SURFACE CHEMISTRY 51 



Therefore the number of incident atoms which go directly into the first 

 layer may be put equal to ao (1—0) l-i. The fate of the other incident 

 atoms, viz., those that first strike adsorbed atoms, will depend on 

 many factors, some of which we shall discuss later. A very simple, although 

 not very probable, assumption is that all these atoms reevaporate so fast 

 that they do not have opportunities to find positions in the first layer. On 

 these assumptions we find 



a^i = ofo(l — ©)/< . (i6) 



Substituting this and Eq. (15) into Eq. (11) and solving for 0, we 

 obtain the following simple adsorption isotherm, 



This equation has been found to apply with reasonable accuracy to a 

 suprisingly large number of cases of adsorption on plane surfaces. Con- 

 sidering the nature of the simplifying assumptions made in its derivation, 

 it should of course not be looked upon as a general equation for the adsorp- 

 tion isotherm. The cases where this equation is most likely to apply are 

 those in which the adsorption occurs only in elementary spaces which are 

 so far separated from one another that the adatoms in the separate spaces 

 do not exert appreciable forces on one another. This can justify the assump- 

 tion of Eq. (15). Also in this case the condensation may reasonably occur 

 according to Eq. (16), because if a given space is occupied, which has a 

 probability proportional to 0, the incident atom cannot merely slip into 

 an adjacent elementary space but must fall on to an area on which it is 

 held with so little force that it evaporates before it can move into any 

 vacant elementary space. These assumptions will give us an equation like 

 Eq. (17) except that the significance of and of the coefficient ao is some- 

 what modified. 



Recent experiments have shown that in the mechanism of condensation 

 mobility plays an important part (30) . Thus in general an incident molecule 

 striking a surface already covered may be assumed to move an appreciable 

 distance before finally settling into a position in the first layer. Certainly 

 if the surface is homogeneous so that all parts of it are available for adsorp- 

 tion, an incident molecule striking an isolated adsorbed molecule can hardlv 

 be regarded as being even temporarily in a second layer. Such an atom will 

 slip into a position in the first layer before having any occasion to rebound 

 or evaporate from the surface. An atom cannot be in a second layer even 

 temporarily unless it is supported by at least three or more often four atoms 

 in the underlying layer. Even if there is no mobility, the probability that 

 an incident atom could occupy a place in the second layer would be propor- 

 tional to 0°, where n is at least as great as 3 or 4. If the rate of evaporation 



