222 PHENOMENA, ATOMS, AND MOLECULES 



of gravity of the positive and negative particles coincide. From Debye's 

 point of view such molecules may correspond to quadrupoles, octopoles, 

 etc. For example, positive and negative charges arranged alternatively 

 at the corners of a square will give a quadrupole, at the corners of a cube 

 an octopole. In forming clear conceptions of the attractive forces between 

 molecules it is useful to consider the actual magnitude of the forces 

 involved. 



IONS 



The electric field at a distance r from a univalent ion having a charge e 

 is e/zr~, where 8 is the dielectric constant of the medium. The charge of 

 the electron, e, is equivalent to 1.43 X 10"'^ volt centimeter and thus the 

 electric field is 1.43 X 10" V^^^ volts per centimeter, and the electric poten- 

 tial corresponding to this force is 1.43 X 10' V^''- I^ we take for r the value 

 3 X 10"^ cm., which corresponds roughly to the distance between two 

 ions in contact, we find the electric field to be 1.6 X 10^ volts per centimeter 

 and the potential to be 4.8 volts. Taking for e the value 80, corresponding 

 to the dielectric constant of water, we would obtain values only one- 

 eightieth of those given. However, it is doubtful if the conception of 

 dielectric constant is entirely justified at distances as short as this for we 

 can hardly speak of two molecules in contact as being in a medium having 

 known electrical properties. At distances several times greater than the 

 molecular diameter the use of dielectric constant in this way is justified. 



The applications of the Debye-Hiickel theory to electrolytes prove that 

 the forces at these larger distances are of vital importance in an under- 

 standing of the properties of ions. According to the Coulomb law the force 

 between two ions varies inversely as the square of the distance. In electro- 

 lytic solutions the increased concentration of positive ions around negative 

 ions, and vice versa, causes the force between two given ions to decrease 

 with increasing distance more rapidly than according to the inverse square 

 law. 



POLAR MOLECULES 



At a distance r from a dipole molecule having an electric moment \i the 

 electric potential is \x cos d/r~, where Q is the angle between the radius 

 vector r and the axis of the dipole. It can thus be found that at a distance r 

 along the dipole axis the electric field is —2\x./r^, this force being in a direc- 

 tion of the polar axis. At a distance r in the equatorial plane of the dipole 

 the electric force is also in a direction parallel to the polar axis but has the 

 magnitude -|-[x/^-^. 



