# 0.18 Reaction equilibrium in the gas phase  (Page 3/6)

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This reasoning reveals that the amounts of reactant and product present at equilibrium are determined by therates of the forward and reverse reactions. If the rate of the forward reaction ( e.g. decomposition ofN 2 O 4 ) is faster than the rate of the reverse reaction, then atequilibrium we have more product than reactant. If that difference in rates is very large, at equilibrium there will be much moreproduct than reactant. Of course, the converse of these conclusions is also true. It must also be the case that the rates of theseprocesses depends on, amongst other factors, the volume of the reaction flask, since the amounts of each gas present atequilibrium change when the volume is changed.

## Observation 2: equilibrium constants

It was noted above that the equilibriumpartial pressures of the gases in a reaction vary depending upon a variety of conditions. These include changes in the initial numbersof moles of reactants and products, changes in the volume of the reaction flask, and changes in the temperature. We now study thesevariations quantitatively.

Consider first the reaction here . Following on our previous study of this reaction, we inject an initial amount ofN 2 O 4 (g) into a 100L reaction flask at 298K. Now, however, we vary theinitial number of moles of N 2 O 4 (g) in the flask and measure the equilibrium pressures of both thereactant and product gases. The results of a number of such studies are given here .

Equilibrium partial pressures in decomposition reaction
Initial ${n}_{{\text{N}}_{2}{\text{O}}_{4}}$ ${P}_{{\text{N}}_{2}{\text{O}}_{4}}$ (atm) ${P}_{\text{N}{\text{O}}_{2}}$ (atm)
0.1 0.00764 0.033627
0.5 0.071011 0.102517
1 0.166136 0.156806
1.5 0.26735 0.198917
2 0.371791 0.234574
2.5 0.478315 0.266065
3 0.586327 0.294578
3.5 0.695472 0.320827
4 0.805517 0.345277
4.5 0.916297 0.368255
5 1.027695 0.389998

We might have expected that the amount of NO 2 produced at equilibrium would increase in direct proportion to increases in the amount ofN 2 O 4 we begin with. [link] shows that this is not the case. Note that when we increase the initial amountof N 2 O 4 by a factor of 10 from 0.5 moles to 5.0 moles, the pressure of NO 2 at equilibrium increases by a factor of less than 4.

The relationship between the pressures at equilibrium and the initial amount ofN 2 O 4 is perhaps more easily seen in a graph of the data in [link] , as shown in [link] . There are some interesting features here. Note that, when the initial amount ofN 2 O 4 is less than 1 mol, the equilibrium pressure of NO 2 is greater than that of N 2 O 4 . These relative pressures reverse as the initial amount increases,as the N 2 O 4 equilibrium pressure keeps track with the initial amount but the NO 2 pressure falls short. Clearly, the equilibrium pressure of NO 2 does not increase proportionally with the initial amount of N 2 O 4 . In fact, the increase is slower than proportionality, suggestingperhaps a square root relationship between the pressure of NO 2 and the initial amount of N 2 O 4 .

We test this in [link] by plotting ${P}_{\text{N}{\text{O}}_{2}}$ at equilibrium versus the square root of the initial number of moles ofN 2 O 4 . [link] makes it clear that this is not a simple proportional relationship, but it is closer. Note in [link] that the equilibrium pressure ${P}_{{\text{N}}_{2}{\text{O}}_{4}}$ increases close to proportionally with the initial amount of N 2 O 4 . This suggests plotting ${P}_{\text{N}{\text{O}}_{2}}$ versus the square root of ${P}_{{\text{N}}_{2}{\text{O}}_{4}}$ . This is done in [link] , where we discover that there is a very simple proportional relationshipbetween the variables plotted in this way. We have thus observed that

#### 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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