How Does Gibbs' Phase Rule Limit the Number of Coexisting Phases in a System?

[RJWills]

Homework Statement

"By applying Gibbs' phase rule to show that for an n component system, no more than n+2 phases may coexist at equilibrium

Homework Equations

P+F=C+2

The Attempt at a Solution

Because the question says that P = n +2 I subbed this in => n+F=C. I'd like to sub some numbers into prove that you can't have more than n +2 phases, but with regards to the other numbers surely you can have a very large number of degrees of freedom and many components.

So what do I do? I really don't understand how I can prove this sensibly

 

[TSny]

Make sure you understand the meaning of each symbol in the phase rule. For example, if you have an n component system, what symbol in the phase rule is equal to n?

Rearrange the phase rule so that you have it solved for the number of phases.

You should be able to see by inspection what the maximum number of phases can possibly be. (Hint: It occurs when something else in the phase rule is as small as possible.)