ChemicalThermodynamicseasyFE ExamCoursework

Degrees of Freedom for a Binary Two-Phase System

A binary mixture (two chemical species) exists in vapour-liquid equilibrium — two phases, no chemical reaction.

Using the Gibbs phase rule, find the number of intensive degrees of freedom.

Given

C	2 -	Number of components
P	2 -	Number of phases

Hint 1

The Gibbs phase rule relates components, phases, and independent intensive variables.

Hint 2

F = C − P + 2, where the 2 comes from temperature and pressure.

Hint 3

Two components, two phases.

Worked solution — try the problem first

$F = C - P + 2$

where $C$ is components, $P$ is phases, and the $2$ accounts for temperature and pressure.

$F = 2 - 2 + 2 = 2$

$\boxed{F = 2}$

What this means physically. Two intensive variables may be fixed independently; everything else then follows. Fix temperature and pressure, and the equilibrium compositions $x$ and $y$ of both phases are determined. Alternatively fix $T$ and $x$ , and the pressure and $y$ follow.

Compare with a pure substance ( $C=1$ ) in two phases: $F = 1 - 2 + 2 = 1$ . That is why boiling water at a given pressure has exactly one temperature, whereas a binary mixture boils over a range — the extra degree of freedom is composition.

Note. The "+2" assumes only $T$ and $P$ matter. With an additional field (electric, magnetic, surface) the constant increases. A chemical reaction at equilibrium reduces $F$ by one per independent reaction.

Concepts:Gibbs phase ruleDegrees of freedomPhase equilibrium

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