Gibbs Phase Rule
The Gibbs phase rule counts independent intensive variables in a system at phase equilibrium.
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Formula
F, C and P are dimensionless counts; F is the number of independent intensive degrees of freedom
Variables & units
| Symbol | Meaning | Unit |
|---|---|---|
| Number of independent intensive degrees of freedom | count | |
| Number of independent chemical components | count | |
| Number of phases in equilibrium | count |
LaTeX
F=C-P+2,\qquad F_{p\,konstant}=C-P+1
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Derivation & background
For a nonreactive system with C components and P phases, F=C−P+2 when both temperature and pressure may vary. If pressure is fixed, one degree of freedom is removed and F=C−P+1. Components are independent chemical constituents after any reaction constraints are accounted for; phases are physically distinct, homogeneous parts. The rule counts variables, not phase amounts. It assumes thermodynamic equilibrium and does not describe how quickly equilibrium is reached or whether a metastable state persists.
Exam blueprint
Validity range
Applies to a nonreactive phase equilibrium without extra constraints. At fixed pressure use F=C−P+1; independent reactions and electrical or mechanical constraints change the component or degree-of-freedom count.
Derivation steps
Each phase has composition and state variables, while equilibrium conditions couple variables between phases.
- 1Count C independent components and P coexisting phases.
- 2Include temperature and pressure as two intensive degrees of freedom when both can vary.
- 3Subtract the phase-equilibrium constraints; for a nonreactive system F=C−P+2 remains.
Rearrangements
Degrees of freedom at constant pressure
An externally fixed pressure removes one independent degree of freedom.
Number of phases
For variable temperature and pressure in the nonreactive case.
Task variant
How many degrees of freedom does water have at its triple point when ice, liquid and vapour coexist?
Water is one component and three phases coexist: F=1−3+2=0.
Temperature and pressure are fixed.
Common mistakes
Count chemical species instead of independent components or keep counting a quantity fixed by an external constraint.
Determine components from independent material balances and remove fixed quantities before interpreting freedom.
Exam context
- Triple point, one- and multicomponent phase diagrams, and degrees of freedom at fixed pressure.
Formula cluster
Phase equilibria and thermodynamics
The phase rule counts allowed state changes; Clausius–Clapeyron describes a specific coexistence line.
Worked example
At water’s triple point, C=1 and P=3, hence F=1−3+2=0: neither temperature nor pressure can vary independently while all three phases coexist. Along a liquid–vapor boundary, P=2 gives F=1. Check: fixing pressure on that boundary leaves no additional independent intensive variable.
Applications
Read phase diagrams and count remaining independent conditions for phase coexistence.
How do you calculate with Gibbs Phase Rule?
Here is how to work through a typical Gibbs Phase Rule (F = C − P + 2; bei konstantem Druck: F = C − P + 1) task step by step:
- 1
Task
How many degrees of freedom does water have at its triple point when ice, liquid and vapour coexist?
Solution path
Water is one component and three phases coexist: F=1−3+2=0.
Temperature and pressure are fixed.
Frequently asked questions about Gibbs Phase Rule
What does the Gibbs phase rule count?+
It counts the independent intensive variables you can change without changing the number of phases or leaving equilibrium. For a nonreactive system without external constraints, F=C−P+2. Temperature, pressure and composition contribute variables, while phase-equilibrium conditions link them. At water’s triple point, ice, liquid and vapour coexist; with one component and three phases, F=0. Temperature and pressure are not freely selectable there. The rule describes degrees of freedom, not the amount of material present. The count describes local freedom of variables, not the number of possible phases or their amounts.
What is the difference between a component and a phase?+
A phase is a spatially uniform region with distinguishable physical properties, such as liquid water or ice. A component is an independent chemical substance needed to describe the compositions of all phases. Water remains the same single component in ice, liquid and vapour; there are three phases but C=1. A salt–water system can instead have two components distributed across several phases. Do not count every species as an independent component when reactions or material balances create dependencies. For reacting systems, also check which species are linked by stoichiometric constraints.
Why does fixing pressure reduce F by one?+
With variable pressure, temperature and pressure can both vary as intensive state variables. If the surroundings hold pressure fixed, one independent variable has already been specified. Therefore F=C−P+1 remains. For pure water in a one-phase state, F=1−1+1=1: at fixed pressure, temperature can vary without immediately forcing a second phase. At a two-phase boundary, F=0; that fixed pressure also determines the coexistence temperature. Constant pressure is therefore a boundary condition, not a new material property. The pressure setting is an external constraint; it does not change the number of chemical components.
How does the rule help read a phase diagram?+
It explains how many independent coordinates are needed to specify an equilibrium state on a diagram. For a pure substance in one phase with variable pressure, F=2 quantities are needed, usually pressure and temperature. On a two-phase line, F=1; pressure and temperature cannot change independently there. At the triple point, three phases coexist and F=0. A diagram shows these constraints geometrically. The rule does not provide the locations of boundaries; those require material data and a phase-equilibrium model. The rule describes the dimension of the equilibrium set, while the diagram shows its location and material properties.
When is the simple phase rule insufficient?+
The equation assumes a closed description of thermodynamic equilibrium without extra constraints. Chemical reactions reduce the number of independent components when they link species. Electric fields, surfaces, membranes or fixed compositions can add further conditions. The independent variables and component basis must then be chosen appropriately; reactive systems have corresponding extended counting methods. A negative F is not a physical degree of freedom, but usually signals that phases, components or constraints were counted incorrectly. The rule gives neither kinetics nor phase amounts. Surface or electrical contributions can add relevant variables, so the simple count may need extension.
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Curated exam set for "Gibbs Phase Rule":
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Which formula describes Gibbs Phase Rule?
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How do you rearrange Gibbs Phase Rule for Degrees of freedom at constant pressure?
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Which common mistake happens with Gibbs Phase Rule?
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Subject references and further reading
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Related formulas
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