# Gibbs' Phase Rule

by cjc0117
Tags: composition, extensive, gibbs, intensive, phase
 P: 19 I'm not really sure what you're asking but I'll take a crack at answering you since nobody else seems to be :) The Gibbs phase rule can't really tell you what phases will be thermodynamically favorable in what proportions for a given system. You need a phase diagram to do that, but phase diagrams have to obey the Gibbs phase rule. But you are correct, you can't find something like two-phase density from a single component system phase diagram. The "one independent, intensive variable that may be specified" refers only to either pressure, temperature, or composition. What this really means is that you never find a two-phase region in a single component system unless that two phase region is one-dimensional. That is what the one degree of freedom thing refers to. (Look at a phase diagram, the "boundaries" between vapor and liquid for example represent a one-dimensional, two-phase region with one degree of freedom. You cannot learn anything about the amounts of each phase present in this two phase region because the two-phase region is a line!) So in your single component system you could vary temperature and pressure together in a precise, dependent way without changing phase (If you walk along the line between liquid and vapor for example). If you have three phases coexisting then you have zero degrees of freedom and your temperature AND pressure have been set. You are now looking at a zero-dimensional POINT on the phase diagram. You can never have 4 phases in equilibrium for a one component system. In the one component system your variables can really only be temperature or pressure (unless you're working with some weird system where an EM field can cause a phase change or something) but typically you're talking about temp or pressure. In your two component system the compositional make-up of the system is another variable. You needn't think about things like "vapor mole fraction of component 1" because if you've specified a composition, call it $$X_a$$ then the vapor mole fraction of component 1 at $$X_a$$ = liquid mole fraction of component 1 at $$X_a$$. If you specify a composition, then there's no way a phase change can alter the composition. The composition DOES count as an intensive variable (but if you've got a two component system then the composition can only be one variable because fraction of component 2 = 1-(frac component 1) ) Total vapor fraction IS something you can get from a two component system's phase diagram (as you said, if the chemical compositions of each phase are known. And it so happens that if you know the total chemical composition then you can easily determine the chem composition of each phase given you have a phase diagram). You use a tie line to find the compositions of each phase and the lever rule to find the amount of each phase. See here for a brief overview: http://www.southampton.ac.uk/~pasr1/tielines.htm#page1 I think the heart of your question involved interpreting the Gibbs phase rule, and I'm not sure I've described it very well, but hopefully that at least helped.