Unit 3: Phase Equilibrium
Course Code: CHM-DSC-251
Paper: Physical Chemistry - II
Table of Contents
1. Gibbs Phase Rule
The phase rule is a general relation used to determine the number of independent variables (degrees of freedom) required to define the state of a system in equilibrium.
F = C - P + 2
- P (Phases): A physically distinct, homogeneous, and mechanically separable part of a system.
- C (Components): The minimum number of independent chemical constituents needed to express the composition of every phase.
- F (Degrees of Freedom): The number of intensive variables (like P, T, concentration) that can be changed independently without altering the number of phases.
2. Clausius-Clapeyron Equation
This equation relates the temperature and pressure dependence of phase equilibria.
dP / dT = ΔH / (T * ΔV)
Applications: Used to calculate the enthalpy of vaporization, sublimation, or fusion, and to predict how boiling and melting points change with pressure.
Fugacity and Activity
For non-ideal systems, pressure (P) is replaced by Fugacity (f) and concentration is replaced by Activity (a) to maintain the form of ideal thermodynamic equations.
3. One Component Systems
In a one-component system (C=1), the phase rule becomes F = 3 - P.
Water (H2O) System
The phase diagram of water features three areas (Liquid, Solid, Gas), three curves (Vaporization, Fusion, Sublimation), and a Triple Point where all three phases coexist (P=3, F=0).
[Image of the phase diagram of water]Carbon Dioxide (CO2) System
Unlike water, the fusion curve for CO2 has a positive slope, and its triple point occurs at pressures higher than atmospheric (5.11 atm), explaining why it exists as "dry ice" (solid to gas) at 1 atm.
4. Two Component Systems
For binary systems, pressure is often kept constant, leading to the "Reduced Phase Rule": F' = C - P + 1.
| System Type | Example | Description |
|---|---|---|
| Eutectic Mixture | Pb-Ag (Lead-Silver) | Two components are miscible in liquid state but do not react or form compounds in solid state. |
| Congruent Melting | Zn-Mg (Zinc-Magnesium) | The compound formed melts at a constant temperature to give a liquid of the same composition. |
| Incongruent Melting | Solid Solutions | A solid compound decomposes into a new solid phase and a liquid of different composition. |
5. Three Component Systems
Commonly represented using Triangular Plots (Gibbs Triangle).
Example: Water-Chloroform-Acetic Acid. This system involves two partially miscible liquids (Water and Chloroform) and one liquid (Acetic Acid) miscible with both.
6. Exam Focus & FAQs
- Derivation: Be ready to derive the Phase Rule or the Clausius-Clapeyron equation.
- Diagrams: Practice drawing the Pb-Ag eutectic diagram and the H2O phase diagram.
- Definitions: Clearly distinguish between congruent and incongruent melting points.
Frequently Asked Questions
Q: What is a Triple Point?
A: It is the specific Temperature and Pressure at which the solid, liquid, and gas phases of a substance coexist in equilibrium.
Q: What is the degree of freedom at a eutectic point?
A: Since C=2 and P=3 (Liquid + Solid A + Solid B), F' = 2 - 3 + 1 = 0 (Invariant).
Q: Why is the slope of the ice-water curve negative?
A: Because the volume of ice is greater than the volume of liquid water (ΔV is negative), which is an anomaly.