Page 49 - The engineering of chemical reactions

Stoichiometry 33

For our NO decomposition example NO -+ $N2 + $O,, from an 0 atom balance we
see that
kNNo + No, = constant

while an N atom balance gives

1 NN~ + NN~ = constant
and subtracting these, we obtain
NN~ - No2 = constant
in a closed system. The stoichiometry of the molecules requires that the moles of these
species are related by these relations.
Subtracting the initial values (subscript o), we obtain relations such as

NNO - NNO, = ANN,, - ANN,
or
ANNO = -MANN,
In general, for any single reaction we can write

all j

and we can write S - 1 independent combinations of these relations among S chemical
species in a reaction to relate the change in number of moles of all species to each other.
There is therefore always a single composition variable that describes the relationship
among all species in a single reaction. In the preceding equation we defined x as the relation
between the Nj S,
Nj = Njo+VjX
and we will call the quantity x the number of moles extent.
For simple problems we most commonly use one of the reactants as the concentration
variable to work with and label that species A to use CA as the variable representing
composition changes during reaction. We also make the stoichiometric coefficient of that
species VA equal to - 1.
Another way of representing a single reaction is fractional conversion X, a dimen-
sionless quantity going from 0 with no reaction to 1 when reaction is complete. We define
X through the relation
NA = NA,(~ - X)
To make 0 < X < 1 we also have to choose species A as the limiting reactant so that this
reactant disappears and X approaches unity when the reaction is complete. We can then
define all species through the relation
Nj - Nj, = NA,X
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