Page 325 - Elements of Chemical Reaction Engineering Ebook

296 Multiple Reactions Chap. 6

6.3.2 Net Rates of Reaction

Having written the mole balances, the key point for multiple reactions is
to write the net rate of formation of each species (e.g., A, B). That is, we have
to sum up the rates of formation for each reaction in order to obtain the net
rate of formation, e.g. rA. If q reactions are taking place

Reaction 1: A + B k,A > 3C+D
Reaction2: A+2C -% 3E

Reaction 3: 2B + 3E 4F

1 kqA
Reaction q: A + - B >G
2
Then the net rates of reaction of A and B are

4
rA = r1A + r2* + r3A + . . . + rqA = 2 rlA
Net rates 1=1
of reaction 4
r, = YIB + r2, + r3B + *" + rqB 1 rrB
1=1
When we sum the rates of the individual reaction for a species, we note that
for those reactions in which a species (e.g., A, B) does not appear, the rate is
zero. For the first three reactions above, r3A = 0, I,~ = 0, and r2D = 0.
To write the reactions above in more compact notation we could let
AI = A, A, = B, and so on, to arrive at the generic sequence of q reactions
shown in Table 6-2. The letter A, represents a chemical species (e.g.,
A, = HCl, A, = NaOH). The first subscript, i, in the stoichiometic coefficient
r1J vE, and in the reaction rate rlJ refers to the reaction number while the second
subscript, j, refers to the particular species in the reaction. We are now in a
~ position to evaluate the total rate of formation of each species from all reac-
k ~ number ~ ~ ~ ~ n

1 V~~ ',k 'cp