<< Chapter < Page Chapter >> Page >

Based on our observations and deductions, we take as the postulates of our model:

  • A gas consists of individual particles in constant and random motion.
  • The individual particles have negligible volume.
  • The individual particles do not attract or repel one another in any way.
  • The pressure of the gas is due entirely to the force of the collisions of the gas particles with the walls of thecontainer.

This model is the Kinetic Molecular Theory of Gases . We now look to see where this model leads.

Derivation of boyle's law from the kinetic molecular theory

To calculate the pressure generated by a gas of N particles contained in a volume V , we must calculate the force F generated per area A by collisions against the walls. To do so, we begin by determining the number of collisions of particles withthe walls. The number of collisions we observe depends on how long we wait. Let's measure the pressure for a period of time Δ t and calculate how many collisions occur in that time period. For a particle to collide with the wall within the time Δ t , it must start close enough to the wall to impact it in that period of time. If the particle is travelling with speed v , then the particle must be within a distance v Δ t of the wall to hit it. Also, if we are measuring the force exerted on the area A , the particle must hit that area to contribute to our pressure measurement.

For simplicity, we can view the situation pictorially here . We assume that the particles are moving perpendicularly to the walls. (This is clearly not true. However,very importantly, this assumption is only made to simplify the mathematics of our derivation. It is not necessary to make thisassumption, and the result is not affected by the assumption.) In order for a particle to hit the area A marked on the wall, it must lie within the cylinder shown, which is of length v Δ t and cross-sectional area A . The volume of this cylinder is A v Δ t , so the number of particles contained in the cylinder is × A v Δ t N V .

Collision of a particle with a wall within time δt

Not all of these particles collide with the wall during Δ t , though, since most of them are not traveling in the correct direction. There are six directions for aparticle to go, corresponding to plus or minus direction in x, y, or z. Therefore, on average, the fraction of particles moving inthe correct direction should be 1 6 , assuming as we have that the motions are all random. Therefore, the numberof particles which impact the wall in time Δ t is × A v Δ t N 6 V .

The force generated by these collisions is calculated from Newton’s equation, F m a , where a is the acceleration due to the collisions. Consider first a singleparticle moving directly perpendicular to a wall with velocity v as in . We note that, when the particle collides with the wall, the wall does not move, so the collision must generally conservethe energy of the particle. Then the particle’s velocity after the collision must be v , since it is now travelling in the opposite direction. Thus, the change in velocity of the particle inthis one collision is 2 v . Multiplying by the number of collisions in Δ t and dividing by the time Δ t , we find that the total acceleration (change in velocity per time) is 2 A N v 2 6 V , and the force imparted on the wall due collisions is found bymultiplying by the mass of the particles:

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, General chemistry ii. OpenStax CNX. Mar 25, 2005 Download for free at http://cnx.org/content/col10262/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'General chemistry ii' conversation and receive update notifications?