Page 55 - The engineering of chemical reactions

The Batch Reactor 39

[accumulation] = [generation by reaction]
or

for a single reaction or

for multiple reactions. These are simple integral mass balances on species j integrated
over the entire reactor of volume V in a closed batch reactor for a single reaction and for
multiple reactions, respectively.
The number of moles of species j in a batch reactor is simply the reactor volume V
times the concentration
Nj = VCj
so the above equation becomes
d(VCj) dC. dV
-= VJ + Cj- = VVjY(Cj)
dt dt dt
If the reactor is at constant volume, then we can divide each term by V to yield

which is usually thought of as the “mass balance for a single reaction in a batch reactor,”
although it is only valid if the volume of the reactor does not change, as we will discuss
later.

The first-order irreversible reaction

Let us immediately apply this equation to the first-order irreversible reaction
A + B, r = kc..,
The mass-balance equation on species A in a constant-density batch reactor is
dC.4
- = vAr = -kCA
dt
since VA = - 1. We need an initial condition to solve a first-order differential equation,
and for this system we assume that the reactor is charged initially with reactant A to give
CA = CA,, at t = 0. The variables can be separated

I2=-kdt/