chemical reactions are slow
some chemical reactions are fast and
this is again as we said in addition to
the factors effect in the chemical
reaction rate chemical we
action speed the mechanism is also
important which is the molecular level
view of the path from reactants to the
products what happens as the reactant
goes to the products now factors that
affect the reaction rates let's look at
those first one is the physical state of
the reactants what does that means that
means whether your reactants are gas
liquid or solids that affects actually
the rate of a chemical reaction speed of
a chemical reaction second factor is
concentrations of the reactant
particularly if you're in solution or in
gaseous reactions the concentrations of
the reactants are very very important as
we will explain it affects the rate of
the reaction because if we simply
consider that a chemical reaction will
take place when two molecules collide
with each other right and then the
product will form sometimes three but
it's very seldom actually because to
have the collisions of three molecules
at the same time at the same point in
space is very very rare and the
probability of that is very very low
close to zero so that means that
reactants has to collide with each other
to lead to the product now when you
consider that reactant concentration
means more molecules reactant molecules
more reactant molecules me as more
collusions more collusion means more
product form in a given time that means
the rate of the reaction will increase
with the reactant concentration we will
see in detail those reaction temperature
is also important why because again
remember when he increased the
temperature the kinetic energy of the
molecules increases what does that means
that means the molecules start moving
faster when the molecules are moving
faster means you will have more
collisions and also you will have more
molecules which have enough energy
actually to lead to the product we will
see that again
as activation energy now the presence of
catalyze this is another way effect in
the rate of the reaction as we again see
that we catalyze changes the mechanism
of the reaction in other words it
changes the path from reactant to the
product so that the activation energy of
the new way new Road is lower than the
previous one and the rate of the
reaction increases that way but the
catalyze is never been used itself in a
chemical reaction it enters a chemical
reaction it comes out from a chemical
reaction but the rate speed of the
reaction increases as a matter of fact
due to the change of the mechanism as we
will see now let's these are each of
these physical state of the reactants we
said affects the speed of the reaction
how the more readily the reactants
collide the more rapidly they react so
more collusions means rapid reactions
homogeneous reactions are often faster
what we mean homogeneous reactions
reactions are taking place in solutions
or reactions that are taking place in
gas phase right but the solid state the
reactions are not that slow unless the
reaction is taking place only on the
surface of the solid as we will see so
homogeneous reaction solutions and gas
reactions are faster now heterogeneous
reactions that involve solids are faster
if the surface area is increased that
means if one of your reactants is a
solid and you have a heterogeneous
reactions this the more the surface area
of the solid particles actually the
faster is the reaction as a matter of
fact the surface area of the solid will
increase as the size of the particles of
the solid decreases as a matter of fact
more small particles more face and then
that means faster reaction this is what
a surface area is related to the size of
the particles for example fine powders
reacts much faster than palette or
tablet if you have fine dust in fact in
a solid form that reacts much much
faster as a matter of fact now reactant
concentrations another factor that
affects the rate of a reaction increase
in the reactant concentration generally
increases reaction rate yes since there
are more molecules more collisions occur
again higher concentration means more
molecules per unit volume more molecules
mean more collisions more collusion
means faster chemical reaction faster
chemical reactions now temperature is
another factor as we said reaction rate
generally increases with increased
temperature kinetic energy of the
molecules why here explains its kinetic
energy of the molecules is related to
the temperature at higher temperatures
molecules more more quickly increase in
the numbers of collusion and the energy
of the molecules possessed during the
collisions because normally if you
increase the temperature
you're not only increase in the speed of
the chemical reactions there so the
number of collisions that will take
place per unit time but you also
increase in the average energy of the
molecules colliding molecules and that
means more molecules will have enough
energy to go to the product collide and
go over the transition state and go to
the product side that's what it simply
says here molecules possession during
that now presence of catalyze again as
we said catalyze affect the rate without
being in overall balanced equation that
means it is not consumed actually during
the chemical reaction it's still there
the catalyze affects the kind of
collusions change in the mechanism this
is really important
the catalyzed changes the rate of a
reaction by changing the mechanism and
change in mechanism actually changes the
activation energy as we will describe
later that means minimum energy of the
molecules should have to give the
product in fact
now cattle eyes are critical in many
biological reactions particularly in
industries catalyzed very important why
because you try to increase the speed of
your chemical reaction which you use to
produce product goods in fact and per
given time and that is very very
important in chemical industry - but in
biological reactions usually the
catalyzed are large molecules what we
call them what do we call them enzymes
yes enzymes in fact without enzymes in
fact the life is not possible the
enzymes are very large molecules and
they only increase the rate of
particular reactions we will see that
particular reactions that's design so
cleanly in fact the enzymes and those
actually adjust the speed of the
chemical reactions taking place in
living organisms in fact the speed of
chemical reactions in living organisms
is very important as a matter of fact if
the reactions is too fast it will really
harm the life if the reactions is too
slow it was also harm to life that means
the life will end that's all I mean now
reaction rate again the speed or you can
call it reaction speed how do we define
the reaction rate as here rate is a
change in concentration over a time
period now it is get usually given as
Delta something here - delta T for
example if I simply have a reaction
let's say a going to the product like
this so the rate of this reaction is
given as the change of the concentration
of a now this is the molar concentration
divided by change
in a certain period delta T as a matter
of fact and this is - why it is -
because the concentration as the
concentration decreases the time
increases right so those two changes are
opposite when you have those two changes
are opposite nominator and denominator
this sign is negative that's what it
shows actually now here again you see
that is the rate we can call that equals
to the rate of this reaction rate of
this reaction now Delta means the change
in so when we have Delta that means the
molar concentration molar concentration
and Delta molar concentration means the
change of molar concentration of the
reactant or maybe product we just follow
reactant either reactant or product per
unit time per unit time so T is the time
types of rate measured now average rate
that means if you measure the
concentration of reactant for example at
a given time and then the concentration
of the reactant in another time and take
the difference between the concentration
and divided by the time elapsed the
delta T actually and that will give you
the average rate between those two
points right average rate or you can
have instantaneous rate that means the
rate of the reaction at a particular
time instantaneously that just just that
rate or you can have the initial rate
that means you just as you start the
reaction when T is equal to 0 there is
rate there as its ad that's called the
initial rates now let's look at these
again now this is the example following
the reaction rates again how we follow
the reaction rates we follow the
concentration change of reactants or
products it really doesn't matter both
will give us the rate or the speed of
the reaction now here is the reaction
butyl chloride actually hydrolyzes to
give butanol and hydrochloric acid right
this is our reactions so rate of the
reaction is measured using concentration
of the reactant or product over time now
how we measure it for example but we can
use spectroscopy right and look at the
absorption due to this or the absorption
to this if they have absorption actually
by simply measuring the absorption at
different times we can calculate the
concentration that means one way to do
that is that or we can simply take the
solutions and at given different times
determine the concentrations of
hydrochloric acid by titrate in that
solution with base right by titration
you can also determine the
concentrations of the acid so when you
determine the concentration is in fact
with various ways any of the reactant or
the product you can determine the rate
of that reaction usually the average
rate of the reaction now here is the
example we have simply we start the
reaction at zero time this is the
initial concentration point one zero
zero molar
butyl chloride and now after five fifty
seconds we measure the concentration
again it becomes 0.09 or five then what
we do to calculate the average rate
between zero and fifty seconds we take
this value and subtract this and we find
out the delta concentration that means
molar concentration change and we
divided by the time which is fifty
seconds we get this right now for this
one for example from here to there we
take the difference between these two
concentrations and divided by again 50
seconds this is 50 seconds here and we
get that you see again how we calculate
the concentrate of the reactions now
what we see here that the rate of the
reaction decreases as the reaction
proceeds to the product right here the
highest at the beginning this is what we
call initial rate actually we can say
that initial rate sort of initial rate
1.9 10 to minus 4 this one is 0.56
10 to the minus 4 that means about 4
times more than 3 times
decrease in the rate again now uh okay
then
when we plot the concentration versus
time here and we get this plot which
shows the concentration change of butyl
chloride with time right now from this
curve here we can simply show you what
we mean by the initial rate and then
instantaneous rate and the average rate
right now instantaneous rate means the
rate of the reaction at a given time at
a given time right now as you see here
if I have this slope like this curve
here like this and if I would like to
get the instantaneous rate at this time
right here that time T I just draw a
tangent line to this curve at that point
and the slope of this line will be equal
to the instantaneous rate of this
reaction at this point here again you
see as we go up here the instantaneous
rate will increase we go down the
instantaneous rate will decrease now the
initial rate is the instantaneous rate
at the beginning right here at 0 is
called the initial rate that means it is
a slope of the line which is tangent at
time T is equal to 0 that is initial
rate so we can calculate the average
rate in fact by between two T values as
I have shown you just take the
concentrations at two different T values
and the divided by the time elapsed
between that that will give us
the average rate but the important one
is the instantaneous rate that's very
important actually instantaneous rate
now uh how do we express the rate of a
chemical reaction we simply said that
the rate of a reaction chemical reaction
can be expressed in terms of reactant
concentration change or in terms of
product concentration change so if I
simply write that we actually gain c4h9
chloride gas that's not for the state
plus h2o and that's going to c4h9 OAH
plus HCL this is the alcohol and this is
the butyl chloride like this so in this
case if I simply write down the rate of
rate of change of butyl chloride it
would be again as follow the
concentration of butyl chloride change
at two different times divided by delta
T this is - again like this now how
about the rate in terms of the product
butyl butanol actually normal be - no I
can also write it down as follow the
concentration of c-4 c9o H no c4h9 or H
here and divided by delta T and again
this is also the rate of the chemical
reaction rate of the chemical reaction
but in terms of concentration change of
the product this is the concentration
change of the reactant in terms of
concentration
both are simply rate now this is -
always because as the concentration
decreases time increases this is
positive because the concentration
simply increases as the concentration
increases time also increases too so
these two are the same as a matter of
fact we can write down those than they
are equal right like this both are equal
why because from the equation here I can
see that this equation balanced chemical
equation tells me that when one mole of
butyl chloride consumed one mole of
butanol will form in the same time so
what does that mean that means that the
rate of consumption of the reactant will
be equal to the rate of the productions
of the product right product but
sometimes it is not that way
consider for example this reaction here
the decomposition of ozone to oxygen
like this so here I can let's write that
I can write two rates actually for this
reaction one can be the rate of
consumptions of ozone and that will be -
simply let me let me write it down here
rate
let's call that consumption of ozone and
this will be equal to - simply Delta
concentrations of ozone and delta T like
this this is the rate now how about the
rate in terms of concentration change of
oxygen or production of the oxygen and
let let's write it down as a game rate
all - that means that the rate with
respect to a change of the oxygen in the
molecule that will be equals to Delta
all -
divided by delta-t I like this this may
be at the same time actually now the
question is are these two rates are
equal no why no because this reaction
why looking at this balance equation
over here we see that when two ozone
molecules decompose it gives us three o2
oxygen molecule so the change molar
concentration change of ozone will not
be equal to the molar concentration
change of the oxygen which one is
greater the molar concentration change
of oxygen will always be larger than the
molar concentration change of the oh
three can we relate it in fact
mathematically sure this simply says
that two oxide ozone gives you three
oxygen molecule that means that the rate
of formation of oxygen is equal to 3
over 2 times the rate of formation rate
of consumptions of ozone right in this
reaction so if I simply write it down
here I will simply let's put it rate
boson three will not be equal to rate of
let's say all true like in that case
both the rate of the consumption and the
production reactant and a product is the
same because one to one ratio here is
different they're not the same can we
relate them sure we can relate them as
follow if we just take minus one over
two and then Delta all three from the
equation again we just divided by the
coefficients in balanced equation delta
T and this will be equals to 1 over 3
Delta concentration change of oxygen
divided by tau
t-this is it these two are equal right
there that equal ha how about can we
relate these two now you know we can
relate that rate owes on three all three
actually is equals to minus Delta owes
on three divided by delta T here and
that is equal to if I just consider this
right here take that over there right
and then this will be equal to two over
three Delta o two or delta T and that
means it will be equal to two over three
Delta o two delta T over here now what
is this equal to actually this is equals
to this and I can simply write it again
as followed two over three and now I
should say rate of change of oxygen rate
with respect to change of oxygen you see
again these two are related that is
equal to two over three of rate o 2 or
this one will be equal to 3 over 2 this
is 2 over 3 this will be 3 over 2 and so
on is this clear so usually in fact if
you have a chemical reactions and the
reactants and the products has different
coefficients like over here in balanced
equation we usually write down the rate
in fact expression in this form we just
write down the change of the
concentrations of the species and
divided by the coefficients in the
balanced chemical equation in
stoichiometric balance chemical
equations actually
right so the stoichiometry determines
how the rate of consumptions and the
rate of productions are related to each
other in a chemical reactions okay now
how about the concentration in fact
determining the concentration effect on
the rate here what we simply run
experiments and
in these experiments we change the
concentrations of one reactant and keep
the concentration of the other reactants
constant two different experiments and
measure the rate of the reaction and
find out how the concentration change of
one reactant affects the rate for
example when you double the
concentration of one reactant if the
rate of the reaction doubles that means
that it is directly proportional to the
concentrations right now but sometimes
when you double the concentrations of
one reactant keeping the concentrations
of the other reactant constant then the
rate actually quadruples what does that
means that means that the rate of the
reaction is proportional to the square
of the concentrations of that reactant
right so this is what is explained here
let's look at what it says we keep every
concentration constant except one
reactant and see that what happens to
the rate then we change the different
reactant we do this until we have show
how each reactant has affected the rate
let's look at the example here here is
the example for example if you consider
this reaction between ammonium cation in
Acuras solutions with the nitrite in
aqueous solutions to get the nitrogen
and to water and from this data here
actually these are the experiment this
is the first experiment second
experiment and third experiment you see
again in the first experiment the
concentration is off the ammonium cation
is 0.01 and the concentration is all
point of zero in the second experiment
again let's see we we keep the
concentrations of no.3 minus nitride ion
same double the concentrations of simply
ammonium cation and we see that the rate
is doubled right this is the initial
rate again the a rate is double what
does that means that means that the rate
is proportional to the concentration of
this and we do the same things for there
we also find out that the rate is also
proportional to the concentrations of
that then we write down this equation
rate is equal to K times the
concentrations of ammonium cation and
the concentrations of nitride these are
actually the reactants over here and
this equation is called the rate law of
the reaction rate law it's very very
important called rate law and it chimney
simply tells you how the concentrations
of the reactants affect the rate of the
reaction rate of the reaction now how
about k k is called the rate constant
rate constant and as long as the
temperature is the same as long as we
have the same chemical reaction rate
constant will always be the same rate
constant will always be the same now
let's look at over here again now the
exponents of the reactant in the rate
law equations remember those
concentrations of ammonium cation and
concentrations of nitrate ion the
exponents of those the order is called
the order of the reaction with respect
to that species that reactant now let's
go here again now the exponent here for
ammonium cation is one concentration to
the one and this is concentration to the
one two that means that the rate is
proportional to the concentrations right
and and that we say that the order of
this reaction with respect to the
ammonium cation is 1 because the
exponent is 1 now the order of the
reaction with respect to the
concentrations of nitrite ion is also 1
right now the overall order of the
reaction is obtained by adding the order
of each reactant here in this case 1
plus 1/2 that means that this reaction
we say is a second-order reaction if
that order is total sum of the orders
exponents of the concentrations is 1
means it is first-order if it is three
then that means it is third order and so
on so that gives you the order of the
reaction sometimes the concentration of
the reactants do not change the rate
usually heterogeneous reactions actually
and that case we call it zero order
reaction zero order reaction right
because if these are simply zero zero
here and that means rate will be equal
to K that's what the zero order reaction
is means that the rate is constant
always the same so the reaction is
second order when you have plot one plus
one is equal to two we just add up all
of the reactant orders to get the
reaction order what is K as we said the
K is rate constant and it is temperature
dependent only as long as the
temperature is the same it is always the
same now let's take each order reaction
separately and examine those first order
reaction so some reactions it says
depends only on the reactants to the
first power and these are called the
first order reaction a simple example is
the rate law for the first order
reaction rate will be equal to K times
concentrations of a for example if a
goes over here and rate is equal to this
K times a that means this is the first
order reaction so this one is said the
rate law for the first order reaction
now remember rate in this case is always
equals to minus molar concentration
change Delta a divided by delta T right
we don't write it there but it's
remember that now relate in time to the
concentration in a first order reaction
this is the important again this simply
allows us what is the concentration of a
reactant or product at a particular time
after we start the reaction let's look
at how it simply goes in the first order
reaction this is the first order
reactions and remember I said the rate
equal to minus Delta e over delta T and
then so the I can rearrange this and
obtain ka is equal to this here and
rearrange it and obtain this now this is
let's think about this expression there
now the form is actually this Delta a
over Delta no just a right and equals to
minus K times delta T now it was a point
again we can also write it in this form
d a divided by a concentration equals to
minus K times DT what is the difference
here between these two expressions
I replaced the Delta with D what does
that means mathematically that means D
is a differential amount very very small
change this represents very small change
in the concentration but that represents
some measurable change as we have seen
right so now when you have it in this
form that means you can integrate it in
this case from initial concentration a
zero to final concentration a and here
what will be the limit T is equal to
zero to time T and when you integrate
that we get this here right here we get
that right from the calculus if you look
at the integrations of this you have
logarithm natural logarithm of a divided
by a0 minus KT now this equation is
called the integrated rate law for the
first order reaction for the first order
reaction right
so again
what does that means that means if I
know for example the initial
concentration and then I can always
calculate what will be if I know the K
also I can always calculate what will be
the concentration after time T five
minutes later seven minutes later or ten
minutes later
right or vice versa in fact if I know
the concentration I can calculate what
time elapsed from the beginning of the
reactions and so on so this is a very
important reaction as a matter of fact
now that is rearranged form again in
this form we just take the remember the
natural logarithm of this is equal to
the natural logarithm of a
concentrations of a minus natural
logarithm of concentrations of a zero
and when you pass it on this side this
becomes plus over here so I have the
final equations
Ln a simply equals to minus KT plus Ln a
initial concentrations now this equation
actually here the integrated rate law of
the first-order reaction looks like the
equation for a straight line right
equation for a straight line so Y
actually represents the concentration
logarithm of the concentration and X
represents the T M represents the minus
K actually and B is constant which is Ln
a0 now what does that mean that means if
I have the concentrations of the
reactant a versus time and if I make a
plot I should get a straight line right
I should get a straight line and that is
what really happens versus time and
there it is
here I have ISO nitrile yes reaction
okay this is actually the pressure of
the acid or nitrile this is actually ISO
nitrile and this is the
trial now the difference here again you
see in one case nitrogen bonded to this
carbon in the other case carbon is
bonded to this carbon right that is the
isomerization reaction is called
isomerization isomerization this is a
Seto nitrile or nitrile in general and
this one is ISO nitrile iso nitrile and
this reaction is first-order reaction
again as we see when we plot the
pressure of the I saw nitrile versus
time we get this that's what we should
have and when we simply not pressure and
tour yes this is the if when we plot the
logarithm of this logarithm of pressure
versus time and we get a straight line
what does that mean that means that this
is a first-order reactions again you see
if I have a reaction and if I have a
data rate data for that reaction as
concentration versus time data now if I
plot the logarithm of concentration
versus time if I get a straight line
that means that the reaction is
first-order reaction if I don't get a
straight line that means the reaction is
not a first-order reaction so again you
see I use that integrate low for the
first-order reaction to check whether
the reaction is first-order or others
right others in this case it is
first-order reaction now remember here
we use the pressure of the iso nitrile
and instead of the concentration it
would be exactly the same because
remember PV is equal to NRT ideal gas
equations and from here if I simply
divide both sides by V I can have this V
over N n is the number of moles times RT
what is n over V is the number of moles
per liter and this is actually molar
concentration right
molar concentration so this is I can put
it again here molar concentration of the
reactants times RT so if you simply
replace a in that equation integrated
rate law equations with P over RT and
this put it in the first order
integrated rate law equations you will
see that it wouldn't make any difference
you can use the pressure change or you
can use the molar concentration change
to make these plots again and they will
give you exactly the same results
exactly the same results
okay now once I have the rate data that
means concentration versus time data I
can all I can check whether the reaction
is first-order or not as I as we have
shown but once we have that graph we can
also calculate the rate constant of the
reaction right rate constant of reaction
so this is what it simply says remember
that the integrated rate law is equal to
this the plot will give a line and its
slope will be equal to minus K right
there remember Y is equal to MX plus B
that straight line equation in that case
the slope is equal to M there in this
case M is represented by minus K so the
slope of the let's look at that again
here the slope of this line gives me
directly the rate constant of that
reaction you see how we can determine
the rate constant of a reaction 2 now
half-life is another term that we use in
chemical reaction and definitions of the
half-life as from the name very simple
the amount of time that it takes for 1/2
of a reactant to be used up in a
chemical reaction that means if you
start with 1 molar concentrations of the
reactant the time required to decrease
that concentration to 0.5 1/2 molar is
the half time right half time so that is
the definition again for the first order
reaction we can actually calculate the
half-life in terms of rate constant and
the concentration if they're using this
integrated rate law this is our
integrated rate law now what we mean we
want this to be half of that so we
replace the a here with half of the
initial concentration and replace that T
with 1/2 the time there will be
half-life and if you work it out you can
find out that the
half life of the first-order reaction
will be equal to logarithm 2 divided by
K now logarithm to this is a natural
logarithm actually off to is 0.693
divided by K so what does that means
that means that the half-lives of a
first-order chemical reaction will be
independent of the concentrations it
will only be dependent rate constant
that's all it is
so it will be all the same for example
as we see over here we started with 150
units of pressure nanum I guess this is
tour and the time required to get it to
half 75 is the half-life 1 half-life now
from this point on to get it to the half
of 75 which is thirty seven point five
is another half-life right this is
another half-life that's another
half-life all of these half-lives are
the same for the first order reaction as
long as the temperature is constant and
as long as the temperature is constant
now let's look at the second order
reaction in a second-order reaction the
rate law is equals to K times a to the
square this is a gain same reactant we
have one reactant but it's a
second-order it's possible now let's
look at yes this is okay solving the
second-order reaction for a to the
products let's continue rate is equal to
that and rate is equal to minus Delta e
over T rearrange that and rearrange it
now in this form here if I take the
integral make these as differential of a
divided by a to the squared minus K T DT
differential of T take the integral as I
did here from a zero to a and here from
zero to T and I would get the integrated
rate law
of the second-order equation so we get
this one over a is equal to 1 over a 0
plus KT so you see again in this case
the linear relationship is different
than the first-order reaction first
order reactions how if I simply plot 1
over concentration of a reactant versus
T then I will get a straight line right
and in this straight line again in this
case the straight line will be like this
and this is constant from the slope I
can get the K values just like in the
first-order reaction here is the example
and the reaction is this the
compositions of no.2 to n Oh nitrogen
monoxide and the oxygen when we plot the
logarithm of the concentrations of this
versus time you see we don't get a
straight line why because it is not a
first-order right at least it tells us
that it's not a first-order but if I
simply plot 1 over concentrations of
no.2 versus time as in given in the
integrated rate law I get a straight
line here like this now this straight
line tells me that the reaction is
second order and the slope of this
straight line will give me the rate
constant of the reaction actually the
rate constant of the reactions now be
half-life of the second-order reactions
by using exactly the same approach we
did for the first order reaction is
calculated as 1 over K times constant
initial concentrations of a so you see
again the half-life of the second-order
reaction changes as the reaction goes on
and it is dependent on the initial
concentration of the reactant initial
concentrations of the reactant and we
can simply show that second car depends
quantity for the second-order reaction
so half-life is a concentration
dependent quantity for the second-order
reaction this is the concentration
dependent values again okay I guess we
will stop here any questions this is
very simple actually I'm sure you have
an idea from high school