Physical Principles Slides 5

8/3/2019 Physical Principles Slides 5

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Principles of Physical

ChemistryProperties of Gases

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The Gas Phase

The gas phase differs

from the other phases in

that there are only weakinteractions between

particles.

Relatively simplemodels can be used to

describe the gas phase.


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Course Outline

Ideal & Real gases

Kinetic theory of gases

Calculating macroscopic properties from microscopic

properties.

Applications of Kinetic theory

Effusion, diffusion, thermal conductivity and viscosity.


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Characteristics of a Gas


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A collection of particles in constant,

rapid, random (Brownian) motion.

A gas fills any container it occupies,

consistent with the second law of

thermodynamics.

The effects of intermolecular forces

are generally very small, and may

often be ignored.


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p ?


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p T

p N


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p T

p N

p 1/V


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p T

p N

p 1/V


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Ideal Gas Assumptions

The molecules obey Newton's law of motion.

There are no attractive or repulsive interactionsbetween molecules.

The molecules undergo perfectly elastic collisions.

The volume occupied by the molecules is negligiblysmall in comparison to the size of the container.


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The physical state of a pure gas may be defined by

four physical properties

p -pressure

T - temperature

V - volume

n - amount of substance

If we know any three variables, we can use an

equation of state to determine the fourth.


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Pressure

Force exerted by the gas per unit area

SI units of Newtons per square metre (N m-2), more

commonly known as Pascals (Pa).1 Torr = 1 mmHg = 133.3 Pa

1 bar = 1000 mbar = 100 000 Pa

Force arises from collisions of the gas particles with

the surface at which the pressure is measured.


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Barometric Pressure


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Temperature

Temperature is a measure of the average kinetic energy of the

particles in a gas.

Temperature therefore reflects the velocity distribution of theparticles.

The velocity of a single particle is constantly changing due to

collisions. However, the total number of particles with a given velocity

is constant.

The distribution of molecular speeds in an ideal gas at temperature T is

given by the Maxwell-Boltzmann distribution.

Since temperature is a direct result of the motion of particles, it is only

a meaningful concept when describing matter.


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Maxwell-Boltzmann

Distribution

Depends on the ratio m/T.

Increasing the temperature broadens the

distribution and shifts the peak to higher

velocities.

Decreasing the mass of the particles has the

same effect as increasing the temperature .

This is the origin of the absolute

temperature scale.

Absolute zero is the temperature at which the

particles have minimal motion.


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Real Gases

Ideal gas assumptions:

1. There are no intermolecular forces between particles

2. The volume occupied by the particles is negligible

3. The only interactions between particles and with the

chamber walls are perfectly elastic collisions.

Compare this to a real gas:

Interact through a variety of intermolecular forces.

Have a finite size.

Undergo elastic, inelastic and reactive collisions.


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Real Gases

The ideal gas equation breaks down when molecular

size effects or intermolecular forces becomeimportant.

High P: Particles forced closer together and interact more

strongly.

Low T: Particle motion is slow, so forces have a long time to

act.


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The compression factor, Z

Quantifies the deviations of a real gas from ideal gas

behaviourProvides information on the dominant types of

intermolecular forces acting

Z = 1 No intermolecular forces, ideal gas behaviour

Z < 1 Attractive forces dominate, molar volume reduced

Z > 1 Repulsive forces dominate, molar volume increased

The behaviour of Z as a function of pressure (or

temperature) reflects the intermolecular potential.


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The Boyle Temperature

For an ideal gas, Z = 1 and dZ/dp =

0.

For a real gas, Z -> 1 at low pressure,

but dZ/dp does not necessarily tendtowards zero.

However for real gases, there is a

single temperature at which dZ/dp ->

0, and Z -> 1 as p -> 0.

This is the Boyle temperature. Herethe attractive and repulsive

interactions balance and the real gas

behaves ideally.


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Real gases may be treated by taking the ideal gas equation as

the first term in a series expansion.

This is called a virial expansion. B and C are virial coefficients.

The first virial coefficient, B, is equal to zero at the Boyle

temperature.

Equations of State for Real Gases


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Equations of State for Real Gases

An alternative is to use the van der Waals equation.

a and b are temperature independent constants called the

van der Waals coefficients, whose values depend on the

gas species.


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Physical Principles Slides 5