chapter Ten 



FORCES NEAR THE SURFACES OF 



MOLECULES 



In the early development of the kinetic theory, during the last century, 

 it was usual to consider the molecules of gases as rigid spheres, which 

 exerted no forces on one another except at the instant of contact. In 

 this way it was possible to account quantitatively with fair -accuracy not 

 only for the effects of pressure and temperature on the volume, but also 

 for the viscosity, heat conductivity, and diffusion of gases, and other 

 phenomena involving the free paths of the molecules. 



By considering also attractive forces which varied with some power 

 of the distance between the centers of the molecules, van der Waals was 

 able to account for the main features of the transition from the gaseous to 

 the liquid state, and also explained in a satisfactory manner the departures 

 from the ideal gas laws which are shown by all gases at high pressures. 



As new properties of matter are brought into consideration, or as a 

 deeper understanding of them is needed, it is necessary to postulate addi- 

 tional properties of the molecules, and to know more accurately the nature 

 of the forces acting between them. For example, to deal with the properties 

 of electrolytes it is necessary to consider electric charges on the molecules 

 or ions. In 191 2 Debye showed that the electrical properties of many 

 dielectrics could be accounted for by assuming that the center of gravity 

 of the electrons in a molecule did not coincide with the center of gravity 

 of the positive charges of the nuclei. Thus the molecule possessed what 

 we call a dipole moment, which can be measured as the product of an 

 electric charge by the distance through which it is displaced. It is found, 

 for example, that a molecule of water possesses a dipole moment of 

 1.8 X 10"^^ electrostatic units. A moment of this magnitude could be pro- 

 duced by having an electron at a distance of 0.37 X 10"^ cm. from a 

 proton. Since there are 10 electrons in a water molecule, it is only necessary 

 that the center of gravity of these electrons shall lie at a distance of 

 0-037 X 10"^ cm. from the center of gravity of the three nuclei in the 

 molecule. Thus displacements of the electrons to distances minute com- 

 pared with the diameter of the molecule can account for even the largest 

 values of dipole moments that have been observed. 



218 



