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Gases KT.pdf, Slides of Molecular Chemistry

Postulates of Kinetic Molecular Theory. 1. A gas is made up of vast number of particles, and these particles are in constant random motion.

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11.11.2013
1
Postulates of Kinetic Molecular Theory
1. A gas is made up of vast number of particles, and these
particles are in constant random motion
İmage source: http://www.docstoc.com/docs/113002286/Kinetic-Molecular-Theory
2. Particles in a gas are infinitely small, they occupy no
volume
Postulates of Kinetic Molecular Theory
Volumeless - Most of the volume occupied by a gas is empty space
Accounts for lower density compared to solid and liquids.
Accounts for compressibility of gases.
Postulates of Kinetic Molecular Theory
3. Particles in a gas move in straight lines exc ept when they
collide with other molecules or with the walls of the
container. All collisions are elastic, so that the total
kinetic energy of the particles is conserved
İmage source: http://en.wikipedia.org/wiki/Kinetic_theory
Postulates of Kinetic Molecular Theory
4. Particles in a gas interact with each ot her only when
collisions occur.
Assumes no force of attraction/repulsin between gas particles
Postulates of Kinetic Molecular Theory
5. The average kinetic energy of the particles in a gas is
proportional to the absolute temperature of the gas and
does not depend on the identity of the gas
The average Kinetic Energy of gas particles depends on
Temperature of the gas:
TKEav
Maxwell-Boltzmann Speed Distributions
pf2

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Postulates of Kinetic Molecular Theory

1. A gas is made up of vast number of particles, and these

particles are in constant random motion

İmage source: http://www.docstoc.com/docs/113002286/Kinetic-Molecular-Theory

2. Particles in a gas are infinitely small, they occupy no

volume

Postulates of Kinetic Molecular Theory

Volumeless - Most of the volume occupied by a gas is empty space

  • Accounts for lower density compared to solid and liquids.
  • Accounts for compressibility of gases.

Postulates of Kinetic Molecular Theory

3. Particles in a gas move in straight lines except when they

collide with other molecules or with the walls of the

container. All collisions are elastic, so that the total

kinetic energy of the particles is conserved

İmage source: http://en.wikipedia.org/wiki/Kinetic_theory

Postulates of Kinetic Molecular Theory

4. Particles in a gas interact with each other only when

collisions occur.

  • Assumes no force of attraction/repulsin between gas particles

Postulates of Kinetic Molecular Theory

5. The average kinetic energy of the particles in a gas is

proportional to the absolute temperature of the gas and

does not depend on the identity of the gas

The average Kinetic Energy of gas particles depends on Temperature of the gas:

KE T

av

Maxwell-Boltzmann Speed Distributions

Deviations from Ideality - “Real” Gases

(a) At high pressure

(b)At low temperature

At high pressure

İmage source: http://wps.prenhall.com/wps/media/objects/3311/3391331/blb1009.html

At low temperature

van der Waals Equation

V nb nRT

V

an

P  

The magnitude of the deviations from ideal gas behavior can be

illustrated by comparing the results of calculations using the ideal gas equation and the van der Waals equation

Sumup exercise

a) Calculate the pressure for 1.00 mole of CO 2 at 0 oC in a container of 22.4 L

volume.

According to the ideal gas equation,

atm L

K

molK

Latm mol

V

nRT P 1. 00

  1. 4

Substituting what we know about CO 2 into the van der Waals equation,

K atm molK

Latm mol

mol

L

L mol L

mol mol

Latm

P

2

2 2

2

Percentage correction : 0.5%

b) Let's now repeat this calculation, assuming that the gas is compressed so that it fills a container that has a volume of only 0.200 liters.

According to the ideal gas equation, the pressure

The van der Waals equation, however, predicts that the pressure

Percentage correction:

atm L

K

molK

Latm mol

V

nRT P 112

  1. 200

K atm molK

Latm mol

mol

L

L mol L

mol mol

Latm

P

2

2 2

2

A conceptual question

 van der Waals equation provides a much better fit with the behavior of a “real” gas than the “ideal” gas equation, but with a cost! What do you think the cost is?

Answ. : Loss in generality!