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Chap. 6 Multiphase Systems

All chemical processes involve multiphase operations:

- Phase-change operations: freezing, melting, evaporation, condensation

- Separation and purification processes: leaching, absorption, distillation,

extraction, adsorption, crystallization, …

(Examples)

1. Brewing a cup of coffee - leaching(침출)

2. Removal of sulfur dioxide from a gas stream - absorption(흡수)

S SO2 in the air SO3 H2SO4(acid rain)

3. Recovery of methanol from an aqueous solution - distillation

4. Separation of paraffinic and aromatic hydrocarbons - liquid extraction(추출)

5. Separation of an isomeric mixture - adsorption(흡착), crystallization

-Molecular sieve

6. Concentrate O2 for breathing –impaired patients - adsorption

7. Obtain fresh water from seawater-evaporation, reverse osmosis

Driving force in the separation processes concentration difference

phase equilibrium

6.1 SINGLE –COMPONENT PHASE EQUILIBRIUM

6.1a Phase Diagram

A phase diagram of a pure substance is a plot of one system variable

against another ( mostly PT diagram ) that shows the conditions at which

the substance exists as a solid, a liquid, and a gas.

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PT diagram

vapor-liquid equilibrium: boiling point/vapor pressure

solid-liquid equilibrium: melting point(freezing point)

solid-vapor equilibrium: sublimation point

triple point

critical point: critical temperature/critical pressure

*Freezing point of water decreases with increasing pressure:

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CO2 Crystal

H2O Liquid

ice

*Molecular crystals: many small, discrete, covalently bonded

molecules by van der Vaals or hydrogen bonding

Methane(below -183C): FCC

H2O(Ih at atmospheric pressure): HCP

Many organic compounds: energetic materials, …..

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6.1b Estimation of Vapor Pressure

-The volatility of a species: the degree to which the species tends to transfer

from the liquid (or solid) state to the vapor state

-The vapor pressure of a species: a measure of its volatility

-Often vapor pressure data are not available at temperatures of interest.

- Measure the vapor pressure at the desired temperature

- Estimate the vapor pressure using an empirical correlation

Clapeyron equation: relationship between the vapor pressure of a pure

substance ( *p ) and the absolute temperature (T )

lg

v

VVT

H

dT

dp

ˆˆ

ˆ*

(6.1-1)

Where lg VV ˆ,ˆ : vapor와 liquid의 specific molar volume

vH : Latent heat of vaporization

When pressure is not extremely high: glglg VVVVV ˆˆˆ,ˆˆ

The vapor is assumed to be ideal gas: *

ˆp

RTVg

*

* ˆ

p

RTT

H

dT

dp v

2*

* ˆ

T

dT

R

H

p

dp v

Td

R

Hpd v 1ˆ

ln *

R

H

Td

pd vˆ

)1

(

ln * (6.1-2) used to determine heats of vaporization.

Clausius-Clapeyron equation: Suppose that the heat of vaporization of a

substance ( vH ) is independent of temperature,

BRT

Hp v

ˆln *

(6.1-3) Plot of *ln p vs.

T

1 should be straight line.

Antoine equation: an empirical equation

CT

BAp

*

10log ( CTmmHgp :,:* , constants A,B,C: Table B.4 )

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6.2 THE GIBBS PHASE RULE

Extensive variable(크기변수): depend on the system size(mass, volume, …)

Intensive variable(세기변수): temperature, pressure, density, …

degree of freedom(자유도, DF) : the number of intensive variables that can be

specified for a system at equilibrium.

Gibbs phase rule

cDF 2 , where : number of phase

c : number of species

Ex. 6.2-1 The Gibbs Phase Rule

Josiah Willard Gibbs (February 11, 1839 – April 28, 1903): an American

theoretical physicist, chemist, and mathematician. He devised much of the

theoretical foundation for chemical thermodynamics as well as physical

chemistry. As a mathematician, he invented vector analysis (independently of

Oliver Heaviside). Yale University awarded Gibbs the first American Ph.D. in

engineering in 1863, and he spent his entire career at Yale.

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6.3 GAS-LIQUID SYSTEMS: ONE CONDENSABLE COMPONENT

Saturation: the gas phase contains all the vapor of a condensable species it

can hold at the system temperature and pressure.

In an air-water system: humidity

Raoult’s law, single condensable species: )(* TpPyp iii

Superheated vapor: a vapor present in a gas in less than its saturation

amount: )(* TpPyp iii

Dew point: if a gas containing a single superheated vapor is cooled at constant

pressure, the temperature at which the vapor becomes saturated:

dpiii TpPyp *

Degree of superheat of the gas: the difference between the temperature and

the dew point of a gas

Boiling point of the liquid at the given temperature: the temperature at which

Pp *

Relative saturation (relative humidity) : %100)(*

i

i

rrp

phs

Molal saturation (molal humidity):gasdryvaporfreeofmoles

vaporofmoles

pP

phs

i

i

mm)(

)(

Absolute saturation (absolute humidity): gasdryofmass

vaporofmass

MpP

Mphs

dryi

ii

aa

)(

Percentage saturation (percentage humidity):

%100/

/%100

***

ii

ii

m

m

pppPp

pPp

s

shs

Ex. 6.3-1) composition of a saturated gas-vapor system

Ex) 6.3-2) Material Balances around a Condenser

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6.4 MULTICOMPONENT GAS-LIQUID SYSTEMS

6.4a Vapor-Liquid Equilibrium data

6.4b Raoult’s law and Henry’s law

Raoult’s law: )(* TpxPyp AAAA : Generally valid when Ax is close to 1.

Henry’s law: )(THxPyp AAAA : )(TH A is the Henry’s constant. Generally

valid when Ax is close to 0 provide that A does not dissociate, ionize, or react in

the liquid phase.

Ideal solution:

Ex.6.4-2) Raoult’s Law and Henry’s Law

6.4c Vapor-Liquid Equilibrium Calculations for Ideal Solutions

bubble point: the temperature at which first bubble forms when a liquid is

heated slowly at constant pressure.

dew point: the temperature at which the first liquid droplet forms when a vapor

is cooled slowly at constant pressure.

Suppose an Ideal solution follows Raoult’s law and contains species A, B, C,

… If the mixture is heated at constant pressure P to its bubble-point temp.,

bpT , the further addition of a slight amount of heat will lead to the formation of a

vapor phase. The partial pressures of the components are given by Raoult’s law.

,,,,* CBAiTpxp bpiii

bpiii TpxpP *

bpT may be calculated by trial and error. Tpi

* can be obtained by Antoine

equation or tables.

Bubble point pressure: the pressure at which the first vapor forms when a

liquid is decompressed at a constant temperature. The mole fraction in the

vapor in equilibrium with the liquid (ideal liquid) is

bp

ii

bp

ii

P

Tpx

P

py

)(*

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Suppose a gas phase contains the condensable components A, B, C, … and a

noncondensable component G at a fixed pressure P. If the gas mixture is

cooled slowly to its dew point, it will be in equilibrium with the first liquid that

forms. Assuming that Raoult’s law applies, the liquid phase mole fractions

are:

excludingGCBAiTp

Pyx

dpi

ii ,,,,

)(*

1)(*

dpi

ii

Tp

Pyx

Dew point pressure: the pressure at which the first liquid droplet forms when a

vapor is compressed at a constant temperature

)(

1

* Tp

yP

i

i

dp

Ex. 6.4-3) Bubble and dew-point calculations

6.4d Graphical Representation of Vapor-Liquid Equilibrium

Figure 6.4-1

Boiling: a specific type of vaporization process in which vapor bubbles form at

a heated surface and escape from the liquid.

Vaporization: molecular evaporation of liquid from a gas-liquid interface, which

may occur at temperatures below the boiling point.

Ex. 6.4-4) Bubble and Dew-point Calculations using Txy Diagrams

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6.5 SOLUTIONS OF SOLIDS IN LIQUIDS

6.5a Solubility and Saturation

Solubility of a solid in a liquid: the maximum amount of that substance which

can be dissolved in a specified amount of the liquid at equilibrium.

In general, g solute dissolved/100g solvent.

Saturated solution: A solution

that contains as much of a

dissolved species as it can at

equilibrium

Supersaturation: difference

between actual and equilibrium

concentrations.

Figure 6.5-1 Solubilities of inorganic solutes

Metastable zone width

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6.5b Solid Solubilities and Hydrate Salts

Polymorphism ( 다형(多形), 동질이형(同質異形), 동질다상(同質多像) )

- Ability of any element or compound to crystallize into at least two different

crystalline structures, but they should be identical in the liquid or gaseous

state.

- The different structures are called polymorphs, polymorphic modifications.

- If the material is an element, polymorphs are called allotropes.

- Differences in morphological appearance do not necessary reflect

polymorphism.

-Molecular conformation and packing caused by various intermolecular

forces, hydrogen bonding, van der Waals forces, interactions with solvents and

additives, etc..

-Which polymorphic form of a compound is formed depends on the

preparation and crystallization conditions: method of synthesis,

temperature, pressure, solvent, cooling and heating rate, seed crystals,

etc.

Ex 1)

C(fullerene)

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Example 2) Ammonium Nitrate ( NH4NO3 )

Ind. Eng. Chem. Res. 49, 12632-12637, 2010

6 polymorphs between - 200 and 125 C

I: Cubic, II: Tetragonal, III: Orthorhombic, IV: Orthorhombic, V: Tetragonal

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Pseudopolymorphism

Solvates (Hydrates) which form as the result of compound formation with the

solvent (water). Stoichiometric

*Clathrate 내포화합물·포접(包接)화합물: adductive crystallization, inclusion

compound (the host and the guest). Nonstoichiometric

Example ) Ind. Eng. Chem. Res., 40, 6111-6117, 2001

L-phenylalanine ( C6H5CH2CH(NH2)CO2H )

One of the essential amino acid

Pharmaceutical intermediate

Food intermediate-Aspartame (l-aspartyl-

phenylalanine methyl ester)

(L-aspartic acid)

Monohydrate Anhydrate

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6.5c Colligative Solution Properties

Colligative properties(결합특성, 총괄성): properties of a solution that depend

on the number of solute particles present but not on the chemical properties of

the solute: vapor pressure, freezing point, boiling point, osmotic pressure

Consider a solution in which the solute mole fraction is x and assume that the

solute is nonvolatile, nonreactive, and nondissociative and Raoult’s law

holds.

By Raoult’s law, effective solvent vapor pressure: ** )1( sses pxpp

Vapor pressure lowering: ****** )1()( sssesss xppxpppp

The lowing of solvent vapor pressure has two important consequences. The

solvent in a solution at a given pressure boils at a higher temperature and

freezes at a lower temperature than does the pure solvent at the same pressure.

Relationship between concentration and both boiling point elevation and

freezing point depression (Proof: prob. 6.87)

Boiling point elevation: xH

RTTTT

v

bbbsb ˆ

2

00

Freezing point depression: xH

RTTTT

m

mmsmm ˆ

2

00

ex) 6.5-4

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6.6 EQUILIBRIUM BETWEEN TWO LIQUID PHASES

6.6a Miscibility and Distribution Coefficients

Ex.6.6-1) extraction of acetone from water

Water/Chloroform-immiscible,

Water/Acetone-miscible, Chloroform/Acetone-miscible

Water/acetone solution + chloroform acetone/water + acetone/chloroform

distribution coefficient (partition ratio):

72.1

phaseWA

phaseCA

x

xK

6.6b Phase Diagram for Ternary Systems

Figure 6.6-1

Triangular phase diagram for water-acetone-MIBK (methyl isobutyl ketone) at

25C (1941)

Region A: a single liquid, Region B: two phases/tie line

Point K: 15wt% water, 65%acetone, 20%MIBK

Point M: 55wt% water, 15% acetone, 30% MIBK

two phases: point L(85% water, 12%acetone, 3%MIBK)

point N (4%water, 20%acetone, 76%MIBK)

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6.7 ADSORPTION ON SOLID SURFACES

ADSORPTION: The surface of a solid represents a discontinuity of its

structure. The forces acting at the surface are unsaturated. Hence, when

the solid is exposed to a gas, the gas molecules will form bonds with it

and become attached. ADSORBENT /ADSORBATE

Industrial sorbents

Activated carbon: 320m2/g

Molecular Sieve Carbon

(carbon molecular sieve)

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Activated Alumina

Silica Gel

Zeolite

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Macropores: d > 500 Å (50nm)

Mesopores: 20 Å < d < 500 Å

Micropores: d < 20 Å

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ADSORPTION ISOTHERM: adsorbate equilibrium data on a specific

adsorbent are often taken at a specific temperature.

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DETERMINATION OF AN ISOTHERM: CCl4/activated carbon (p.234)

Langmuir isotherm: iL

iL

ipK

paKX

1

*

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