The Schreinemakers Method
B. Mishra
PART – 3 THE SCHREINEMAKERS METHOD: A GEOMETRIC APPROACH FOR CONSTRUCTING PHASE EQUILIBRIA Derivation of the Gibb’s phase rule
Important feature of the Gibb’s phase rule is to remember that the phase rule is simply an accounting of the number of equations and unknowns and identities of the unknown are totally lost in the process of such accounting. Here, we first try to identify the unknowns (variables) and the equations, necessary for deriving the phase rule.
Unknowns If we represent the compositions of all the phases in the system in theirs of mole fractions of their components (x1, x2, ……. etc.), then there will a mole fraction term for each component in every phase, so that there will be ‘cp’ compositional variable. In addition, considering P and T as the other two variables, the total number of unknowns = cp + 2.
Equations We can write equations relating compositional variables in each phase as follows C
∑X i =1
i
=1
(1)
For ‘p’ no. of phases, there will be ‘p’ equations of the above type. Furthermore, since transfer of chemical components takes place in the direction of decreasing chemical potential, at equilibrium, chemical potentials of every component is the same in every phase in which it appears. Thus, μ iα = μ iβ = ............... = μ1p
(2)
1