Page 105 - The engineering of chemical reactions

Conversion in a Constant-Density CSTR 89

( Cjo-Cj =-TVjl 1

This will be the most used form of the mass-balance equation in the CSTR in this book.
Students should either memorize this equation or preferably be able to derive it from an
integral mass balance on the reactor. This equation requires three major assumptions:

1. A steady state,
2. A single reaction, and
3. No density change with reaction.

CONVERSION IN A CONSTANT-DENSITY CSTR

For a reactant species A (VA = - 1) the steady-state mass balance becomes
CA,, - CA = tr(CA)
and we will now solve this equation for some simple rate expressions.

Irreversible reactions

Consider the &h-order irreversible reaction
A -+ products, r = kcp
For first-order kinetics, IZ = 1, the mass balance becomes

CA0 - CA = tkCA
which can be rearranged to solve for CA

and then solved explicitly for t

Note that we simply had to solve an algebraic equation to find CA (t ) or t (CA).
In a CSTR with any single reaction rate r(CA), we can always solve explicitly for t
as

If this reaction is A + B, we can find Cs by simply substituting from stoichiometry,