Page 53 - Chemical equilibria Volume 4

Similarly, for the chemical potential of the component i, which is added,
we obtain: Properties of States of Physico-Chemical Equilibrium 29
⎛ ∑ n ⎞
∂ μ i = RT ⎜ j j − 1 ⎟ [2.10]
n ∂ i ∑ n j ⎜ ⎜ n i ⎟ ⎟
j ⎝ ⎠
By substituting expressions [2.9] and [2.10] back into equation [2.8], we
find:

⎛ ∑ n ⎞
∂A = RT ⎜ ν −ν j j ⎟ ⎟∑ [2.11]
n ∂ i ∑ n j ⎜ ⎜ j j i n i ⎟
j ⎝ ⎠
and the direction of evolution is obtained by feeding expression [2.11] back
into equation [2.1], which gives us:

⎛ ∑ n ⎞
RT ⎜ ν − ν j j ⎟ ⎟∑ ℜ > [2.12]
'0
∑ n j ⎜ ⎜ j j i n i ⎟
j ⎝ ⎠

This inequality can be written more simply, using x i to denote the molar
fraction of the component added in its phase, in the form:

⎛ ν ⎞
'0
⎜ ν − i ⎟∑ ℜ > [2.13]
j
⎝ j x i ⎠
In order to draw conclusions, we need to discuss inequality [2.13].

First case: the transformation takes place without varying the number of
moles in the phase of the element, added which can be expressed by:
∑ ν = 0 [2.14]
j
j
– if the component added is a reagent, its algebraic stoichiometric
coefficient is negative and relation [2.13] yields ℜ>
'0. The equilibrium
shifts from left to right in the formulation of the balance equation.