The Phase Rule

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The phase rule is a method to count the number of degrees of freedom (how many independent variables are sufficient to specify a multi-component, multi-phase system.

The idea is from Gibbs and the derivation of the equation is:

Consider the general case: C components and P phases.
At equilibrium all pressures, temperatures, and each chemical potential is constant: <math>\begin{align}
 & p_{a}=p_{b}=\ldots =p_{P} \\ 
& T_{a}=T_{b}=\ldots =T_{P} \\ 
& \mu _{ia}=\mu _{ib}=\ldots =\mu _{iP};\text{    }i=1,2,\ldots C \\ 


The number of unknowns in each phase is (C+1): p, T, and (C-1) mole fractions
times the number of phases P
or <math>=\left( C+1 \right)P</math>]
The number of equations: <math>=\left( P-1 \right)\left( C+2 \right)</math>
Therefore the degrees of freedom are: <math>F=\left( C+1 \right)P-\left( P-1 \right)\left( C+2 \right)=C+2-P</math>
The phase rule: the number of degrees of freedom is: <math>F=C+2-P</math>

All about Phase Rule

Phase Rule A devise for relating the effect of the least number of independent variables upon the various phases that can exist in an equilibrium system containing a given number of components. Phase A consistent, physically distinct segment of a system that is separated from other segments of the system by binding surfaces. Degrees of Freedom1 Intensive variables that must be known to describe the system completely. Ex. temperature, concentration, pressure, density, etc. Components or Chemical Entities Constituents by which the composition or make-up of each phase in the system can be expressed. Usually the chemical formula or chemical equation is used. The phase rule is used to study and understand the way that temperature, pressure, concentration, etc. effect the phase of a substance.

The phase rule equation is as follows: F = C - P + 2 The F is the least number of degrees of freedom, the C is the least number of components in the system, the P is the number of phases present, and the 2 is the constant.

Understanding the number of degrees of freedom is usually the hardest part of understanding the phase rule. What we really need to know is which properties would we have to know to exactly duplicate that particular system. The number of degrees of freedom can be found out by working the equations, but you must decide which property you need to know.

The number of components is not necessarily that hard if you really think about it. Lets say we have a three phase system (liquid, solid, and gas). Water, ice, and water vapor are the phases. What is the number of components? You might say 3. You are wrong. 1 is the correct answer because all have the same chemical formula H2O. Now what about a 3 phase system CaCO3 = CaO + CO2 . Here any phase can be expressed using the other two phases therefore there are only 2 components.

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