Grafts et al. — 20 — Water in Plants 



(6) 



Internal Attractive Repulsive Thermal External 



Pressure Pressure Pressure Pressure Pressure 



a = the constant of the van der Waals equation, 

 V = the molal volume of the liquid, 

 c = a constant, and 



r^;; measures an intermolecular force of attraction between the molecules of a liquid. 



The difficulty often experienced in using such an equation is in evaluat- 

 ing the energy factor E from data on osmotic pressure, or thermal prop- 

 erties. HiLDEBRAND and others have determined values for the internal 

 pressure of liquids by measuring changes of pressure with temperature at 



constant volume / ^ \ and substituting these in equation (5). 

 \ ^T )v 



The Forces Between Atoms and Molecules: — The properties of 

 solutions depend ultimately upon the molecules and the electric forces 

 within and between them. The ideal gas law assumed that there was no 

 attraction between molecules but experiment proved that at low tempera- 

 tures and high pressures attractive forces existed. 



Deviations from ideality in solutions are even greater than in gases. 

 Much of the modern theory of solutions deals with analysis of the forces 

 between atoms and molecules. 



The electrons within a molecule are in constant motion. The average 

 positions can be so designated that the potential at a distance from a mole- 

 cule due to its charge can be calculated. If e represents charge and r dis- 

 tance, the field strength of a charge varies as -^ according to Coulomb's 

 law. This field strength is zero for a neutral atom. Atomic ions such as 

 Na"" or CI" will have fields varying as - . More complex neutral mole- 

 cules or ions in general have potentials varying as -7^ ' -p ' etc. The term -^ 



represents the field strength of a dipole. The term ^ represents a qua- 



drupole moment, important when the effective dipole is small. 



By similar treatment it is possible to calculate the force upon a second 

 particle located at a distance from the first. An ion in a field of the type 

 mentioned above experiences a force of translation ; a neutral molecule with 

 an electrical moment does so only if the field is non-uniform. Characteris- 

 tics of the above forces of interaction are summarized in Table 3, num- 

 bers 1, 2, and 5. 



Table 3. — Characteristics of molecular interaction 

 (front Bateman, in Hober, 1945) : — 



Type Attractive force 



number Interacting particles proportional to 



1 Ion — Ion e, e', • r"^ 



2 Ion — Permanent dipole =p u' e, • r"^ 



3a Permanent dipoles coaxial u u' • r"* 



3b Permanent dipoles at right angles o 



4 Ion — Induced dipole a ei^ • r"^ 



5 Permanent dipole — Induced dipole a u^ • r"''^ 



6 Transient dipole — Transient induced dipole a^ • r"^ 



Ci, e'l denote ionic charge. a denotes polarizability. 



u, u' denote dipole moment. r denotes distance between centers. 



