Page 165 - Modelling in Transport Phenomena A Conceptual Approach
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5.3. RATE OF GENERATION IN MASS TRANSPORT 145
then
(5.3-26)
Therefore, Xi is negative if i appears as a reactant; Xi is positive if i is a product.
Example 5.5 For the reaction
3A+B+C
express the reaction rate in terms of the time rate of change of species A, B, and
C.
Solution
Application of Eq. (5.3-24) gives the rate as
If V is constant, then Eq. (1) reduces to
Comment: The rate of reaction is equal to the time derivative of a concentration
only when the volume of the reacting mixture is constant.
u (5.3-27)
In the case of several reactions, Ri is defined by
& =
“ij rj
where rj is the rate of jth reaction.
The reaction rate is a function of temperature and concentration and is assumed
to be the product of two functions, one is dependent only on the temperature and
the other is dependent only on the concentration, i.e.,
r(T Ci) = W)f (ci) (5.3-28)
The function k(T) is called the rate constant and its dependence on the temperature
is given by
k(T) = ATrne-€lRT (5.3-29)
where A is a constant, E is the activation energy, R is the gas constant and T is
the absolute temperature. The power of temperature, m, is given by
0 from the Arrhenius relation
m = { 1/2 from the kinetic theory of gases (5.3-30)
1 from statistical mechanics