# 0.1 The kinetic molecular theory  (Page 2/7)

 Page 2 / 7

## Observation 1: limitations of the validity of the ideal gas law

To design a systematic test for the validity of the Ideal Gas Law , we note that the value of $\frac{PV}{nRT}$ , calculated from the observed values of $P$ , $V$ , $n$ , and $T$ , should always be equal to 1, exactly. Deviation of $\frac{PV}{nRT}$ from 1 indicates a violation of the Ideal Gas Law . We thus measure the pressure for several gases under a variety of conditions by varying $n$ , $V$ , and $T$ , and we calculate the ratio $\frac{PV}{nRT}$ for these conditions.

Here , the value of this ratio is plotted for several gases as a function of the "particledensity" of the gas in moles, $\frac{n}{V}$ . To make the analysis of this plot more convenient, the particle density is given in termsof the particle density of an ideal gas at room temperature and atmospheric pressure ( i.e. the density of air), which is $0.04087\frac{\mathrm{mol}}{L}$ . In this figure , a particle density of 10 means that the particle density of the gas is 10 times the particle density of air at roomtemperature. The x-axis in the figure is thus unitless.

Note that $\frac{PV}{nRT}$ on the y-axis is also unitless and has value exactly 1 for an ideal gas. We observe inthe data in this figure that $\frac{PV}{nRT}$ is extremely close to 1 for particle densities which are close to that of normal air. Therefore, deviations fromthe Ideal Gas Law are not expected under "normal" conditions. This is not surprising, since Boyle's Law , Charles' Law , and the Law of Combining Volumes were all observed under normal conditions. This figure also shows that, as the particle density increases above the normalrange, the value of $\frac{PV}{nRT}$ starts to vary from 1, and the variation depends on the type of gas we are analyzing. However, even forparticle densities 10 times greater than that of air at atmospheric pressure, the Ideal Gas Law is accurate to a few percent.

Thus, to observe any significant deviations from $PV=nRT$ , we need to push the gas conditions to somewhat more extreme values. The results for such extreme conditions areshown here . Note that the densities considered are large numbers corresponding to very high pressures. Under theseconditions, we find substantial deviations from the Ideal Gas Law . In addition, we see that the pressure of the gas (and thus $\frac{PV}{nRT}$ ) does depend strongly on which type of gas we are examining.Finally, this figure shows that deviations from the Ideal Gas Law can generate pressures either greater than or less than that predictedby the Ideal Gas Law .

## Observation 2: density and compressibility of gas

For low densities for which the Ideal Gas Law is valid, the pressure of a gas is independent of the nature of the gas, and is therefore independent of the characteristics of theparticles of that gas. We can build on this observation by considering the significance of a low particle density. Even at thehigh particle densities considered in this figure , all gases have low density in comparison to the densities of liquids. To illustrate,we note that 1 gram of liquid water at its boiling point has a volume very close to 1 milliliter. In comparison, this same 1 gram of water, onceevaporated into steam, has a volume of over 1700 milliliters. How does this expansion by a factor of 1700 occur? It is not credible that theindividual water molecules suddenly increase in size by this factor. The only plausible conclusion is that the distance betweengas molecules has increased dramatically.

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
Preparation and Applications of Nanomaterial for Drug Delivery
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
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
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
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers! By Kevin Moquin By OpenStax By OpenStax By Brenna Fike By John Gabrieli By Janet Forrester By OpenStax By OpenStax By Richley Crapo By David Corey