Derivation of the lever rule in thermodynamics in mineralogy.
Question
Suppose a mixture consisting of the components A and B has the
composition . Suppose further
that at some P and T, A and B react with each other forming the phases
and , with compositions and , respectively. The question to
be answered is: what are the molar proportions of the two phases.
Answer
We know
and
and
, if we give eq and
to eq we will have
For the same reason， we have
and
, so and , and if we give them to
eq, we have
. If we divide both sides of the eq by at the same time,
we can say
