Phase Equilibrium

Why it matters

Phase equilibrium is crucial in many engineering applications, such as the design of separation processes, chemical reactors, and refrigeration systems. Understanding phase equilibrium helps engineers predict how substances will behave under different temperature and pressure conditions, which is essential for optimizing industrial processes.

Key ideas

• Phase: A phase is a region of space where physical and chemical properties are uniform. Common phases include solid, liquid, and gas.
• Phase Equilibrium: This occurs when multiple phases coexist at equilibrium, meaning there is no net change in the amount of each phase over time.
• Gibbs Phase Rule: This rule provides the number of degrees of freedom (variables that can be changed independently) in a closed system at equilibrium. It is given by F = C - P + 2, where F is the degrees of freedom, C is the number of components, and P is the number of phases.
• Lever Rule: A graphical method used to determine the proportion of phases in a two-phase system.
• Clapeyron Equation: Describes the relationship between pressure and temperature along the phase boundary.

Formulas

• F = C - P + 2
  • F: Degrees of freedom (unitless)
  • C: Number of components (unitless)
  • P: Number of phases (unitless)
• dP_sat/dT = L/(T·Δv)
  • dP/dT: Slope of the phase boundary (Pa/K)
  • L: Latent heat of transition (J/kg)
  • T: Temperature (K)
  • ΔV: Change in specific volume (m³/kg)

For the stated phase rule, count independent components, not simply every reacting chemical species, and assume equilibrium with only temperature and pressure as external variables. Fixing pressure removes one degree of freedom. Phase equilibrium additionally requires equal temperature, pressure and each component’s chemical potential across coexisting phases. The Clapeyron relation uses latent heat and specific-volume change on the same mass basis.

Worked example

Problem: Calculate the number of degrees of freedom for a system with 2 components and 3 phases.

Given:

• Number of components, C = 2
• Number of phases, P = 3

Solution:

1. Use the Gibbs Phase Rule formula: F = C - P + 2
2. Substitute the given values: F = 2 - 3 + 2
3. Calculate: F = 1

Answer: The number of degrees of freedom is 1.

Common mistakes

• Confusing the number of components with the number of phases.
• Misapplying the Gibbs Phase Rule by not accounting for all components and phases.
• Incorrectly using the Clapeyron equation without proper units.

For GATE ME

Questions on phase equilibrium often involve calculating degrees of freedom using the Gibbs Phase Rule or applying the Clapeyron equation to find relationships between pressure and temperature. Practice problems involving multi-component systems and phase diagrams.

Quick check

1. What is the Gibbs Phase Rule formula?
2. How many phases are in a system with 2 components and 1 degree of freedom?
3. What does the Clapeyron equation relate?

Answers: 1. F = C - P + 2, 2. 3 phases, 3. Pressure and temperature along a phase boundary.