The analytical relationship among the total pressure P (or the volume per total mol of all species,
V*), the composition, and partial pressures of species is discussed for the equilibrium gas mixture of A-B-C...-N system at a constant temperature, ideal behaviour of each species being assumed.
The n components are chosen so that
1) they are necessary and sufficient to define the composition of the gas under the study,
2) there are n “component species”, defined as the species having the same formula with corresponding components, and
3) any species other than “component species”, are compound or associated molecules of several “component species”, or dissociated molecules from a single “component species”.
As long as the components are chosen as above, the partial pressures of “component species” are defined as
PA,
PB..., and
PN, and mole fractions of components are defined as
XA,
XB, ..., and
XN, it follows that 1)
XH/
XA increases monotonously with
PH if
T,
P (or V*),
PB (or
XB/
XA),
Pc (or
Xc/
XA), ...,
PG (or
XG/
XA),
PI (or
XI/X
A) and
PN (or
XN/
XA) are kept constant, 2)
P (or 1/
V) increases monotonously with
PA if
T,
PB,
PC and
PN are kept constant, 3) condition:[
T;
P (or 1/
V*);
PB (or
XB/
XA),
Pc (or
Xc/
XA), ...,
PN (or
XN/
XA)] is in one-to-one correspondence with condition:[
T;
PA,
PB,
PC, ...,
PN], and is necessary and sufficient to describe the state.
To compute gas equilibria a new technique, which is 1) initial estimates-free, 2) convergence-guaranteed, and 3) iteration parameter-free, is developed by combining the “monotone rule” derived above with the method of nested iterations.
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