PHASE EQUILIBRIA
AND ITS
CALCULATION
LIQUID LIQUID EQUILIBRIUM
SOLID SOLID EQUILIBRIUM
PRESENTATION GROUP 6
NAMES:
ROLL
NUMBERS:
ABUBAKAR ASIM
2K20-CHE-121
TALAL TARIQ
2K20-CHE-130
MUHAMMAD FAIZAN
2K20-CHE-231
HAMMAD BASHIR
2K20-CHE-123
ISRAR AHMED
2K20-CHE-236
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PHASE EQUILIBRIUM
Phase equilibria is a fundamental concept in thermodynamics that
deals with the coexistence of multiple phases in a system at
equilibrium. It explores the conditions under which different phases,
such as solids, liquids, and gases, can stably exist together.
Understanding phase equilibria is crucial in various fields, including
chemistry, materials science, and engineering.
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CALCULATIONS:
 Multiple phases at the same T and P are in equilibrium when the
chemical potential of each species is the same in all phases.
 one fundamental equation commonly used in phase equilibria
calculations is the Gibbs phase rule. The Gibbs phase rule
relates the number of components, phases, and degrees of
freedom in a system at equilibrium.
 The Gibbs phase rule can be expressed as follows:
F = C - P+ 2
 In this equation, F represents the degrees of freedom, C is the
number of components (chemically independent species) in the
system, and P is the number of phases coexisting at
equilibrium.
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 Phase equilibria calculations involve determining the
conditions at which different phases coexist in a system.
 These calculations are based on principles of
thermodynamics and require knowledge of the system's
composition, temperature, and pressure.
 The change in the total Gibbs energy of the two-phase
system is the sum of the equations for the separate
phases. the sum is:
 d(nG) = (nV)dP − (nS)dT + ∑ i μi αdni α + ∑ i μi β dni β
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LIQUID LIQUID
 Liquid-liquid equilibrium (LLE) refers to the state of equilibrium between
two immiscible liquid phases in a system. In thermodynamics, the
equilibrium condition for liquid-liquid equilibrium can be described using
the concept of chemical potential.
 For a two-component liquid-liquid system, the chemical potential of each
component in each phase must be equal at equilibrium. Mathematically,
this can be expressed as:
 μ₁(A, X₁, T, P) = μ₂(A, X₂, T, P)
 LLE is commonly observed in systems where two liquids are partially
soluble in each other but exhibit limited miscibility. Examples include the
separation of organic compounds in extraction processes, such as the
extraction of caffeine from coffee beans using organic solvents.

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 To determine the liquid-liquid equilibrium, phase diagrams known as ternary
diagrams are often used. Ternary diagrams visualize the composition space
of the system by plotting the concentrations of the three components in a
triangular diagram.
 The phase boundaries on the diagram represent the regions where different
liquid phases coexist. By locating the desired composition and temperature
point on the diagram, one can determine the equilibrium phases and their
relative amounts.
 Calculating liquid-liquid equilibrium can be complex, and various
thermodynamic models and experimental techniques are used to predict or
measure the equilibrium conditions accurately. These methods include tieline calculations, activity coefficient models, and experimental measurements
such as liquid-liquid extraction experiments.
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 The equations used to describe liquid-liquid equilibrium (LLE)
depend on the specific system and thermodynamic models
employed. One commonly used model is the NRTL (NonRandom Two-Liquid) model, which describes the activity
coefficients of the components in each liquid phase.
 In the NRTL model, the equation for liquid-liquid equilibrium can
be expressed as:
 ln(γ₁/γ₂) = α₂₁*(τ₁/(τ₁+τ₂))²
 In this equation, γ₁ and γ₂ are the activity coefficients of
Component 1 and Component 2, respectively, in their respective
liquid phases. α₂₁ is the interaction parameter between
Component 2 in the rich phase and Component 1 in the lean
phase. τ₁ and τ₂ are defined as:
 τ₁ = α₁₁ + α₁₂*(X₂/X₁) + α₁₃*(X₃/X₁) + …
 τ₂ = α₂₂ + α₂₁*(X₁/X₂) + α₂₃*(X₃/X₂) + ...
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SOLID LIQUID
EQUILIBRIUM
 Solid-liquid equilibrium (SLE) refers to the state of
equilibrium between a solid phase and a liquid phase in a
system. It occurs when the solid and liquid phases
coexist under specific conditions of temperature,
pressure, and composition.
 Solid-liquid equilibrium is commonly encountered in
processes such as melting, crystallization, and
dissolution. It is characterized by the equilibrium between
the dissolution of solute molecules or ions in the liquid
phase and their precipitation or crystallization in the solid
phase.
 To understand and predict solid-liquid equilibrium, phase
diagrams are often used. . Phase diagrams represent the
relationships between temperature, pressure, and
composition for a given system.
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 In the case of solid-liquid equilibrium, the phase diagram shows the
regions where the solid phase and the liquid phase coexist, as well
as the melting points and composition ranges of the solid phase.
 The calculation of solid-liquid equilibrium typically involves
thermodynamic models and experimental data. Thermodynamic
models, such as phase equilibrium models and activity coefficient
models, can be used to predict the solubility of solids in liquids and
vice versa. Experimental techniques, such as determining melting
points or conducting solubility experiments, provide data for
validating and refining these models.
 It enables the optimization of processes involving solid-liquid
transformations, such as crystallization processes for purifying
substances or controlling the formation of desired solid phases.
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THANK YOU
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