Concise Physical Chemistry

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

PROBLEMS AND EXAMPLES 355

which can be compared with the Arrhenius equation

kobserved=se−Ha/RT

Noting thatHain Arrhenius theory is the same thing asH∗in Eyring’s theory,

the preexponentialsmust be

s=κ

RT

NAh

eS

∗/R

This expression gives a preexponential that is a function of the temperature as con-

trasted to Arrhenius’ conclusion thatsis constant. Accurate measurements have

indeed shown the temperature dependence of the supposed constants.

21.10 THE STRUCTURE OF THE ACTIVATED COMPLEX

If the activated complex has a “tight” structure, its formation implies a reduction

of freedom in the system, therefore a negative entropy changeS. If the activated

complex has a loose structure by comparison to the reactants,Sis positive hence

the preexponential factor is large as well. For some reactions,e−Ha/RTmay be

unfavorable but the reaction rate is appreciable because of a large preexponential.

The reactions

NO+O 3 =NO 2 +O 2

and

CH 3 I+HI=CH 4 +I 2

have been shown to have second-order rate constantsk= 6. 3 × 107

√

Te−^2300 /RT

andk= 5. 2 × 1010

√

Te−^33 ,^000 /RT, respectively. Analyzing these two results, we

conclude that the first reaction has a low activation barrier relative to the second and

it has a lower preexponential than the second reaction. The entropy of activation is

more negative for the nitric oxide oxidation than the iodine abstraction, suggesting

a tightly bound structure for the first activated complex and a loose structure for the

second activated complex.

PROBLEMS AND EXAMPLES

Example 21.1 A C C Bond Dissociation Enthalpy (BDE)

Find the enthalpy of dissociation (BDE) of the C C bond in ethane in the G3(MP2)

model chemistry.