nonideal behavior dicky dermawan @gmail.com itk-234 termodinamika teknik kimia ii

Nonideal Behavior

Dicky Dermawanwww.dickydermawan.net78.net

dickydermawan@gmail.com

ITK-234 Termodinamika Teknik Kimia II

Nonideal Behavior, Outline

Introduction: Effect of Nonideality Partial Molar Properties Residual Properties

Fugacity & Fugacity Coefficient

Excess Properties Activity & Activity Coefficient

Intorduction: Effect of Nonideality:

Tetrahydrofuran(1)/Carbon-tetrachloride(2)

t-x-y diagramP-x-y diagram

30oC 1 atm

P-xy Diagram Acetonitril(1)/Nitrometana(2) @

0 0.2 0.4 0.6 0.8 1

x1, y1

txy diagram Acetonitril(1)/Nitromethane(2)

0 0.2 0.4 0.6 0.8 1x1, y1

@ P = 70 kPa

Effect of Nonideality: Chloroform(1)/Tetrahydrofuran(2)

30oC 1 atm

0 0.2 0.4 0.6 0.8 1

x1, y1

0 0.2 0.4 0.6 0.8 1x1, y1

@ P = 70 kPa

Effect of Nonideality: Furan(1)/Carbontetrachloride(2)

30oC 1 atm

0 0.2 0.4 0.6 0.8 1

x1, y1

0 0.2 0.4 0.6 0.8 1x1, y1

@ P = 70 kPa

Effect of Nonideality: Ethanol(1)/Toluene(2)

65oC1 atm

0 0.2 0.4 0.6 0.8 1

x1, y1

0 0.2 0.4 0.6 0.8 1x1, y1

@ P = 70 kPa

Effect of Nonideality: x – y Diagram at Constant P = 1

a. Tetrahydrofuran(1)/Carbon-tetrachloride(2)

b Chloroform(1)/Tetrahydrofuran(2)

c. Furan(1)/Carbontetrachloride(2)

d. Ethanol(1)/Toluene(2)

Partial Molar Properties

.etc,Gor ,V ,S ,H ,UM iiiiii

ii Mx MSolution Properties:

….are properties of component i in the state of mixtures, which, in general

different from that in the state of pure species

Partial Properties:

Pure-species Properties: .etc,Gor ,V ,S ,H ,UM iiiiii

NOT: ii Mx M

What physical interpretation can be given for, viz. partial molar

volume ?

Methanol – Water Mixture, An Example

For pure species at 25oC:Methanol (1) : V1 = 40.727

cm3/molWater (2) : V2 = 18.068 cm3/molWhat is the volume of 10 moles of methanol/water solution containing 30% mol of methanol?

Most people would think, logically:

Mol of methanol : 0.3 x 10 moles = 3 moles

Mol of water : (1-0.3) x 10 moles = 7 moles

Volume of methanol : 3 moles x 40.727 = 122.181 cm3

Volume of water : 7 moles x 18.068 = 126.476 cm3

Thus, the total volume : 122.181 + 126.476= 248.657 cm3

Wrong answer! The correct answer is 240.251 cm3

Thus there is 240.251 – 248.657 = -8.406 cm3 deviation from expected value

ii Mx M

More on Partial Molar Properties

jn,P,Ti

nMnMd i

n,P,Tin,Tn,Pj

.),.........n,n,n,P,T(MnM 321

.....dn

2,...n,n,P,T2

1,...n,n,P,T1

n,Tn,P

ii Mx MNOT: ii Mx M

Chemical Potential as Partial Molar Property

Criteria for Vapor - Liquid Equilibria

jn,P,Tii n

The chemical potential of i-th component is

defined as:

Chemical Potential as Partial Molar Property

jn,P,Ti

nGnGd i

n,P,Tin,Tn,Pj

If we set M = G:

jn,P,Tii n

The definition of chemical potential:

Evaluation of Partial Molar Properties Methanol – Water Mixture Example

Methanol mol fraction

Molar volume, mL/mol

0 18.10.114 20.30.197 21.90.249 23.00.495 28.30.692 32.90.785 35.20.892 37.9

1 40.7

0 0.2 0.4 0.6 0.8 1

ii Mx M

ExerciseA group of students came across an unsuspected supply

of laboratory alcohol, containing 96 mass-percent ethanol and 4 mass-percent water.

As an experiment they decided to convert 2 L of this material into vodka, having a composition of 56 mass-percent ethanol and 44 mass-percent water. Wishing to perform the experiment carefully, they search the literature and found the following partial-specific volume data for ethanol – water mixtures at 25oC and 101.3 kPa.

The specific volume of water at 25oC is 1.003 L/kg. How many L of water should be added to the 2

L of laboratory alcohol, and how many L of vodka result?

1.243 1.273 L/kg ,V

0.953 0.816 L/kg ,V

In vodka ethanol 96% In

Fugacity, f

PlndTRdG ig

flndTRdG

lndTRdGR

Ideal gas :

Real gas :

igR GGG Residual Gibbs energy :

Fugacity coefficient :

At constant T

Residual Property

igR VVV

RT)1Z(VR

dPVdTSdG

Evaluation of Pure Component Fugacity, fi

dPVdG Ri

Real gas :

Pure Component Fugacity Coefficient:

The fugacity :

Ri lnTR

At constant T:

dP)1Z(

dP)1Z( ln

RT)1Z(V i

From the following compressibility data for hydrogen at 0oC, determine the fugacity of

hydrogen at 950 atm

P, atm Z P, atm Z

100 1.069 600 1.431200 1.138 700 1.504300 1.209 800 1.577400 1.283 900 1.649500 1.356 1000 1.720

From the following compressibility data for isobutane,

determine the fugacity of butane at various temperature and pressure

P/bar 340 K 350 K 360 K 370 K 380 K

Evaluation of Pure Component Fugacity, fi from

Equation of State

PB ln i

c BBTR

Virial :

422.0083.0B

172.0139.0B

Critical Constants & Accentric Factors:Paraffins

Tc/K Pc/bar Vc/10-6m3.mol-1 Zc

Critical Constants & Accentric Factors:

Olefin & Miscellaneous Organics

Miscellaneous Organic CompoundsTc/K Pc/bar Vc/10-6m3.mol-1 Zc

Elementary Gases

Miscellaneous Inorganic CompoundsTc/K Pc/bar Vc/10-6m3.mol-1 Zc

Evaluation of Pure Component Fugacity, fi from Virial Equation of State, Example

Using virial equation of state,

calculate the fugacity and fugacity coefficient of:

1. Pure methyl-ethyl-ketone

2. Pure toluene

at 50oC and 25 kPa.

The required data:

ij Tcij/K Pcij/bar Vcij/cm3.mol-1 Zcij wij

11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257

Evaluation of Pure Component Fugacity, fi from

Equation of State

TR42748.0a

Redlich-Kwong:

5.1TRb

aZ)h1(ln1Z ln

TR08664.0b

}to be solved simultaneously

Evaluation of Pure Component Fugacity, fi from Redlich-Kwong Equation of StateUsing Redlich - Kwong equation of state,

2. Pure toluene

at 50oC and 25 kPa.

The required data:

11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257

Evaluation of Pure Component Fugacity, fi :

Pitzer’s Generalized Correlation

T,Pf rr0

T,Pf rr1

Evaluation of Pure Component Fugacity, fi : Pitzer Correlation

Using Pitzer Correlation,

2. Pure toluene

at 50oC and 25 kPa.

The required data:

11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257

Evaluation of LiquidPure Component Fugacity, fi

Poynting factor

Fugasity of saturated vapor,

calculated exactly as calculating gas phase fugacity

PPVexpP f

satiisat

Since Vl is a weak function of P at temperatures well below Tc:

Estimation of Liquid Density

Rackett Equation:

2857.0r )T1(

ccsat ZVV

Examples ofEvaluation of Liquid Pure Component Fugacity, fi

Estimate the fugacity of liquid acetone at 110oC and 275 bar.

At 110oC the vapor pressure of acetone is 4.36 bar and the molar volume of

saturated-liquid acetone is 73 cm3.mol-1

Estimate the fugacity of liquid n-butane at 120oC and 34 bar.

At 120oC the vapor pressure of n-butane is 22.38 bar and the molar volume of

saturated-liquid n-butane is 137 cm3.mol-1

Examples ofEvaluation of Liquid Pure Component Fugacity, fi11.10

The normal boiling point of n-butane is 0.5oC.

Estimate the fugacity of liquid n-butane at this temperature

and 200 bar.

The normal boiling point of 1-pentene is 30.0oC.

Estimate the fugacity of liquid 1-pentene at this temperature

and 350 bar.

The normal boiling point of isobutane is -11.8oC.

Estimate the fugacity of liquid isobutane at this temperature and

150 bar.

Examples ofEvaluation of Gas & Liquid Pure Component Fugacity, fi

253 P1041.11P1086.91Z

Prepare plots of f vs P and f vs P for isopropanol at 200oC for the pressure range

from 0 to 50 bar. For the vapor phase, values of Z are given by:

Where P is in bars. The vapor pressures of isopropanol at 200oC is 31.92 bar, and

the liquid-phase isothermal compressibility k at 200oC is 0.3.10-3 bar-1,

independent of P.

Hint: Critical constants:

Vc = 219 cm3/mol Tc 508,8 K

Pc = 53,7 bar Zc = 0,278

Examples ofEvaluation of Gas & Liquid Pure Component Fugacity, fi

Prepare plots of f vs P and f vs P for 1,3-butadiene at 40oC for the pressure range

from 0 to 10 bar. At 40oC The vapor pressures of 1,3-butadiene is 4.287 bar.

Assume virial model to be valid for the vapor phase.

The molar volume of saturated liquid 1,3-butadiene at 40oC is 90.45 cm3.mol-1

Fugacity of Steam and Water,Using Steam Table

P* : lowest value of P in steam table

At P >= Pisat, i.e. liquid phase water:

PPVexpP f

satiisat

Up to Pisat, i.e. gas phase water (steam):

Example of Steam and Water Fugacity Calculation Using Steam Table

From data in the steam tables, determine a good estimate for f/fsat of liquid water at

100oC and 100 bar, where fsat is the fugacity of saturated liquid at 100oC.

Steam at 13000 kPa and 380oC undergoes an isothermal change of state to a pressure of

275 kPa. Determine the ratio of the fugacity in the final state to that in the initial

Steam at 1850 psia and 700oF undergoes an isothermal change of state to a pressure of

40 psia. Determine the ratio of the fugacity in the final state to that in the initial

Fugacity of Mixtures

By Byy2ByB 222

21221112

cijjiij BB

ji ByyB

Are formulated exactly as calculation for pure component, but we use Mixing

Rules to obtain the parameters

Virial

For binary mixtures, i = 1,2 and j = 1,2

icomponent pure of BBB iii

)k1(TTT ijcjcicij2

cijcijcij V

cjcicij

cjcicij 2

PB ln i

Example of Calculation forFugacity of Mixtures Using Virial EquationEstimate the fugacity and fugacity coefficient of an equimolar mixture of methyl-ethyl-ketone

(1) and toluene (2) at 50oC and 25 kPa

The required data are as follows:

11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257

Fugacity of Components in Mixture

f̂ˆ i

lnn ˆln

jnP,T,ii

Ri ˆ lnTR

Ri lnTR

is partial molar property of)ˆln( i )ln( i

Virial, binary mixtures:

)yB(RT

Pˆ ln

)yB(RT

Pˆ ln

12111212 BBB2

Fugacity of Components in Binary Mixtures, Example using Virial Eqn.Estimate the fugacity and fugacity coefficient of methyl-ethyl-ketone (1) and toluene (2) for an

equimolar mixture at 50oC and 25 kPa.

Set all kij = 0

The required data are as follows:

11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257

Estimate the fugacity and fugacity coefficient of ethylene (1) and propylene (2) for a binary

mixture of 25% ethylene as a gas at 200oC and 20 bar.

Set all kij = 0

More on Virial Eqn:Fugacity of Ternary and Multicomponent Mixtures

iiikikkk )2(yy

Pˆ ln

cijjiij BB

ji ByyB

Mixing Rules :

For ternary mixtures, i = 1,2,3 and j = 1,2,3

icomponent pure of BBB iii

kkiiikik

More on Virial: Fugacity ofTernary & Multicomponent Mixtures Example

Estimate the fugacity and fugacity coefficient of each component in a ternary mixture of

methane (1) / ethane (2) / propane (3) at 40oC and 20 bar with the composition of 17%

methane and 35% ethane

Set all kij = 0

Evaluation of Mixture Fugacity, f, from Equation of

ijji ayya

Redlich-Kwong:

5.1TRb

aZ)h1(ln1Z ln

ii byb

}to be solved simultaneously

Evaluation of Mixture Fugacity, f , using Redlich-Kwong Equation of StateUsing Redlich - Kwong equation of state,

calculate the fugacity and fugacity coefficient of an equimolar mixture of methyl-ethyl-

ketone (1) and toluene (2) at 50oC and 25 kPa

The required data:

11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257

Evaluation of Component Fugacity in Mixture Fugacity, f, from

Equation of State

)h1ln(a

a)h1(Zln)1Z(

bˆ ln kk1k

Redlich-Kwong:

5.1TRb

aZ)h1(ln1Z ln

)h1ln(a

a)h1(Zln)1Z(

bˆ ln kk2k

Evaluation of Mixture Fugacity, f , using Redlich-Kwong Equation of StateUsing Redlich - Kwong equation of state,

calculate the fugacity and fugacity coefficient of MEK and toluene in equimolar

mixture of methyl-ethyl-ketone (1) and toluene (2) at 50oC and 25 kPa

The required data:

11=MEK 535.6 41.5 267 0.249 0.32912=Toluene 591.7 41.1 316 0.264 0.257

Excess Gibbs Energy

igR GGG

jn,P,Ti

Partial Properties:

Residual Property

Excess Property idE GGG Partial Property of the Excess Property id

Partial Property of the Excess Property igii

Ri GGG

Excess Gibbs Energy

igR GGG

.etc,Gor ,V ,S ,H ,UM iiiiii

Partial Properties:

Residual Property

Excess Property idE GGG Partial Property of the Excess Property id

Partial Property of the Excess Property igii

Ri GGG

Activity Coefficient

f̂lnTRGG

flndTRdG

)xln(TRGG iiid

Definition of fugacity:

Integration

iidii fx

f̂lnTRGG

The definition of activity coefficient gi

(Ideal solution)

in,P,Ti

Models for Binary Mixtures Activity Coefficient:Margules(1856 – 1920)

21212121

jn,P,Ti

RT/Gnln

22112212

11221122

x)AA(2Axln

Models for Binary Mixtures Activity Coefficient:van Laar

jn,P,Ti

RT/Gnln

xA1Aln

Models for Binary Mixtures Activity Coefficient:Wilson

x& T of tindependen ,tstanconsa,a

2 & 1 liquid pure of memolar volu V ,V

Models for Binary Mixtures Activity Coefficient:Renon: NonRandom Two-Liquid (NRTL)

Models for Multicomponent MixturesActivity Coefficient:Wilson

kikijji

xxln1 ln

j)(i 1

j)(i RT

ncompositio & T of tindependen ,tstanconsa

i liquid pure of memolar volu V

Models for Multicomponent Mixtures Activity Coefficient:

UNIversal QUAsi Chemical (UNIQUAC)(Abrams & Prausnitz)

UNIquac Functional-groupActivity Coefficient (UNIFAC)(Aa Fredenslund,Rl Jones & JM Prausnitz)

Cii ln ln ln

UNIFAC: Rk & Qk

Example

UNIFAC: amk

nonideal behavior dicky dermawan @gmail.com itk-234 termodinamika teknik kimia ii

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