# 0.1 The kinetic molecular theory  (Page 6/7)

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What do the deviations from ideality tell us about the gas particles? Starting with very low density andincreasing the density as in , we find that, for many gases,the value of $\frac{PV}{nRT}$ falls below 1. One way to state this result is that, for a given value of $V$ , $n$ , and $T$ , the pressure of the gas is less than it would have been for an ideal gas. This must be theresult of the interactions of the gas particles. In order for the pressure to be reduced, the force of the collisions of theparticles with the walls must be less than is predicted by our model of an ideal gas. Therefore, the effect of the interactions isto slow the particles as they approach the walls of the container. This means that an individual particle approaching a wall mustexperience a force acting to pull it back into the body of the gas. Hence, the gas particles must attract one another. Therefore, theeffect of increasing the density of the gas is that the gas particles are confined in closer proximity to one another. At thiscloser range, the attractions of individual particles become significant. It should not be surprising that these attractiveforces depend on what the particles are. We note in that deviation from the Ideal Gas Law is greater for ammonia than for nitrogen, and greater for nitrogen than for helium. Therefore,the attractive interactions of ammonia molecules are greater than those of nitrogen molecules, which are in turn greater than thoseof helium atoms. We analyze this conclusion is more detail below.

Continuing to increase the density of the gas, we find in that the value of $\frac{PV}{nRT}$ begins to rise, eventually exceeding 1 and continuing to increase. Under theseconditions, therefore, the pressure of the gas is greater than we would have expected from our model of non-interacting particles.What does this tell us? The gas particles are interacting in such a way as to increase the force of the collisions of the particleswith the walls. This requires that the gas particles repel one another. As we move to higher density, the particles are forcedinto closer and closer proximity. We can conclude that gas particles at very close range experience strong repulsive forcesaway from one another.

Our model of the behavior of gases can be summarized as follows: at low density, the gas particles aresufficiently far apart that there are no interactions between them. In this case, the pressure of the gas is independent of the natureof the gas and agrees with the Ideal Gas Law . At somewhat higher densities, the particles are closer together and the interactionforces between the particles are attractive. The pressure of the gas now depends on the strength of these interactions and is lowerthan the value predicted by the Ideal Gas Law . At still higher densities, the particles are excessively close together, resultingin repulsive interaction forces. The pressure of the gas under these conditions is higher than the value predicted by the Ideal Gas Law .

## Observation 3: boiling points of simple hydrides

The postulates of the Kinetic Molecular Theory provide us a way to understand the relationship between molecular properties and the physical properties of bulk amounts ofsubstance. As a distinct example of such an application, we now examine the boiling points of various compounds, focusing onhydrides of sixteen elements in the main group (Groups IV through VII). These are given here .

how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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