PHASE
EQUILIBRIA
Ternary Systems
• Types:
 (Liquid –Vapor) ternary systems
 (Liquid – Solid ) ternary systems
Section 12
Today’s Topic :
• The Three component system , L-V type
– Degree of freedom analysis
– How to determine compositions ?
– The phase diagram
– Isothermal section
– Dew and bubble point calculations
Ternary Systems
• Applications of ternary systems:
1. Steel Industry
2. Refractories
3. Ceramics
4. Distillation
5. Liquid - Liquid Extraction
6. Leaching
7. Tea !!!
Ternary Systems
• Degree of Freedom Analysis:
• F=C–P+2–r
• = 3 – P + 2 -1 [ Isobaric diagrams]
• F=4-P
Ternary Systems
• Degree of Freedom Analysis:
• Fmax = 3
• These 3 independent variables are : T , x1 , x2
Three component system
• Method of representation :
• Use the Composition triangle
Three component system
Three component system
1 – Any vertex represent a one component system.
Three component system
2 – Any side represent a two component system
Three component system
3 – Any point inside the triangle represent a ternary system
4 – Any parallel line to a side of the triangle , represents a
locus of constant percentage of the third component
In this figure:
• We have a line parallel to the side BC
• Then , it contains a fixed percentage of A ( 30% )
• This line is a locus for all of the mixtures containing 30 % A
In this figure:
• We have a line parallel to the side AB
• Then , it contains a fixed percentage of C ( 30% )
• This line is a locus for all of the mixtures containing 30 % C
Three component system
5 – Any point inside the triangle can be located knowing two
compositions only.
Locate the mixture of the following composition :
30% A & 50 % B
Locate the mixture of the following composition :
30% A & 50 % B
Locate the mixture of the following composition :
30% A & 50 % B
Liquid Vapor Equilibrium in Ternary
systems
• The Binary Diagram :
• Assumptions:
– Total liquid solubility
– Ideal system
Liquid Vapor Equilibrium in Ternary
systems
• The Binary Diagram :
• Assumptions:
– Total liquid solubility
– Ideal system
Liquid Vapor Equilibrium in Ternary
systems
Liquid Vapor Equilibrium in Ternary
systems
Liquid Vapor Equilibrium in Ternary
systems
• Comparing binary and ternary diagram:
• Vaporous curve vs Vaporous Surface
• Liquidus line vs Vaporous Surface
Liquid Vapor Equilibrium in Ternary
systems
Vaporous Surface
Liquid Vapor Equilibrium in Ternary
systems
Liquid Vapor Equilibrium in Ternary
systems
Liquid Vapor Equilibrium in Ternary
systems
Liquid Vapor Equilibrium in Ternary
systems
• Comparing binary and ternary diagram:
1.Phases got on cooling :
• V
• L+V
• L
Liquid Vapor Equilibrium in Ternary
systems
Liquid Vapor Equilibrium in Ternary
systems
• Comparing binary and ternary diagram:
1.Phases got on cooling :
• V
• L+V
• L
Comparing binary and ternary
diagrams:
2.Method to get composition and amounts:
In binary system :
• Draw a tie line then use lever arm principle
In Ternary system:
• The first step is to draw the “ ISOTHERMAL SECTION”
L
L+V
V
L
L
L+V
V
L +V
V
Liquid Vapor Equilibrium in Ternary
systems
• How to draw a tie line :
• Lever Arm Principle: