# 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.

how can chip be made from sand
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Got questions? Join the online conversation and get instant answers!

#### Get Jobilize Job Search Mobile App in your pocket Now! By Megan Earhart By John Gabrieli By Tony Pizur By OpenStax By JavaChamp Team By OpenStax By Angelica Lito By By OpenStax By Janet Forrester