## ABSTRACT

Recall from Chapter 4 that our generalized system of mass balance differential equations written in matrix form is

d

dt ( ( ) )

( ) R c Vc

Ac f c b= + + (4.22 repeated)

For steady-state problems, the chemical mass balance equations comprise a set of simultaneous (coupled), algebraic equations. For a linear problem, the system is

0 Ac b= +

and, for a nonlinear system

0 Ac f c b= + +( )

Because there is one mass balance equation per chemical per compartment, we are always dealing with the same number of unknowns (concentrations) and number of equations. That is, we always have N equations in N unknowns (N = NEQN in our GEM notation) or a symmetric problem that typically* has a unique solution-and the unique solution is what the GEM seeks.