Page 114 - Elements of Chemical Reaction Engineering 3rd Edition

86 Rate Laws and Stoichiometry Chap. 3

To calculate the number of moles of species B remaining at time t we
recall that at time t the number of moles of A that have reacted is NAOX. For
every mole of A that reacts, b/a moles of B must react; therefore, the total
number of moles of B that have reacted is

moles B reacted
moles B reacted = moles A reacted
moles A reacted

Because B is disappearing from the system, the sign of the “change” is nega-
tive. N,, is the number of moles initially in the system. Therefore, the number
of moles of B remaining in the system, N,, is given in the last column of
Table 3-2 as

The complete stoichiometric table delineated in Table 3-2 is for all species in
the reaction
b c d
a
-C+-D
A+ - B + a (2-2)
a
The stoichiometric coefficients in parentheses (dla + c/a - b/a - 1) repre-
sent the increase in the total number of moles per mole of A reacted. Because
this term occurs often in our calculations it is given the symbol 6:
I I
(3-23)
I I
The parameter 6 tells us the change io the total number of moles per mole of
A reacted. The total number of moles can now be calculated from the equation

NT = NTo + SNAOX
We recall from Chapter 1 that the kinetic rate law (e.g., -rA = kC2) is a
function solely of the intensive properties of the reacting materials (e.g., tem-
We want perature, pressure, concentration, and catalysts, if any). The reaction rate, - rA,
=
usually depends on the concentration of the reacting sbecies raised to some
power. Consequently, to determine the reaction rate as a function of conversion
X, we need to know the concentrations of the reacting species as a function of
conversion.
The concentration of A is the number of moles of A per unit volume:
Batch
concentration

After writing similar equations for B, C, and D, we use the stoichiometric
table to express the concentration of each component in terms of the conver-
sion X