Page 117 - Chemical equilibria Volume 4

Molecular Chemical Equilibria 93
A 2A 1, then the system evolves as the reaction progresses, in accordance with
very specific compositions set by the initial conditions and the
stoichiometric numbers β 1, β 2 and β 3. The curve, passing through a specific
point M and giving all the compositions of the system during the reaction, is
called the iso-composition curve.
At a given pressure and temperature, the iso-composition corresponding
to the chosen initial state intersects the iso-Q curve at point E representing
the state of thermodynamic equilibrium at the chosen temperature and
pressure and for the chosen initial composition.

We shall quantify those data by establishing the iso-Q and iso-
composition curves in the case of perfect solutions. First, though, we shall
demonstrate an important property of equilibria with perfect solutions.

3.5.2. Molar fractions at equilibrium and initial composition

We consider equilibria which involve a poly-component perfect phase,
and demonstrate the following theorem:

THEOREM 3.1– In such equilibria, the molar fraction of a formed component
is, at thermodynamic equilibrium, maximal when that equilibrium is
achieved on the basis of the reagents taken in stoichiometric proportions.

This theorem is very general, as long as several components belong to the
same phase. We shall now demonstrate it in the case of the three-component
reactions given by balance equation [3R.26].

Hence, we consider the initial mixture of a mole and containing u moles
of A 1 and 1–u moles of A 2. Let z denote the number of moles of A 3 formed.
We can see that the quantities of the different components are given by:

n =− z [3.81]
u
1
β
1 u −
n =− 2 z [3.82]
2
β 1
β
n = 3 z [3.83]
β 1
3