Kinetic Theory of Gasesand Non-Ideal Gases

Kinetic Theory of GasesAn Attempt to Explain Why the Gas Laws Work

Origin of the postulates of the Kinetic Theory of Gases

Origin of postulates part 2

Molecular Motion of Gases

• Far apart

• Free from one another

• Randomly moving

mean free path: average distance traveled between collisions

typically ~ 10-5 cm molecular size ~ 10-8 cm

diffusion: irregular motion of molecules

Velocity of gas molecules and Mean free path

Rotating disk method of measuring velocity distribution

Maxwell-Boltzmann distribution of molecular speeds

same gas (N2) at different temperatures

Maxwell-Boltzmann distribution of molecular speeds different gases at same temperature

Graham’s Law of EffusionEffusion is the leaking of a gas through a small hole.

A Hydrogen fountainillustrating the highdiffusion rate of H2 gas.

Diffusion is related but not identical to effusion.

The collection of a gas over water using a pneumatic trough. This method should not be used for gases that dissolve in water (then use Hg like Priestley).

Dalton’s Law of Partial Pressures

Representative partial pressures (in torr)in inhaled and exhaled air.

In the respiration process, we use O2 and emit CO2as well as humidifying the air that passes through our lungs.

A corollary of Dalton’s Lawis Ptotal = XA P

= mole fraction of gas A times the partial pressure of gas

A

Gay-Lussac’s Law of Combining Volumes

Avogadro’s Hypothesis

Non-Ideal GasesReal gases condense to a liquid.

An ideal gas cannot.

A British term for what we callUHF, Ultra High Frequency

View

Modernview

Air Liquefier

Dewar flask (or thermos bottle)

The Compressibility Factor, PV/nRT

Real Gases• Deviation from “Ideal” Gas Law

PV = nRT for an ideal gas at STP, 1 mole = 22.414 L

Experimental Data 1.0000 mole of gas

Gas Volume (L) Deviation from Ideality

H2 22.433 +0.085 %He 22.434 +0.089 %

N2 22.404 - 0.045 %

O2 22.397 - 0.076 %

CO2 22.260 - 0.687 %

NH3 22.079 - 1.495 %

Properties of Real Gases

Properties of Real Gases

Decrease due toIntermolecularAttractive Forces

Increase due toMolecular Volumesignificant

The destructive effectof higher temperatures

Van der Waals’ equationwhich corrects for the non-ideal properties of gases

Correcting for Deviations from Ideal Gases

• for ideal gas: PV = nRT (Ideal gas law)

• for “real” gas:

(Preal + a n2 )(Vreal – nb) = n RT

V2

attractive forcecorrection

molecularvolume

correction

Van der Waals’Equation

The a and b factors in Van der Waals’ equation

Table continued

Two calculations

Solution of the Van der Waals equation to find the Critical Temperature and Critical Pressure

Liquid NitrogenAir that is so cold that it becomes a liquid (probably the coolest stuff you will ever see)

Liquid NitrogenIce Cream