Page 100 - Elements of Chemical Reaction Engineering 3rd Edition

72 Rate Laws and Stoichiometry Chap. 3

(E3-1.2)
(2.3) (R) log(k,/k,)
E= --
1/T2- 1/T,
To use the decade method, choose l/Tl and 1/T2 so that k, = O.lk,. Then,
log(kllk2) = 1.

When k, = 0.005: - - 0.00303
-
Tl
When k, = 0.0005: - - 0.00319
-
T2
Therefore,

2303R - (2.303)(8.314 Jho1.K)
E= -
1 /T2 - 1 /TI (0.003.19 - 0.00303)/K
I = 120 - 28.7 kcal/mol
w
or
mol

The rate does not There 1s a rule of thumb that states that the rate of reaction doubles for
for every 10°C increase in temperature. However, this is true only for a specific
a temperature
increase of looc combination of activation energy and temperature. For example, if the activa-
tion energy is 53.6 kJ/mol, the rate will double only if the temperature is
raised from 300 K to 310 K. If the activation energy is 147 kJ/mol, the rule
will be valid only if the temperature is raised from 500 K to 510 K. (See Prob-
lem P3-5 for the derivation of this relationship.)
The larger the activation energy, the more temperature-sensitive is the rate
of reaction. While there are no typical values of the frequency factor and activa-
tion energy for a first-order gas-phase reaction, if one were forced to make a
guess, values of A and E might be IOl3 s-l and 300 kJ/mol. However, for fam-
ilies of reactions (e.g., halogenation), a number of correlations can be used to
estimate the activation energy. One such correlation is the Polanyi-Semenov
equation, which relates activation energy to the heat of reaction (see Problem
P3-20). Another correlation relates activation energy to differences in bond
strengths between products and reactant^.^ While activation energy cannot be
currently predicted a priori, significant research efforts are under way to calcu-
late activation energies from first principle^.^ (Also see Appendix J)

M. Boudart, Kinetics of Chemical Processes (Upper Saddle River, N.J.: Prentice Hall,
1968), p. 168. J. W. Moore and R. G. Pearson, Kinetics and Mechanics, 3rd ed. (New
York: Wiley, 1981), p. 199. S. W. Benson, Thermochemical Kinetics, 2nd ed. (New
York: Wiley, 1976).
S. M. Senkan, Detailed Chemical Kinetic Modeling: Chemical Reaction Engineering
of the Future, Advances in Chemical Engineering, Vol. 18 (San Diego: Academic
Press, 1992), pp. 95-96.