Concise Physical Chemistry

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

THE EYRING THEORY OF REACTION RATES 349

21.5 ISODESMIC REACTIONS

Ab initioenthalpy calculations ofH^298 for hydrocarbons containing more than 2

or 3 carbon atoms are often converted to thermodynamic values by setting up an

isodesmicreaction in which an experimentalfH^298 is known for all participants

but one (Hehre et al., 1970). The single remaining unknownfH^298 is calculated

from the known experimental values by difference. ComputedfH^298 values for

individual molecules on the right and left of the equation may suffer considerable

error; but if the bond types are the same on both sides of the reaction, errors tend

to cancel because they arise from similar computational defects. Isodesmic reactions

are usually set up such that a relatively complicated molecule is compared to several

simple molecules like methane and ethane, for which the experimental values are

thought to be very accurate.

21.6 THE EYRING THEORY OF REACTION RATES

Henry Eyring (1935) worked out a theory of reaction rates, which explains the

Arrhenius lawof temperature dependence and which leads to a conceptual picture

that has been widely used in many branches of chemistry. In Section 20.2, we based

our qualitative thinking about complicated molecules on the system of the hydrogen

molecule ion because it is the only molecule simple enough to describe completely.

So we would like to base our thinking about complicated reaction mechanisms on

the simpler system of one hydrogen atom substituting for another^1 :

H+H−H→H−H+H

The attack of a hydrogen atom on a hydrogen molecule encounters an ellipsoidal

repulsive field with the minimum repulsion at either end of the molecule.

H H

Under the simplifying assumption that the attack of the hydrogen atom on H 2 is an

end-on attack, only two distances are necessary to describe the reacting system, the

distance from the the attacked hydrogen molecule to the incoming H, and the distance

from the opposite end of the molecule to the outgoing H. Call these distancesrHH′ and

(^1) Experimentally, deuterium atoms D were used because they can be distinguished from H by their
difference in mass.