For the case of a constant-volume batch reactor, a mole balance of the poison in the gas phase combined with the rate law for poisoning [Equation (10-109)] gives
(CD10-4.1)
where k A =kC T0 is the initial total concentration of unpoisoned site, C P•S is the concentration of the poisoned sites, and ƒ is the fraction of the poisoned sites. Taking the ratio of Equation (10-111) to Equation (CD10-4.1)
and then integrating with limits a = 1 and C P =C P0
(CD10-4.2)
or
(CD10-4.3)
Constant-
volume
batch
The decay can now be written in the form
(CD10-4.4)
which is of the form:
(CD10-4.5)
where