Week 02 - Molecular Description of Gases (Kinetic molecular theory of gases)

Chapter 2 - The Molecular description of Gases

2.1 Introduction

The molecular-kinetic description of matter recognizes that the constituent atoms or molecules of a substance are in ceaseless motion, with a kinetic energy that increases with increase of temperature. The cohesive intermolecular forces that hold molecules close together in the condensed state are opposed by this thermal agitation. In the solid state of a substance, its molecules vibrate about average positions of a fixed array, which is ordered if the material is crystalline, disordered if it is not.

At higher temperatures, in the liquid state rigidity is lost and molecules move more freely but are still held together in close proximity by cohesive forces. Thus, volume changes when a solid melts are very small.

However, at the boiling temperature of a liquid, the intermolecular bonds are broken and the energy of the gas becomes kinetic energy of free translation of its molecules, now occupying a much greater space than they did as a liquid. Thus the average distance of a molecule from its neighbors in the gaseous state at atmospheric pressure is about 10 times the molecular diameter.

Freed from the bonding of the condensed state, the energy of a simple Monatomic gas is purely kinetic energy of translation, and its molecules travel with speeds of typically several hundreds of meters per second. Diatomic molecules have similar speeds but rotational energies in addition.

2.2 The Maxwell–Boltzmann Distribution of Molecular Speeds

The density of molecules in gases is such that frequent collisions are inevitable, and so they travel in straight “free paths” between the successive collisions that cause their directions and speeds to be changed. Because of the enormous number of molecules involved, we must expect that there will be a range of molecular speeds and of the free paths traveled between collisions.

Most probable speed (Vα):

The speed with which maximum number of molecules move

                                                               

Mean or Average speed:                      

                                                               

Mean Square Speed:

                                                   

 

                             Fig. Maxwell - Boltzmann distribution of Moecular speeds

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