Concise Physical Chemistry

c21 JWBS043-Rogers September 13, 2010 11:30 Printer Name: Yet to Come

350 PHOTOCHEMISTRY AND THE THEORY OF CHEMICAL REACTIONS

rHH. At some instant, the incoming H and the departing H must be equidistant from

the central hydrogen atom so that the three atoms form an energetic intermediate:

H+H−H=

⎡

⎣H

r′HH

︷︸︸︷

···H

rHH

︷︸︸︷

···H

⎤

⎦=H−H+H

Thebond-formingconfiguration is on the left and thebond-breakingconfiguration is

on the right of the central structure, which is theactivated complex.

21.7 THE POTENTIAL ENERGY SURFACE

In the study of molecular structure, we plotted the potential energy of the molecule as

a function of internuclear distance and found that it has a minimum at the equilibrium

bond length. Some of the qualities of this potential energy curve carry over to the

activated complex, but now the potential energy is a more complicated function of two

variablesr′HHandrHH. It requires a three-dimensional surface or a two-dimensional

contour map for its representation. Eyring has constructed such a surface represented

by the equivalent contour map in Fig. 21.2.

This contour map is drawn in the same way that a forest service map of Western

Montana would be drawn. Each contour corresponds to a constant potential energy

that would occupy the dimension out of the plane of the paper if the three-dimensional

representation were used. The hyperbola connecting the two arrows is the locus of

potential energy minima of the system as the reaction takes place. Contour 4 bounds

a potential energy plateau.

rHH

r'HH

V

1

2

3

4

FIGURE 21.2 Eyring potential energy plot for the reaction H+H H→H H+H.