Page 112 - Elements of Chemical Reaction Engineering 3rd Edition

84 Rate Laws and Stoichiometry Chap. 3

3.3 Stoichiometric Table
Now that we have shown how the rate law can be expressed as a function of
concentrations, we need only express concentration as a function of conversion
in order to carry out calculations similar to those presented in Chapter 2 to size
reactors. If the rate law depends on more than one species, we must relate the
concentrations of the different species to each other. This relationship is most
easily established with the aid of a stoichiometric table. This table presents the
stoichiometric relationships between reacting molecules for a single reaction.
That is, it tells us how many molecules of one species will be formed during a
chemical reaction when a given number of molecules of another species disap-
pears. These relationships will be developed for the general reaction
aA+bB e (2- 1)
cC+dD
Recall that we have already used stoichiometry to relate the relative rates of
reaction for Equation (2-1):
4
rA
_- ---- (2-20)
‘C - ‘D
‘B
’a -b c d
In formulating our stoichiometric table we shall take species A as our
basis of calculation (i.e,, limiting reactant) and then divide through by the sto-
ichiometric coefficient of A,
b c d
A+ - B + -C+-D (2-2)
U u a
in order to put everything on a basis of “per mole of A.”
Next, we develop the stoichiometric relationships for reacting species that
give the change in the number of moles of each species (Le., A, B, C, and D).

3.3.1 Batch Systems
Figure 3-1 shows a batch system in which we will carry out the reaction
given by Equation (2-2). At time t = 0 we will open the reactor and place a
number of moles of species A, B, C, D, and I (NAo, N,, , Nco, N,,, and N,,
respectively) into the reactor.
Species A is our basis of calculation and NAo is the number of moles of
A initially present in the reactor. Of these, NA,X moles of A are consumed in
the system as a result of the chemical reaction, leaving (NAo - NAoX) moles
of A in the system. That is, the number of moles of A remaining in the reactor
after conversion X has been achieved is

NA = NA, - NAOX = NAo (1 - X)

The complete stoichiometric table for the reaction shown in Equation (2-2)
taking place in a batch reactor is presented in Table 3-2.