Page 60 - Chemical equilibria Volume 4

36 Chemical Equilibria
.A = 0, so (λ
However, if A = 0, then λ
.E) still represents a balance
equation at equilibrium. This application is such that:
– regardless of the value of E in E R, where 1 represents the neutral
element of the multiplication on R :
1.E = E [2.33]
– irrespective of α, β of R and regardless of the value of E of E , we
have the following if ⊗ is the symbol of multiplication on R :

( . αβ .E ) (α= ⊗ β ).E [2.34]

and:

(α + β ).E α= .E ⊕ β .E [2.35]

Regardless of the values of λ for R and E 1 and E 2 of E , we have:

λ ( . E ⊕ E 2 ) λ= .E ⊕ λ .E 2 [2.36]
1
1
Hence, the E R has an external multiplication law on the set of real
numbers.

Thus, the set E R, which has an internal composition law of addition and
an external multiplication law on the set of real numbers, is a vector space.

2.2.2. Linear combinations of balance equations

As the set E constitutes a vector space, any linear combination with a
R
balance equation such that:

E λ E ⊕ λ 2 E ⊕ ... λ ρ E ⊕ ... λ R E R [2.37]
⊕
=
⊕
ρ
1
2
1
is also a balance equation that represents a resulting transformation.
The coefficients λ ρ are multiplicative coefficients of the balance equations
ρ in the combination in question.