Page 327 - Elements of Chemical Reaction Engineering Ebook

298 Multiple Reactions Chap. 6

Applying Equation (6-17) to reaction 2 above [i.e., (A+2C 3E)
2
where r2A = -kZACACC], the rate of formation of species E, 9E, is

and the rate of formation. of C is

Y2E - 2 2
tt species r2, = - r2A = -2k2AC,C,
- 1
reaction
number
To relate the relative rates of formation in more compact notation sup-
pose the rate law for the rate of formation of species A, is given in reaction i
as

To find the rate of formatiOn of species A, in reaction i, rr, , we multiply the
rate law for species A, in reaction i by the ratio of stoichiometric coefficients
of species A,, v,], and species A,, v,,. in reaction i:

Relative rates of
reaction in reaction i 'ik 1 (6- 18)
in compact notation [ "ij

This relationship only holds for relative rates in the same reaction (i.e.,
reaction i ). When relating relative rates of formation the stoichiometric coeffi-
cients, v~,, of reactants are taken as negative and the coefficients of products as
positive.
In analyzing the multiple reactions in Table 6-2, we carry out the proce-
dure shown in Table 6-3 (not necessarily in exact order) when the rate Iaw is
known for at least one species in each of the individual reactions.

TABLE 6-3. STEPS IN ANALYZING MULTIPLE REACTIONS
1. Number each reaction.
2. Wnte the mole balances for each species.
3. Determine the rate laws for each sp-cies in each reaction.
4. Relate the rate of reaction of each species to the species for which the rate law
The multiple- is given for each reaction.
reaction algorithm
for isothermal 5. Determine the net rate of formahon of each species.
reachons 6. Express rate laws as a function of concentration, C,, for the case of no volume
change.
7. Express the rate laws as a function of moles, N, (batch), or molar flow rates,
5 (flow) when there is volume change with reaction.
8. Combine all of the above and solve the resulting set of coupled differential
(PFR, PBR, batch) or algebraic (CSTR) equations.