Page 74 - Chemical equilibria Volume 4

50 Chemical Equilibria
The stability condition [2.53] becomes:
A ' S < 0 [2.55]
However, we can write:

⎛ ∂A ⎞
A ' S = A S + ⎜ S ⎟ dξ [2.56]
⎝ ∂ξ ⎠ ξ = 0

Two cases may therefore arise.

– if system S is at thermodynamic equilibrium, then A = 0 and therefore:
S
⎛ ∂A ⎞
A ' S = ⎜ S ⎟ dξ [2.57]
⎝ ∂ξ ⎠ ξ = 0

Hence, we have the following conditions of stability of S:

A S = 0 [2.58a]

and:

⎛ ∂A ⎞
⎜ S ⎟ < 0 [2.58b]
⎝ ∂ξ ⎠ ξ = 0

– if the system is at false equilibrium, then ℜ= 0 A S ≠ 0; if we ignore
S
the second term in expression [2.56], then the condition of stability of S
becomes:

ℜ= 0 [2.59a]
S

and:

A < 0 [2.59b]
S
NOTE 2.4.– These conditions can, of course, very easily be expressed in
terms of chemical potentials by using expressions [1.23] and [1.42].