Relating Bulk Concentration to Surface Coverage

How can we relate fractional surface coverage or surface concentration to bulk concentration, considering that the two have different units This could be done, if we recognize that concentration can also be represented by the average distance between atoms or molecules, and calculate for any given value of fractional surface coverage, 0, the value of the bulk concentration, cy, for which the average distance between the solute molecules is the same. 

We have seen previously (cf Section 4.1) that full coverage of hydrogen on Pt is Tmax = 1.3 X 10 atoms cm. This corresponds to 3.6 x 10 x 3.6 x 10 atom cm in a square array, leading to an average distance of 0.28 nm between atoms. The equivalent bulk concentration, for 0 = 1, is 

Note that we were careful not to use the equal sign here, because volume and surface concentrations have different units and therefore they cannot be equated with each other. The arrow is used instead to indicate that the two can be considered equivalent, if the criterion applied is that the average distance between the species on the surface and those in the bulk are the same. On the other hand, one should take into account that an atom in the bulk is surrounded spherically by all other atoms in the phase, while at the surface it enjoys only hemispherical symmetry. Thus, for a given average distance between molecules in the bulk and on the surface, the total Gibbs energy of interaction could be considered to be about twice as large in the bulk as on the surface. 

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