Page 46 - Chemical equilibria Volume 4

22 Chemical Equilibria
We can apply this condition to a system with only one transformation
with the fractional extent ξ. We then obtain:
dξ = x 0(α) dξ ∑ ν () α = 0 [1.93]
N
dt k dt i= 1 i
or:
ν () α
x k 0(α) = N k [1.94]
∑ ν i α
i= 1
At the initial time, all of the components must be in stoichiometric
proportions in each phase.

Another case encountered when we look at phase-change in multi-
component systems is when each component is involved in only one
transformation, and its stoichiometric number is 1. Thus, in a phase α, we
have:

dξ k () α = x k ∑ ν dξ i () α [1.95]
N
0(α)
dt i= 1 i dt
This can also be written as:

dξ () α
i 0(α)
dt = x i [1.96]
dξ k () α x 0(α)
k
dt

This means that the transformation rates of two components are in a
constant ratio to one another, with the value of that ratio being determined
by the initial conditions.

In addition, if we consider two phases α and β, by applying relation
[1.92] for component A k in the two phases and adding together the
expressions obtained, we find:

dn (α) + dn k (β) − x k ∑ 0(α) N dn (α) − x k ∑ 0(β) N dn i (β) = 0 [1.97]
i
k
dt dt i= 1 dt i= 1 dt