48 PHENOMENA, ATOMS, AND MOLECULES 



where a, the condensation coefficient, in the majority of cases is equal to 

 unity, but in any case can never exceed unity. The rate of evaporation v 

 is in general dependent on the temperature and on a, the surface concen- 

 tration. Of course it also depends on the nature of the solid surface on 

 which adsorption occurs. If the surface is strictly homogeneous, v may be 

 a function of o and T only for a given surface, but it may be possible that 

 different portions of the surface are capable of exerting different forces 

 on adatoms, so that v and o may not be uniform over the surface. 



In a stationary state when o is not changing with time, the general 

 condition that must be fulfilled is 



«" = >', ( 1 1 ) 



If we divide the rate of evaporation v by a, the number of atoms per 

 square cm., we obtain the average probability per second for the evapo- 

 ration of the individual atoms. The reciprocal of this, T, is thus the average 

 life of an adatom on the surface. Thus we have 



T—a/r. (i2) 



This time lag that exists between the condensation and the evaporation 

 of adatoms may thus be looked upon as the fundamental cause of the 

 adsorption of gases on solid surfaces. 



In general v should increase rapidly with temperature like the vapor 

 pressure of substances. Thus the logarithm of v should increase approxi- 

 mately linearly when plotted against the reciprocal of the absolute tempera- 

 ture, and the slope of this line is proportional to the heat of evaporation 

 and is a measure of the magnitude of the forces by which the adatoms 

 are held on the surface. Thus v should be approximately given by an 

 equation of the type 



I' ~ const, exp ( — A/kT) , (13) 



where A. is a measure of the energy required to remove an adatom from 

 the surface. The reason for the large variations of v for different sub- 

 stances is due mainly to variations of X rather than to differences (28) in 

 the constant factor in Eq. (13). This is indicated by such approximate 

 laws as Trouton's rule. 



The forces acting between atoms and molecules are normally of ex- 

 tremely short range (27) (29), so that the forces acting on an adatom, 

 which determine the magnitude of A, and therefore of v, depend mainly 

 upon the atoms with which any given adatom is in contact. When the gas 

 pressure is raised or the temperature is lowered so that increases to such 

 a point that there is no longer room for any additional molecules in the 

 first layer in contact with the solid, a still further increase in a would 



