Ch i l E i i P i i l Chemical Engineering Principles 2

Ch i l E i i P i i l Ch i l E i i P i i l 22Chemical Engineering Principles Chemical Engineering Principles 22((09052120905212))((09050905 ))

Binary and Binary and MulticomponentMulticomponent-- Multiphase Multiphase Binary and Binary and MulticomponentMulticomponent-- Multiphase Multiphase SystemsSystems

Dr.Dr.--Ing. Zayed AlIng. Zayed Al--HamamreHamamreg yg y

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan

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ContentContent

MultiMulti--component gas liquid systemcomponent gas liquid system MultiMulti--component gas liquid systemcomponent gas liquid system Solution of solid in liquidSolution of solid in liquid Equilibrium between tow liquid phasesEquilibrium between tow liquid phases Absorption on solid surfaceAbsorption on solid surfacerpt n n urfacrpt n n urfac


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MultiMulti--component Gas liquid systemscomponent Gas liquid systems When multicomponent gas and liquid phases are in equilibrium,

o Equilibrium relationships for the distribution of components between the two phases

are necessary for determining the different system variables.

o The compositions of the two phases at a given temperature and pressure are not

independentindependent

o Relationships governing the distribution of a substance between gas and liquid phases

are the subject matter of phase-equilibrium thermodynamicsj p q y

Vapor-Liquid Equilibrium Data

Tabulated data in Perry's Chemical Engineers' Handbook , pp. 2-76 through 2-89, gives

partial pressures of vapors over various liquid solutions.

Using Correlations available in Bruce E. Poling, John M. Prausnitz, John P. O’Connell,

The Properties of Gases and Liquids, 5th Edition, McGraw-Hill, New York, 2004


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ExampleExample

Quiz: Draw the flow sheet


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Example Cont.Example Cont. The equilibrium partial pressures of H2O and SO2 over a solution of the indicated

composition are


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Example Cont.Example Cont.


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MultiMulti--component Gas liquid systemscomponent Gas liquid systems

Provide relationships between PA, the partial pressure of A in the gas phase, and xA, the mole fraction of A in the liquid phase.

Valid

o When xA is close to 1, i.e., when the liquid is almost pure A.

o Over the entire range of compositions for mixtures of similar substances, such as

paraffinic hydrocarbons of similar molecular weights.


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MultiMulti--component Gas liquid systemscomponent Gas liquid systems

Valid

For sol tions in hich is close to 0 (dil te sol tions of A) pro ided that A does noto For solutions in which xA is close to 0 (dilute solutions of A) provided that A does not dissociate. ionize, or react in the liquid phase .

o Solutions of noncondensable gaseso Solutions of noncondensable gases

Perry's Chemical Engineers' Handbook.

A gas-liquid system in which the vapor-liquid equilibrium relationship for every volatile

H.W: list values of Henery’s constant for other gases-water/liquid systems

species is either Raoult's law or Henry's law is said to exhibit ideal solution behavior.

An ideal liquid solution is a mixture of liquids that exhibits ideal solution behavior at

ilib i


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10equilibrium.

ExampleExample

Hydrocarbons normally are relatively insoluble in water, so that the solution of ethane is probably

extremely dilute


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MultiMulti--component Gas liquid systemscomponent Gas liquid systemsVapor-Liquid Equilibrium Calculations for Ideal Solutions

Behavior of single species liquid, in a close vessel, upon heating at constant pressure:

o The temperature increases until the boiling point of the liquid is reached, and

thereafter

h li id io The liquid vaporizes at a constant temperature.

o Once the vaporization is complete, further addition of heat raises the temperature of

the vaporthe vapor.

Behavior of several component-liquid (mixture) , in a close vessel, upon heating at constant

pressure:pressure:

o The liquid temperature rises until a temperature is reached at which the first bubble

of vapor forms. p

o The vapor generated generally will have a composition different from that of the

liquid.


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VaporVapor--Liquid Equilibrium Calculations for Ideal SolutionsLiquid Equilibrium Calculations for Ideal Solutionso As vaporization proceeds, the composition of the remaining liquid continuously

changes, and hence so does its vaporization temperature

A i il h if i f i bj d d i A similar phenomenon occurs if a mixture of vapors is subjected to a condensation process at

constant pressure:

o At some temperature the first droplet of liquid forms and thereaftero At some temperature the first droplet of liquid forms, and thereafter

o The composition of the vapor and the condensation temperature both change.

T d i t l ti d ti ti h To design or control an evaporation or condensation process, separation processes such as

distillation, absorption, and stripping also requires information on the conditions at which

phase transitions occur and on the compositions of the resulting phases.

The bubble-point temperature of a liquid at the given pressure is the temperature at which

the first vapor bubble forms when the liquid is heated slowly at constant pressure.

The dew-point temperature at the given pressure is the temperature at which the first

liquid droplet forms when a gas (vapor) is cooled slowly at constant pressure.


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TxyTxy and and PxyPxy diagramsdiagrams

In a two-phase vapor-liquid mixture at equilibrium,

If ll th t i d d t i h i i ilib io If all the components can vaporize and condense, a component in one phase is in equilibrium

with the same component in the other phase.

o The equilibrium relationship depends on the temperature and-pressure, and perhapso The equilibrium relationship depends on the temperature and pressure, and perhaps

composition, of the mixture.

The Txy diagram is a plot of the equilibrium temperature versus the mole fraction of one of The Txy diagram is a plot of the equilibrium temperature versus the mole fraction of one of

the components usually the more volatile one-with curves being drawn for both the liquid

phase (T versus xA) and the vapor phase (T versus yA).

Equilibrium pressure can also be plotted against a mole fraction for a fixed temperature to

generate a Pxy diagram


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TxyTxy and and PxyPxy diagramsdiagramsVapor-liquid equilibrium for a binary mixture

The dashed lines show the equilibrium compositions


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TxyTxy and and PxyPxy diagramsdiagrams

At the pairs of points A and B, and C and D,

Th ti t t th i ti t th ilib io The respective pure components exert their respective vapor pressures at the equilibrium

temperature.

o In between the pairs of points as the overall composition of the mixture changes two phaseso In between the pairs of points, as the overall composition of the mixture changes, two phases

exist, each having a different composition for the same component as indicated by the dashed

lines.

o Two useful linear ("ideal") equations exist to relate the mole fraction of one component in the

vapor phase to the mole fraction of the same component in the liquid phase.


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BubbleBubble--point calculationpoint calculation

Further addition of a slight amount of heat will lead to the formation of a vapor phase in

ilib i ith th li id (th i id l )equilibrium with the liquid (the vapor is ideal gas).

The partial pressures of the components are given by Raoult's law,

II

The sum of the partial pressures must be the total system pressure, P

II

Trial and error calculation is required to find Tbp that satisfies the equation.


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BubbleBubble--point calculationpoint calculation1. Set of relationships for such as the Antoine equation or vapor-pressure charts or

tables.

2. Evaluating the partial pressures of each component from I

3. Substitute the partial pressures into II and find the temperature that satisfy the II.

4. Determining the composition (mole fraction) of each vapor-phase

The pressure at which the first vapor forms when a liquid is decompressed at a constant

temperature is the bubble-point pressure of the liquid at the given temperaturetemperature is the bubble point pressure of the liquid at the given temperature

The pressure for an ideal liquid solution at a specific temperature can be calculated from II

The mole fractions in the vapor in equilibrium with the liquid can then be determined as


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DewDew--point calculationpoint calculation A gas phase contains the condensable components A, B, C, ... and a noncondensable

component G at a fixed pressure P , yi is the mole fraction of component i in the gas.

o If the gas mixture is cooled slowly to its dew point, Tdp, it will be in equilibrium with the

first liquid that forms.

o Assuming that Raoult's law applies the liquid phase mole fractions is calculated aso Assuming that Raoult s law applies, the liquid-phase mole fractions is calculated as

III

o At the dew point of the gas mixture, the mole fractions of the liquid components (those

th t d bl ) t t 1

III

that are condensable) must sum to 1

IV


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DewDew--point calculationpoint calculation The value of Tdp can be found by trial and error once expressions for pi*(T) have been

substituted in IV

The composition of the liquid phase may then be determined from III

The dew-point pressure which relates to condensation brought about by increasing system The dew-point pressure, which relates to condensation brought about by increasing system

pressure at constant temperature. can be determined by solving IV for P

Liquid mole fractions may then be calculated from III with Tdp replaced by the system

temperature, T.


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Typical problemsTypical problems

Material balance is necessary in this caseMaterial balance is necessary in this case


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ExampleExample


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The solution procedure is to

o Choose a temperature, evaluate PA* and PB* for that temperature from the Antoine

o Evaluate f(Tbp ) from the above equation,

o Repeat the calculations until a temperature is found for which f(Tbp ) is sufficiently close

to 0.

Spreadsheet Solution


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H W R l thi bl i N t ' R lH.W: Resolve this problem using Newton's Rule


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The solution procedure is to

o Choose a temperature, evaluate PA* and PB* for that temperature from the Antoine

o Evaluate f(Tbp ) from the above equation,

o Repeat the calculations until a temperature is found for which f(Tbp ) is sufficiently close

to 0.


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In this system condensation brought about by increasing system pressure at constant temperatureIn this system, condensation brought about by increasing system pressure at constant temperature


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Assuming that nitrogen is insoluble in the condensate


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Figure 6.4-1 (p. 262): Txy and Pxy diagrams for benzene-toluene systemFigure 6.4 1 (p. 262): Txy and Pxy diagrams for benzene toluene system.

H.W: Re- generate these figures and show your calculations.


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Graphical Representations of VaporGraphical Representations of Vapor--Liquid EquilibriumLiquid Equilibrium

To determine a bubble-point temperature for a given liquid composition,

o Go to the liquid curve on the Txy diagram for the system pressure and read the desiredo Go to the liquid curve on the Txy diagram for the system pressure and read the desired

temperature from the ordinate scale.

o Move horizontally to the vapor curve to determine the composition of the vapor in y p p p

equilibrium with the given liquid at that temperature

To determine a dew-point temperature,

o Look up the specified mole fraction of A in the vapor phase, read the dew-point

temperature from the corresponding ordinate value of the vapor curve, and

o Move horizontally to the liquid curve and down to read the composition of the liquid in

equilibrium with the vapor

If a noncondensable species is present in the gas phase, follow the procedure in the previous

example


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ExampleExampleWhat will happen if Heat is added to a 55 mole% benzene and 45 mole% toluene liquid mixture

at a fixed pressure of 1 atm.

o The mixture will begin to boil at 90°C, and

o The vapor generated will contain 77% benzene.

o However, once a small amount of liquid has

been vaporized, the remainder no longer

contains 55% benzene; it contains less sincecontains 55% benzene; it contains less, since

the vapor produced is relatively rich in this

component.

o Consequently, the temperature of the system

steadily rises as more and more liquid is

vaporized and the compositions of both phasesvaporized, and the compositions of both phases

change continuously during the process


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ExampleExample


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ExampleExample

QuizQuiz


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

heated surface and escape from the liquid,

It does not refer to molecular evaporation of liquid from a gas-liquid interface, which may

occur at temperatures below the boiling point.

liquid boils at a temperature at which the vapor pressure of the liquid equals the total pressure

of the atmosphere above it.

If i t i h t d l l i t i b bbl ill f t th h t d If a mixture is heated slowly in an open container, vapor bubbles will form at the heated

surface and emerge into the gas phase when the vapor pressure of the liquid equals the

pressure above the liquid.

The boiling point may therefore be determined approximately

For a mixture that is 70 mole% benzene and 30 mole% toluene is to be distilled in a batch

distillation column, Tboiling = 87oC, yb = 88 %, yT = 12 %.


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Solution of Solid in LiquidsSolution of Solid in LiquidsSolubility and SaturationSolubility and Saturation The solubility of a solid in a liquid is the maximum amount of that substance that can be

dissolved in a specified amount of the liquid at equilibrium.

This physical property depends on,

o The solute-solvent pair

o The temperature

A solution that contains as much of a dissolved species as it can at equilibrium is said to be

saturated with that species.

A l ti i ilib i ith lid l t t b t t d ith th t l t if it t A solution in equilibrium with solid solute must be saturated with that solute; if it were not,

more solute would dissolve.

If a saturated solution is cooled the solubility of the solute generally decreases; If a saturated solution is cooled, the solubility of the solute generally decreases;

In order for the cooled solution to return to equilibrium, some solute must come out of

solution as solid crystals.


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Solubility and SaturationSolubility and Saturation The properties of liquids and solids are only slightly affected by pressure, a single plot of

solubility (an intensive variable) versus temperature may be applicable over a wide pressure

rangerange

Supersaturated solution is a solution in a

metastable condition in which the

concentration of the solute is higher than the

equilibrium value at the solution

t ttemperature.

Supersaturation is the difference between

actual and equilibrium concentrations

The solubilities of many substances in water,

ethyl alcohol, and diethyl ether at specified

actual and equilibrium concentrations

Solubilities of inorganic solutes.

temperatures available in Perry's Chemical Engineers' Handbook on pp. 2-7 through 2-47

and 2-121 through 2-124

The effect of temperature on

solubility can vary from system to

system


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38and 2 121 through 2 124 system

ExampleExample


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Both the filtrate and the liquid retained in the filter cake are in equilibrium with solid AgNO3,

crystals.y

Saturated with AgNO3 at 20°C


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Solid Solid SolubilitiesSolubilities and Hydrated Saltsand Hydrated Salts For a two-component system at equilibrium containing a solid solute and a liquid solution,

Specifying temperature and pressure fixes the values of all other intensive variablesSpecifying temperature and pressure fixes the values of all other intensive variables.

When certain solutes crystallize from aqueous solutions, the crystals are hydrated salts,

containing water molecules bonded to solute molecules (water of hydration).

The number of water molecules associated with each solute molecule may vary with the

crystallization temperaturecrystallization temperature.

The solid crystals may also be anhydrous (water free) salt depending on the crystallization

temperature.p


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Solid Solid SolubilitiesSolubilities and Hydrated Saltsand Hydrated Salts Magnesium sulfate and sodium sulfate are solutes that forms hydrated salts, which can exist in

five different forms in different temperature ranges.

hydrated saltshydrated salts


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ExampleExample


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Example Cont.Example Cont.To determine the temperature at which the solution reaches saturation,

The saturation temperature of thisThe saturation temperature of this

solution is 74°C

Assume that the solution leaving the

crystallizer is saturated at 40°Ccrystallizer is saturated at 40 C.


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ExampleExample

A th t th l ti l i th t lli i i ilib i ith th lid t l d Assume that the solution leaving the crystallizer is in equilibrium with the solid crystals and

is therefore saturated with MgSO4.


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Two independent balancesp

Where the molecular weight of anhydrous magnesium sulfate is 120.4 and that of the

heptahydrate salt is 246 4


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49heptahydrate salt is 246.4.

ColligativeColligative Solution PropertiesSolution Properties Physical properties of a solution generally differ from the same properties of the pure solvent.

The changes in the values of several properties depend only on the concentration of solute

in the solution, and not on what the solute and solvent are.

Such properties are referred to as colligative solution properties.

Colligative properties are

o Vapor pressure,

o Boiling point,

o Freezing point and

o Osmotic pressure

Simple solvent-solute system are those with the

o Solute is nonvolatile (i.e., has a negligible vapor pressure at the solution temperature) and

o The dissolved solute neither dissociates (which rules out ionizing acids, bases, and salts)


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50o Nor reacts with the solvent

ColligativeColligative Solution PropertiesSolution Properties For a solution in which the solute mole fraction is x and the vapor pressure of the pure solvent

at the solution temperature is ps*, then the partial pressure of the solvent is

Since the solute is nonvolatile Since the solute is nonvolatile,

o The solvent is the only component of the liquid solution that is also in the vapor.

o The pressure exerted by this vapor is referred to as the effective solvent vapor pressure:o The pressure exerted by this vapor is referred to as the effective solvent vapor pressure:

o Since x-and hence (1 - x )-is less than one, the effect of the solute is to lower the effective

solvent vapor pressure.

o The vapor pressure lowering, defined as the difference between the vapor pressure of the

pure component and the effective vapor pressure of the solvent,


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ColligativeColligative Solution PropertiesSolution Propertieso vapor pressure lowering is a colligative property,

The solvent in a solution at a given pressure boils at a higher temperature and freezes at a 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.

h l i li id d lid li id The solution vapor liquid and solid-liquid

equilibrium curves lie below the solvent

curves,

The effective vapor pressure at a given

temperature and freezing point at a given

Phase-equilibrium curves for pure solvent and

pressure for the solution are lower than those

of the pure solvent.

The higher the solute concentration the Phase equilibrium curves for pure solvent and

solution. The higher the solute concentration, the

greater is the separation between the pure

solvent and the solution curves


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ColligativeColligative Solution PropertiesSolution Properties The effect of the vapor pressure lowering is to lower the triple point of the solution relative to

pure solvent

For dilute solutions, the relationships between

concentration and both boiling point elevation and freezing point depression.

ExampleExample


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the measured boiling point elevation


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Example Cont.Example Cont.The effective solvent vapor pressure at 25°C is determined from the vapor pressure of pure water

at this temperature (found in Table B.3)


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Equilibrium between two liquid phasesEquilibrium between two liquid phasesMiscibility and Distribution CoefficientsMiscibility and Distribution Coefficients

When two fluids (A and B) are mixed with each otherWhen two fluids (A and B) are mixed with each other,

One homogeneous phase could form (the two liquids are totally miscible)

A single phase results if the mixture contains more than a certain limit of A or B by mass A single phase results if the mixture contains more than a certain limit of A or B by mass.

They would be termed immiscible if one phase contained a negligible amount of A and the

other a negligible amount of B.

Partially miscible

Two phase could form with each liquid exists in one phase (totally immiscible)

If a third substance is added to a two-phase liquid mixture, it distributes itself according to its

relative solubility in each phase.


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Miscibility and Distribution CoefficientsMiscibility and Distribution CoefficientsExampleExample Water and methyl isobutyl ketone (MIBK) system.

o If water and MIBK are mixed at 25°C, a single phase results if the mixture contains

more than either 98% water or 97.7% MIBK by mass; otherwise,

Th i t t i t t li id h f hi h t i 98% H O d 2%o The mixture separates into two liquid phases, one of which contains 98% H2O and 2%

MIBK and the other 97.7% MIBK and 2.3% H2O

Acetone-water -chloroform system Acetone water chloroform system

o Acetone is soluble in both water and chloroform, but much more so in chloroform

o Water and chloroform are nearly immiscible liquids.o W e d c o o o e e y sc b e qu ds.

o If a mixture of acetone and water is contacted with chloroform, a substantial portion of

the acetone enters the chloroform-rich phase.

o Separation of the acetone and water may then be accomplished easily by allowing the

mixture to settle and separating the two phases (liquid extraction).


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Miscibility and Distribution CoefficientsMiscibility and Distribution Coefficients

Suppose A and S are two nearly immiscible liquids and B is a solute distributed between the

phases of an A-S mixture.

The distribution coefficient (also known as partition ratio) of component B is the ratio of

the mass fraction of B in the S phase to that in the A phasethe mass fraction of B in the S phase to that in the A phase.

Distribution coefficients for a number of ternary (three-component) liquid systems are

available in the Chemical Engineers' Handbook on pp. 15-10 through 15-14 lists.g pp g

H.W: Find the distribution coefficient of other liquid systems


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ExampleExample

Q i i i i l i b D i i i d h flQuantities are given in volumetric base. Densities required to convert them to mass flow rate.

The densities of the pure substances are given in Table B.1:


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Phase Diagrams for Ternary SystemsPhase Diagrams for Ternary Systems The behavior of partially miscible ternary (three-component) systems may be represented on

a triangular phase diagram, which may take the form of an equilateral triangle or a right

triangle

Each apex of the triangle represents a

single component and edges represent

binary solutions.

Edge b on represents solutions of H O and Edge b on represents solutions of H2O and acetone

Edge a on represents solutions of MIBK g pand acetone

Edge c on represents solutions of H2O and MIBK

Triangular phase diagram for water-acetone-methyl

isobutyl ketone (composition in wt%) at 25°C


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62isobutyl ketone (composition in wt%) at 25 C.

Phase Diagrams for Ternary SystemsPhase Diagrams for Ternary Systems Any mixture whose composition falls in

region A, such as at point K, is a single-

phase liquid

DF = 2 + 3 -1 = 4

phase liquid,

o Point K represents a mixture that is 20.0

wt% MIBK, 65.0% acetone, and 15.0%

water

Any mixture whose overall

composition falls in region B

separates into two phases.

Th li h i hi i B The lines shown within region B

called tie lines connect compositions

of the two liquid phases in

equilibrium with each other


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Phase Diagrams for Ternary SystemsPhase Diagrams for Ternary Systems If MIBK, water, and acetone are blended

so that a mixture with overall composition

at point M (55.0 wt% water, 15.0%

acetone, 30.0% MIBK) results,

o The mixture separates into phaseso The mixture separates into phases

having compositions given by points L

(water rich phase: 85 wt% water, 12%

acetone, 3% MIBK) and N (MIBK rich

phase: 4 wt% water, 20% acetone, 76%

MIBK).MIBK).

o The ratio of the mass of the MIBK-rich

phase to the mass of the H2O -rich

phase is


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Phase Diagrams for Ternary SystemsPhase Diagrams for Ternary Systems

S if i th l f ti f f th

If pressure (which in any case has little effect on liquid properties) and temperature are fixed.

one degree of freedom remainsDF = 2 + 3 -2 = 3

Specifying the mole fraction of one of the

components in one of the phases is therefore

sufficient to determine the compositions of both

phases.

Specifying that the weight fraction of acetone is 25% the MIBK-rich

in the MIBK-rich phase fixes both the composition of

that phase and the composition of the water-rich

phase.

phase

the water-richp the water rich

phase

H2O -rich phase-82.0% H2O, 13%

acetone 5 % MIBK; MIBK rich phaseacetone, 5 % MIBK; MIBK-rich phase-

70% MIBK, 5% H2O, 25.0% acetone.

Mass ratio of MIBK phase to H2O phase


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Phase Diagrams for Ternary SystemsPhase Diagrams for Ternary Systems

Show that a mixture with a composition of 4% acetone, 51% MIBK, and 45% H2O separates

QuizQuiz

into two phases. What is the composition of each phase? Calculate the ratio of the mass of the

MIBK-rich phase to the mass of the H2O -rich phase.

H2O -rich phase-95.0% H2O, 2.5% acetone, 2.5% MIBK; MIBK-rich phase-92.5% MIBK, 2.5%

H2O, 5.0% acetone. Mass ratio of MIBK phase to H2O phase


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ExampleExample


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Example Cont.Example Cont. Since the two product streams are in equilibrium, their compositions must lie on the phase

envelope and must be connected by a tie line

The composition of mR is 5% acetone, 93% H2O and 2% MIBK

The composition of mE is 10% acetone, 87% MIBK, and 3% H2O p E , , 2


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Adsorption on solid surfaceAdsorption on solid surface The attraction of chemical species in gases and liquids to the surfaces of solids.

The solid is known as an adsorbent and the component attracted to the solid surface is an

adsorbate.

The solid characterized by an extremely high surface area (e.g., about 320 m2/g of activated

carbon)carbon).

The specific components in a fluid characterized by high affinity of for the surface of a solid.

For example baking soda or charcoal may be placed in a refrigerator to remove unacceptable For example, baking soda or charcoal may be placed in a refrigerator to remove unacceptable

odors,

Compressed air may be dried and purified by passing it through a bed of calcium chloride to p y p y p g g

remove water vapor

Adsorbate equilibrium data on a specific adsorbent are often taken at a specific temperature

and are referred to as adsorption isotherms.


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Adsorption on solid surfaceAdsorption on solid surface The isotherms are functions or plots that the maximum mass of adsorbate i that

can be held by a unit mass of the adsorbent, to , concentration or partial pressure of

adsorbate i in the fluid contacting the solidadsorbate i in the fluid contacting the solid.

At low adsorbate partial pressures, isotherms may

be linear

The Langmuir isotherm is a more complex

i th t i lid f texpression that is valid for some systems over a

wider range of adsorbate partial pressures or

concentrations

Langmuir adsorption isotherm for carbon

tetrachloride on activated carbon at 34°C.


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ExampleExample


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Ch i l E i i P i i l Chemical Engineering Principles 2