Page 122 - Chemical equilibria Volume 4

98 Chemical Equilibria
if it is an endothermic reaction), then the equilibrium curves will approach
point A 3 as the temperature increases.
3.5.4. Iso-composition curves in perfect solutions

Based on the expressions of the quantities of each of the species if we
begin with an initial ratio u between A 1 and A 2 (relations [3.81], [3.82] and
[3.83]) we calculate:

zβ
x = β + z 3 β i = y [3.91]
1 ∑
3

and:
u − z
x = z [3.92]
1
1+ ∑ β
β i
1
From equation [3.91], we deduce:
β y
z = 1 [3.93]
β − y ∑ β i
3
By substituting back into relation [3.92], we deduce the equation of the
iso-composition curves:
⎛ β + u ∑ β ⎞
−
x 32u− = y ⎜ ⎜ 1 2 1 i ⎟ ⎟ [3.94]
⎝ β 3 ⎠

This is the equation of a straight line whose slope depends on the initial
conditions (value of u).

Consider the intersection of two of those straight lines, obtained for two
arbitrary values of u: u 1 and u 2. Applying relation [3.94] for the two values
u 1 and u 2, we find:

⎛ β + u 1∑ β ⎞
−
x 32u = ⎜ − 1 y ⎜ 1 2 1 i ⎟ ⎟ [3.95]
⎝ β 3 ⎠