# 0.5 Reaction rates  (Page 8/10)

 Page 8 / 10

Although we will not show it here, kinetic molecular theory shows that the fraction of molecules with energygreater than ${E}_{a}$ at temperature $T$ is proportional to $e^{-\left(\frac{{E}_{a}}{RT}\right)}$ . This means that the reaction rate and therefore also the rateconstant must be proportional to $e^{-\left(\frac{{E}_{a}}{RT}\right)}$ . Therefore we can write

$k(T)=Ae^{-\left(\frac{{E}_{a}}{RT}\right)}$
where $A$ is a proportionality constant. If we take the logarithm of both sides of , we find that
$\ln k(T)=-\left(\frac{{E}_{a}}{RT}\right)+\ln A$
This equation matches the experimentallyobserved . We recall that a graph of $\ln k$ versus $\frac{1}{T}$ is observed to be linear. Now we can see that the slope of that graph is equal to $-\left(\frac{{E}_{a}}{R}\right)$ .

As a final note on , the constant $A$ must have some physical significant. We have accounted for the probability ofcollision between two molecules and we have accounted for the energetic requirement for a successful reactive collision. We havenot accounted for the probability that a collision will have the appropriate orientation of reactant molecules during the collision.Moreover, not every collision which occurs with proper orientation and sufficient energy will actually result in a reaction. There areother random factors relating to the internal structure of each molecule at the instant of collision. The factor $A$ takes account for all of these factors, and is essentially the probability that a collision with sufficient energy for reactionwill indeed lead to reaction. $A$ is commonly called the frequency factor .

## Observation 4: rate laws for more complicated reaction processes

Our collision model in the previous section accounts for the concentration and temperature dependence of thereaction rate, as expressed by the rate law. The concentration dependence arises from calculating the probability of the reactantmolecules being in the same vicinity at the same instant. Therefore, we should be able to predict the rate law for anyreaction by simply multiplying together the concentrations of all reactant molecules in the balanced stoichiometric equation. Theorder of the reaction should therefore be simply related to the stoichiometric coefficients in the reaction. However, shows that this is incorrect for many reactions.

Consider for example the apparently simple reaction

$2I\mathrm{Cl}\left(g\right)+{H}_{2}\left(g\right)\to 2H\mathrm{Cl}\left(g\right)+{I}_{2}\left(g\right)$
Based on the collision model, we would assume that the reaction occurs by $2I\mathrm{Cl}$ molecules colliding with a single ${H}_{2}$ molecule. The probability for such a collision should be proportional to $\left[I\mathrm{Cl}\right]^{2}\left[{H}_{2}\right]$ . However, experimentally we observe (see ) that the rate law for this reaction is
$\mathrm{Rate}=k\left[I\mathrm{Cl}\right]\left[{H}_{2}\right]$
As a second example, consider the reaction
$N{O}_{2}\left(g\right)+CO\left(g\right)\to NO\left(g\right)+C{O}_{2}\left(g\right)$
It would seem reasonable to assume that this reaction occurs as a single collision in which an oxygen atom isexchanged between the two molecules. However, the experimentally observed rate law for this reaction is
$\mathrm{Rate}=k\left[N{O}_{2}\right]^{2}$
In this case, the $\left[CO\right]$ concentration does not affect the rate of the reaction at all, and the $\left[N{O}_{2}\right]$ concentration is squared. These examples demonstrate that the rate law for a reaction cannot be predicted from the stoichiometriccoefficients and therefore that the collision model does not account for the rate of the reaction. There must be somethingseriously incomplete with the collision model.

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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