Page 98 - Elements of Chemical Reaction Engineering 3rd Edition
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70 Rate Laws and Stoichiometry Chap. 3
Equation (3-2), known as the Arrhenius equation, has been verified empirically
to give the temperature behavior of most reaction rate constants within experi-
mental accuracy over fairly large temperature ranges.
The activation energy E has been equated with a minimum energy that
must be possessed by reacting molecules before the reaction will occur. From
the kinetic theory of gases, the factor gives the fraction of the colli-
T(K) sions between molecules that together have this minimum energy E. Although
this might be an acceptable elementary explanation, some suggest that E is
nothing more than an empirical parameter correlating the specific reaction rate
to temperature.] (See Appendix G) Other authors take exception to this inter-
pretation; for example, Tolman’s2 interpretation of activation energy is that it
is the difference between the average energy of those molecules that do react
and the average energy of all reactant molecules. Nevertheless, postulation of
the Arrhenius equation remains the greatest single step in chemical kinetics,
and retains its usefulness today, nearly a century later.
The activation energy is determined experimentally by carrying out the
reaction at several different temperatures. After taking the natural logarithm of
Equation (3-2),
Calculation of the In k, = In A - -
activation energy (3-3)
it can be seen that a plot of In kA versus 1/T should be a straight line whose
slope is proportional to the activation energy.
Example 3-1 Determination of the Activation Energy
Calculate the activation energy for the decomposition of benzene diazonium chlo-
ride to give chlorobenzene and nitrogen:
T (Kj 313.0 319.0 323.0 328.0 333.0
M. Karplus, R. N. Porter, and R. D. Sharma, J. Chem. Phys., 43, 3259 (1965); D. G.
Truhlar, J. Chem. Educ., 55(5), 310 (1978).
R. C. Tolman, Statistical Mechanics with Applications to Physics and Chemistry
(yew York Chemical Catalog Company, 1927), pp. 260-270.
