Concise Physical Chemistry

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

354 PHOTOCHEMISTRY AND THE THEORY OF CHEMICAL REACTIONS

reacting because each one-cycle vibration leads to products. Thusk 1 isν(notice that

both are frequencies) and

−

d[A]

dt

=

RT

NAh

K∗[A][B]

If the assumption that all vibrations lead to products does not hold, one includes a

transmission coefficientκ, which is that fraction of activated complexes that break

up to give products. Now,

−

d[A]

dt

=κ

RT

NAh

K∗[A][B]

or

kobserved=κ

RT

NAh

K∗

21.9 ENTROPIES OF ACTIVATION

In general, the free energy change of a reaction varies as the natural logarithm of its

equilibrium constant, so for the steady-state activation equilibrium we write

G◦∗=−RTlnK◦∗

where the superscript designates the standard state of the Gibbs free energy for the

activation pseudo-equilibrium. The equivalent form forK◦∗is

K◦∗=e−G

◦∗/RT

By analogy to a true equilibrium, for which

G◦=H◦−TS◦

we write

K◦∗=eS

∗/R

e−H

∗/RT

The observed rate constant is

kobserved=κ

RT

NAh

eS

∗/R

e−H

∗/RT