Diatomic Hypothesis and Calculation of Condensation Force

Author: Zeljko Prebeg

Lermanova 12a, 10000 Zagreb, Croatia

zeljko.prebeg@zg.tel.hr

Abstract: The concept of a molecular pair as the base of organization for matter successfully describes the polymerization phenomena.  For this reason, a diatomic hypothesis is hereto postulated.  According to the diatomic hypothesis, matter is organized in pairs.  The degrees of freedom for particle movement within the solid, liquid, and gas phase are examined.  The application of the energy conservation law for a two-particle system in a liquid-gas phase transition shows that the condensation force exists. This force is universal and dependent upon the volume of interaction.

Keywords:  diatomic hypothesis, condensation force, phase transition.

Introduction

It has been shown that molecular pair is the base for the organization of ethylene under high pressure.¹ This concept for the organization of the matter successfully describes the polymerization  phenomena (initiation, chain growth, termination, heat of polymerization, stability of radicals, etc.).  In this paper the concept of the molecular pair will be further discussed.

Atomic hypothesis exists.  According to atomic hypothesis, matter has atomic organization. The main triumph of this hypothesis is the kinetic theory of gases, but it is only valid for a system of non-interactive particles.  Characteristic of particle interaction is intermolecular force.  This force causes attraction at long, and repulsion at short intermolecular distances.  The intensity of that intermolecular force depends of intermolecular distance and nature of the particles.  In this paper the intermolecular force will be examined on the basis of the diatomic hypothesis.  The condensation force will be calculated.

Diatomic Hypothesis

Basic difference between solid, liquid, and gas phase is the degrees of freedom for translation particle movement.  Particles in the solid phase do not have the degrees of freedom for translation movement.  Each direction of motion is occupied by intermolecular force (Figure 1a).

Particles in liquid phase show two-dimensional movement (Figure 1b), but they are still under the influence of intermolecular force.  Finally, particles in gas phase show movement in all directions of space (Figure 1c).  According to the kinetic theory of gases, a particle in motion along one coordinate of space has an energy of kT/2.  In three-dimension space, the total kinetic energy of free particle is 3kT/2.  Particles in the liquid phase have two dimensions free for movement.  Its kinetic energy is kT.  Particles in the solid phase do not have degrees of freedom for movement, its kinetic energy is zero.  Particles in solid phase have only potential energy.  During the solid-liquid phase transformation, heat is absorbed.  While potential energy of particles in liquid and solid is the same, the heat of phase transformation is spent on particle movement.  According to this DE_(SàL) = kT_(SàL).

Figure 2 shows the heat of fusion as a function of the melting temperature of elements of the periodic system.²  The slope of a straight line (1,7E-23 J/K) is a good approximation of the Boltzman's constant.

Can we apply this analysis on the liquid-gas phase transformation?  For a better understanding of the liquid-gas phase transformation we shall now postulate diatomic hypothesis, "Matter is organized in pairs."

Figure 3 shows the energy spent for overcoming the attraction force and the increasing of particle movement.  During the liquid-gas phase transition, the particle changes two-dimensional movement  to three-dimensional movement, together with expansion into three dimensions of space:

                (1)

where

DE_L®G (J) is the heat of vaporization

F (N) is the intermolecular force

x_G (m) is the intermolecular distance at gas phase

x_L (m) is the intermolecular distance at liquid phase  

k = 1.38E-23 JK^-1

T _L®G (K) boiling temperature

Intermolecular distance at gas phase is much higher then intermolecular distance in liquid phase. (x_G>>x_L) In that case,

                (2)

Intermolecular distance forms sphere of interaction V

                 (3)

This implicates,

               (4)

According to equation for ideal gases,

                 (5)

This implicates,

          (6)

where P_atm = 101325 Pa

Finally, intermolecular force can be calculated by equation,

                        (7)

For calculation of intermolecular force (7) and intermolecular distance (6), data (heat of vaporization and boiling temperature) for elements of the periodic system are used.²  Figure 4 shows intermolecular force as a function of intermolecular distance.

It is evident that a condensation force exists within matter.  This force is independent from the nature of matter. It depends upon the volume of interaction (V~x³).   Existence of the condensation force is supports the diatomic hypothesis.  It can be therefore concluded that matter is organized in pairs under the influence of a condensation force.

Literature:

1. Zeljko Prebeg, Journal of Theoretics, Vol.2,No.1(2000)

Acknowledgement:  I wish to thank my parents Joseph and Victoria.