Concise Physical Chemistry

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

THE POTENTIAL ENERGY SURFACE 351

H + H-H H-H + H

Activated Complex

a

FIGURE 21.3 Activation of the symmetrical reaction H+H H→H H+H. The height

of the barrier is about 40 kJ mol−^1.

If a slice is taken at the horizontal dotted line at the top of Fig. 21.2, its shape is

that of a typical two-center molecular potential energy curve with a minimum like

those in Fig. 20.2. This is because the distancerHH′ is large and the potential energy

as a function ofrHHis essentially that of an unperturbed H 2 molecule. The same

argument holds for a slice taken at the vertical dotted line to the right of the figure;

rHHis large and the system is an H 2 molecule with the H atom so far away as to have

no effect on it.

The curved line connecting the reactant H H potential energy basin with the prod-

uct H H potential energy basin is the path a system must follow if the transformation

from one H H to the other is to take place. This is thereaction coordinate, leading

from reactants, over anactivation barrierto products. During the reaction, as the sys-

tem moves along the reaction coordinate, there is a rise in potential energy to a saddle

point which is a kind of “mountain pass” between the two potential energy basins.

At the top of the pass,rHH′ =rHHand the system exists as the activated complex. The

potential energy as a function of the reaction coordinate for the system appears as

shown in Fig. 21.3.

The potential energy of products is equal to the potential energy of the reactants

in the case of H+H H→H H+H, but they are different in the general case

of a more complicated reaction. Figure 21.4 shows the activation energy barrier

that a more complicated system must surmount if it is to go from the reactant

Activated Complex

Activation

Enthalpy Reactants

Enthalpy of

Reaction Products

H

rH

aH

FIGURE 21.4 The enthalpy of activation of an exothermic reaction.