228 PHENOMENA, ATOMS, AND MOLECULES 



with chemical tradition, for the chemist has ahvays considered that chemical 

 action between molecules takes place between molecules in contact. 



The physicist, probably ever since the time of Newton, has been rather 

 inclined to consider forces which vary as some power of the distance, or 

 to deal with fields of force which extend throughout space. The remarkable 

 success of the physicist in the development of the atomic theory, and more 

 recently, in some of the applications to chemical phenomena, such as those 

 involved in the properties of electrolytes, seems to have made many 

 chemists and physicists believe that these methods would also provide the 

 solutions to more complicated chemical problems. 



It must be emphasized, however, that the physicist, in attempting to 

 calculate the manner in which dipole molecules or non-polar molecules will 

 interact in liquids, meets problems which are mathematically so complicated 

 that it is necessary to make simplifying assumptions. For example, the 

 potential energy of dipole or non-polar molecules with respect to one 

 another is expressed as an infinite series in which the successive terms 

 involve as factors i/r, i/r^, i/r^, etc. The coefficient of the first term for 

 the case of dipole molecules is o, the coefficient of the second term is then 

 calculated with great care and often with great difficulty ; and although the 

 coefficients of the third and subsequent terms are known not to be zero, 

 these terms are neglected because of the fact that they involve higher 

 powers of r. We have seen, however, that the forces which are primarily 

 important in liquids are those between molecules in contact, and that a 

 small increase in the distance causes the forces to become very small. For 

 example, with a force varying with i/r^, such as Debye finds with non- 

 polar molecules, the energy involved in the approach of two molecules 

 would fall to one-half value if the distance between the molecules were in- 

 creased 15 per cent. This change in energy has its effect in the exponent of 

 the Boltzmann equation, so that most of the actions of importance must 

 occur with only still smaller variations in the distance r. It is obvious, there- 

 fore, that even for the roughest kind of approximation one is not justified 

 in neglecting the term involving i/r^ in comparison with that which in- 

 volves i/r^. 



As another example of the kinds of approximation that are necessary 

 in treating mathematically the forces between dipole molecules, we have 

 Debye's treatment of the relations between dielectric constant and chemical 

 association (11). He considers the effect of dipoles on one another as the 

 concentration of the dipolar molecule increases in a non-polar solvent. 

 Assuming the molecules to be spheres, complicated equations are derived 

 allowing for the interactions. The result is that the dipole moment per 

 molecule increases with concentration because the molecules tend to line 

 up along a common axis. This is due to the fact that the force along the 



