Chapter 13 & 15

Because of its relevance in Distillation

Why is VLE the most studied type of phase equilibrium?

activity coefficient

the _______________ is a correction factor that accounts for deviations from ideal solution behavior by relating a component's actual chemical potential to what it would be in an ideal solution at the same composition.

liquid-phase property

The activity coefficient is understood to be a ______________________

Formula in Gamma/Phi Formulations

• Ideal gas model for gas state

• Ideal solution model for liquid state

What are the two simplest models in VLE?

Raoult’s law

Ideal gas and ideal solution models are combined in the simplest treatment of vapor/liquid equilibrium in what is known as ___________________

1

This then produces the equation for Raoult’s Law

If the vapor phase is assumed to be in its ideal-gas state and the liquid phase is assumed to be an ideal solution, both Φi and γi approach what value?

Francois Marie Raoult

Who proposed Raoult’s Law?

• Only for Ideal mixtures

• The ideal-gas-state assumption means that Raoult’s law is limited in application to low to moderate pressures.

• system are chemically similar.

• it can be applied only to species of known vapor pressure

• this requires each species to be “subcritical,” i.e., at a temperature below its critical temperature.

What are the limitations of Raoult’s Law?

4 types of Bubble and Dew Point Calculations

In modified Raoult's law, what is "modified" is the addition of activity coefficients (γᵢ) to correct for non-ideal solution behavior

What is modified in Modified Raoult’s Law?

• Chemical potential must be equal across all phases

• Partial molar Gibbs energy should be minimized

• Constant T and P

• Fugacity of species i should be equal across all phases

Criterion for VL Equilibrium

Henry's law states that the partial pressure of a component in the vapor phase is directly proportional to its mole fraction in the liquid phase. Henry's constant - typically used for dilute solutions where one component (usually the solvent) follows Raoult's law while the solute follows Henry's law.

What is Henry’s Law?

Gibbs/Duhem

Henry’s law is related to the Lewis/Randall rule through the ______________ equation

Henry’s law applies to a species as it approaches infinite dilution in a binary solution, and the Gibbs/Duhem equation insures validity of the Lewis/Randall rule for the other species as it approaches purity.

Henry’s law applies to a species as it approaches infinite dilution in a binary solution, and the Gibbs/Duhem equation insures validity of the Lewis/Randall rule for the other species as it approaches purity.

• Henry’s law applies to a species as it approaches infinite dilution

• Lewis/Randall rule applies for the other species as it approaches purity

• Gibbs/Duhem equation insures validity

In Henry’s Law/Lewis-Randall Rule binary calculations,

• ___________ applies to a species as it approaches infinite dilution

• _____________ applies for the other species as it approaches purity

• __________________ insures validity

• Redlich-Kister Expansion

• Margules Model

• Van Laar Models

Different G^E models

Margules Equation

Simplified version of Redlich-Kister

Redlich Kister

Pure empirical approach with temperature-dependent parameters

5

Usually, how many parameters are used in Redlich Kister equation?

2, A₁₂ and A₂₁

How many adjustable parameters in Margules?

Van laar equation

they do not incorporate an explicit temperature dependence of their parameters, though this can be supplied on an ad hoc basis.

2

How many parameters in Van laar?

local composition

Theoretical developments in the molecular thermodynamics of liquid-solution behavior are often based on the concept of ________________________

G. M. Wilson in 1964

Who introduced the concept of Local Compositions?

2

How many parameters in Wilson equation?

Non-Random Two-Liquid

What is the meaning of NRTL?

3

How many parameters are used in NRTL?

• They are specific to a particular pair of species

• Independent of composition and temperature

Describe the parameters used in NRTL

• UNIQUAC

• UNIFAC

These are the local composition models of greater complexities

Universal Quasichemical

Meaning of UNIQUAC

UNIQUAC Functional-group Activity Coefficients

Meaning of UNIFAC

ΔG and its first and second derivatives are continuous functions of x1, and the second derivative is positive.

At fixed temperature and pressure, a single-phase binary mixture is stable if and only if

• Constant T and P

• Fugacity of species i is equal across all phases

Equilibrium criteria for LLE

• Crystallization

Phase behavior involving the solid and liquid states is the basis of important separation processes like

• Assume ideal-solution behavior for both phases

• Assume ideal-solution behavior for the liquid phase and complete immiscibility for all species in the solid state

Two cases in Solid-Liquid Equilibrium

sublimation curve

Solid/vapor equilibrium for a pure species is represented on a PT diagram by the _________________