Untitled - Aerobib - Universidad Politécnica de Madrid

22 CHAPTER 1. THERMOCHEMISTRY
between ∆C ij
∆C 1j
ν 1j
= ∆C 2j
ν 2j
= . . . = ∆C lj
ν lj
. (1.87)
Let ξ j be the common value of these relations. ξ j is called the degree of
advancement of reaction j (De Donder [13]). Thus defined, ξ j has the dimensions
mole/gr. The number of moles of species A i produced by reaction j is, therefore,
∆C ij = ν ij ξ j , (1.88)
and the number ∆C i of moles of A i produced by the r reactions is
∆C i = ∑ j
∆C ij = ∑ j
ν ij ξ j . (1.89)
If C i0 is the number of moles of species A i existing when the reactions start,
the number C i that will exists when the degrees of advancement of the reactions are
ξ j , (j = 1, 2, . . . , r), is
C i = C i0 + ∑ ν ij ξ j . (1.90)
j
Similarly the mass fraction Y i of species A i produced by the r reaction is
∑
Y i = M i ν ij ξ j , (1.91)
and if Y i0 is the initial mass fraction of this species, one has
∑
Y i = Y i0 + M i ν ij ξ j . (1.92)
j
j
1.6 Chemical equilibrium
Conditions of equilibrium
Once the reactions are initiated they continue up to the point where the mixture reaches
its state of equilibrium. Such an equilibrium is determined by additional conditions
which fix the state of the system. Let us assume, for example, that the process is
adiabatic and takes place at constant pressure. Such a case has a great practical interest
in the study of combustion processes. Then the First Law of Thermodynamics shows
that the enthalpy of the mixture must be constant. Therefore, the conditions that must
be satisfied by the mixture are as follows
h = h 0 = const., p = p 0 = const. (1.93)