Page 76 - Chemical equilibria Volume 4

52 Chemical Equilibria
Hence:
ℜ> 0 [2.63]
' S
If we choose a positive value for δξ, then the product ℜ ' S δξ is positive,
which runs counter to the stability condition [2.52]. We would find the same
conclusion by choosing A S < 0 , which would give us A S = 0 .

In this case, the affinity of the disturbed system will be:

⎛ ∂A ⎞
A = S δξ [2.64]
' S ⎜ ⎟
⎝ ∂ξ ⎠
and according to de Donder, we should have:

∂A S ℜ δξ > 0 [2.65]
∂ξ ' S

Therefore, the stability condition [2.50] is imposed:

∂A S < 0 [2.66]
∂ξ

Hence, for a system with bilateral variations to be stable, it is necessary
and sufficient that the following two conditions be fulfilled:

A S = 0 [2.67a]

and:

∂A S < 0 [2.67b]
∂ξ

Using relation [1.20], in order for a system with bilateral variations to be
stable, it is necessary and sufficient for the characteristic function to obey the
following two conditions:

∂ Γ = 0 [2.68a]
ξ ∂