Page 50 - The engineering of chemical reactions

34 Reaction Rates, the Batch Reactor, and the Real World
Recall our NO decomposition example, NO + &Nz + ;O,. Starting with NNo =
NNO, initially, and all other species absent, we can relate moles of all species through the
relation
NNO = NNOO(~ - x)

NN~ = ; NNOOX + NN~O
No2 = ;N~oox + Nay,
For multiple reactions we need-a variable to describe each reaction. Further, we cannot
in general find a single key reactant to call species A in the definition of X. However, it is
straightforward to use the number of moles extent xi for each of the R reactions. Thus we
can define the change in the number of moles of species j through the relation

Nj = Njo+kVijxi
i=l
To summarize, we can always find a single concentration variable that describes the
change in all species for a single reaction, and for R simultaneous reactions there must
be R independent variables to describe concentration changes. For a single reaction, this
problem is simple (use either CA or X), but for a multiple-reaction system one must set up
the notation quite carefully in terms of a suitably chosen set of R concentrations or xi s.

REACTION RATES NEAR EQUILIBRIUM

In thermodynamics we learned how to describe the composition of molecules in chemical
equilibrium. For the generalized single reaction

$vjAj=O
j=l
it can be shown that the free energy change in a system of chemically interacting species is
related to the chemical potentials pj of each species through the relationship

AG = 5 VjGj = 5 VjFj
j=l j=l
where Gj is the Gibbs free energy per mole of species j and AG is the Gibbs free energy
change per mole in the reaction. We call /Lj = Gj (actually aG/a Nj, the partial molar free
energy) the chemical potential of species j. The chemical potential of species j is related
to its chemical potential in the standard state (the state in which the activity aj of species j
is unity) by the relation

At chemical equilibrium at constant temperature and pressure the Gibbs free energy
of the system is a minimum and AG = 0. Therefore, we have