Kinetic Theory and Reaction Kinetics - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 277

moles of the reaction mixture including monomer and oligomers, and 3) total number of the
monomer units in the reaction mixture.

6.7. SUMMARY

While reaction rates are empirical in nature, collision theory does provide a means to esti-
mate the reaction rate. Collision theory gives rise to the correct reaction rate dependence on
concentrations and temperature. Based on collision theory, most viable reactions are bimolec-
ular. Reactions with more than three molecules are unfavorable. Therefore, an elementary
reaction usually involves three or less molecules on either side of the reaction.
Nonelementary reactions can be decoupled into elementary reaction steps or reaction
pathways. The reaction system that forms a nonelementary reaction can be analyzed as if
one were dealing with a multiple-reaction system. In many occasions, we find simplification
of the nonelementary reaction is necessary. Some reaction steps are fast than others, or some
or all the reaction intermediates are present in the reaction system in only trace amount. This
observations lead to two methods of simplifying reaction rate expressions: FES and PSSH.
FES stands for FES approximation, while PSSH stands for pseudosteady-state hypothesis.
FES assumes one or more steps are rate-limiting, and the rest steps are in thermodynamic
equilibrium. PSSH assumes that the net rates of formation for the intermediates are zero.
Active reaction intermediates are common as they are means to overcome the activation
energies. Active intermediates can be active complex, transitional state (or activated mole-
cules), and free radicals. Nonelementary reactions usually have complicated reaction rate
expressions than the simple power-law form. Fractional order (1/2, 3/2, ) can be observed

for free-radical reactions. Transitional state theory is based solely on the activated state
approach.
Simple kinetic expressions can be obtained for otherwise a complicated problem when
proper assumptions are made. For acid hydrolysis of polymers, the reaction kinetics may
be approximated by three “first-order reaction rate” relationships of lumped components,
Eqns (6.91) , (6.93) , and (6.94) , despite a complicated composition of the reaction mixture.

.

Reading Materials

Anslyn, E.V., Dougherty, D.A., 2006. Modern Physical Organic Chemistry. Sausalito, CA: University Science
topics.
Frost, A.A., Pearson, R.G., 1961. Kinetics and Mechanism (2nd ed.). New York: John Wiley & Sons, Inc.
Isaacs, N.S., 1996. Physical Organic Chemistry (2nd ed.). NY: Prentice Hall.
Lindemann, F.A. 1922. The radiation theory of chemical reaction. Trans. Faraday Soc. ,17 , 588 e 589.

Moore, J.W., Pearson, R.G., 1981. Kinetics and Mechanism. New York: Wiley.
Steinfeld, J.I., Fransico, J.S., Hase, W.L., 1999. Chemical Kinetics and Dynamics (2nd ed.). Englewood Cliffs, NJ:
Prentice-Hall.