Page 140 - Modeling of Chemical Kinetics and Reactor Design

110 Modeling of Chemical Kinetics and Reactor Design

negative sign. The amounts of the products increase and their rates
of change are therefore positive.

REACTION RATE EQUATION

The rate of a reaction is the number of units of mass of some
participating reactants that is transformed into a product per unit time
and per unit volume of the system. The rate of a closed homogeneous
reaction (that is, no gain or loss of material during the reaction) is
determined by the composition of the reaction mixture, the tem-
perature, and pressure. The pressure from an equation of state can be
determined together with the temperature and composition.
Consider a single-phase reaction

aA + bB → cC + dD (3-1)

The reaction rate for reactant A can be expressed as

− ( r A ) =− 1 dN A = (amount of A disappearing )
V dt (volume )(time )
(3-2)
moles
=
3
m •sec
where the minus sign means “disappearance” and

(–r ) = rate of disappearance of A
A
N = number of moles
A
V = system volume
t = time

The reaction rates of the individual components are related by

−r −r r r
A = B = C = D (3-3)
a b c d

The rate is defined as an intensive variable, and the definition is
independent of any particular reactant or product species. Because the
reaction rate changes with time, we can use the time derivative to
express the instantaneous rate of reaction since it is influenced by the
composition and temperature (i.e., the energy of the material). Thus,