Page 82 - Chemical equilibria Volume 4

58 Chemical Equilibria
There is an extremely simple specific case of the calculation of the
fugacity of the gas i: when we consider that the mixture of gases forms a
perfect solution of imperfect gases, because then we have γ (I) = 1, the
i
fugacity is written as:
f = fy = ϕ i 0 y P [3.5]
0
i
i
i
i
This is what is known as Lewis’ statement. ϕ is the fugacity coefficient
0
i
of the pure gas i at the same total pressure as in the mixture. In this particular
case, albeit one which is encountered frequently, by substituting back into
equation [3.4] we obtain:
⎛ ⎜ ∏ ϕ i o P ⎞ i i ν = K () [3.6]
f
i ⎝ P 0 ⎟ ⎠
In the ideal case of perfect solutions of perfect gases, the fugacity
coefficient for each of the gases is equal to 1, and the fugacity is identical to
the partial pressure. The law of mass action then becomes:

⎛ P ⎞ i ν
P
K () = ⎜∏ i 0 ⎟ [3.7]
i ⎝ P ⎠
P
K () is the equilibrium constant relative to the partial pressures. The
0
reference pressure P is generally taken to be 1 bar.
In order to link the equilibrium constant relative to the partial pressures to
the equilibrium constant K defined by relation [3.3], which pertains to the
molar fractions, because we are dealing with perfect solutions we shall base
our arguments on the law of mass action [3.7] relative to perfect gases, given
that the equilibrium constants are defined on the basis of the standard
conditions, which depend solely on the species in the pure state. We express
the partial pressure as a function of the molar fraction, by:

P = Px i [3.8]
i
The application of relation [3.8] enables us to write:
∑ i ν
P
P
x i ⎜ ∏ i ν ⎛ 0 ⎟ i ⎞ = K () [3.9]
i ⎝ P ⎠