Page 75 - Chemical equilibria Volume 4

Properties of States of Physico-Chemical Equilibrium 51
NOTE 2.5.– These conditions can also be expressed in terms of characteristic
functions. Then by using expression [1.20], if the system is at
thermodynamic equilibrium, condition [2.58] is written:
∂ Γ = 0 [2.60a]
ξ ∂

and:
∂ 2 Γ
ξ ∂ 2 < 0 [2.60b]

The concavity of the curve Γ(ξ) is turned toward positive values of Γ and
exhibits a minimum at the origin. Therefore, for chemical systems, as function
Γ is the Gibbs energy function G, the curve showing this Gibbs energy as a
function of the extent of the reaction has a minimum at the origin.

If the system is at false equilibrium, then condition [2.59] becomes:

∂ Γ ≠ 0 [2.61a]
ξ ∂

and:
∂ 2 Γ
ξ ∂ 2 > 0 [2.61b]

The curve Γ(ξ) does not have a minimum at the origin.

2.6.3. Stability of a system with bilateral variations

The system will be subject to bilateral variations if the disturbance δξ
can have any sign. Let us show that such a system, if it is stable, is
necessarily thermodynamically stable ( A S = 0 ).

Indeed, suppose that it is otherwise, and that A S > 0 , for example. De
Donder’s inequality for the disturbed system, if we discount the variation of
the affinity, gives us:

A S ℜ> 0 [2.62]
' S