Page 59 - Chemical equilibria Volume 4

Properties of States of Physico-Chemical Equilibrium 35
E Σ still represents a balance equation because, according to the definition of
the affinity, it is evident that the affinity A of E Σ is the sum A 1 + A 2 of the
affinities of E 1 and E 1. It stems from this that if the affinities A 1 and A 2 are
null, then the affinity A is also null.
The set (E R, ⊕ ) is a commutative group because with three elements
there is associativity:

E = (E ⊕ E 2 ) ⊕ E = E ⊕ (E ⊕ E 3 ) [2.28]
3
Σ
1
2
1
and we can define a neutral element E 0 in the addition as being the balance
equation:
0 = 0 [2R.5]

and:

E ⊕ E = E ⊕ E = E 1 [2.29]
1
0
0
1
Each element has a symmetrical element. Regardless of E i of (E R, ⊕ ),
,
there exists E of (E R, ⊕ ) such that:
i
E ⊕ E = E ⊕ E = E 0 [2.30]
,
,
i
i
i
i
The addition is commutative because:
E ⊕ E = E ⊕ E [2.31]
1 2 2 1
Hence, there is indeed an internal composition addition law.
2.2.1.2. External multiplication law on the set of real numbers

This law is defined by an application of the set product ( R ⊗ E ) toward
E , which, for every couple has an element of ( R ⊗ E ) associated (λ.E), an
element of E . Indeed, by multiplying each term in a balance equation by λ,
we have:

0 = ∑ νλ .A k [2.32]
k k ρ