Page 168 - Introduction to chemical reaction engineering and kinetics

150 Chapter 6: Fundamentals of Reaction Rates

The attenuation of a light beam as it traverses a volume of light-absorbing material
of thickness dl can be expressed as

r = -dI/dl = Iaca (6.6-11)
The integration of equation 6.6-11 with the boundary condition that I = Z, at 1 = 0
gives the Beer-Lambert law (with c,/mol L-r = CL/N,,):

Z = Z,exp(-acAl) (6.6-12)

where u( = aN,,/lOOO) is called the molar extinction coefficient of the medium. The
cross-section is highly energy dependent and produces characteristic absorption spectra
for each molecule.

6.6.3.2 Elementary Reactions of Molecules in Excited States
An electronically excited molecule can undergo several subsequent reaction steps. In
addition to dissociation and rearrangements, there are processes involving light. These
are:
Light emission (fluorescence): The reverse of reaction 6.6-9

A* + A+hv (6.6-13)

is called fluorescence and can be thought of as another unimolecular reaction, with a
first-order rate expression:

r = k,ci (6.6-14)

The rate constant k, corresponds to the reciprocal of the lifetime of the excited state.
Internal conversion: The excited state can do other things, such as convert some of the
original electronic excitation to a mixture of vibration and a different electronic state.
These are also treated as unimolecular processes with associated rate constants:

A* + A*’ (6.6-15)

Often, the second state formed this way is longer-lived, thus giving the excited molecule
a longer time to undergo other reactions.
Stimulated emission: Another form of photon emission is called stimulated emission,
where a photon of the right energy can cause an excited state to emit an additional
identical photon, that is,

A” + hv + A + 2hv (6.6-16)

The waves of the two “product” photons are in phase; this process is the basis of laser
operation.

6.6.4 Reactions in Plasmas

In specialized processes associated with the materials science industry, a reactive atmo-
sphere is generated by reactions in which charged species are participants. A gaseous
system wherein charged particles (electrons, ions) are important species is called a
plasma, and the response of charged particles to an external field is used to increase