Nonideal Behavior

Nonideal BehaviorDicky DermawanITK-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 diagram30oC1 atm

Effect of Nonideality: Chloroform(1)/Tetrahydrofuran(2)t-x-y diagramP-x-y diagram30oC1 atm

Effect of Nonideality: Furan(1)/Carbontetrachloride(2)t-x-y diagramP-x-y diagram30oC1 atm

Effect of Nonideality: Ethanol(1)/Toluene(2)t-x-y diagramP-x-y diagram65oC1 atm

Effect of Nonideality: x y Diagram at Constant P = 1 atma. Tetrahydrofuran(1)/Carbon-tetrachloride(2)b Chloroform(1)/Tetrahydrofuran(2)c. Furan(1)/Carbontetrachloride(2)d. Ethanol(1)/Toluene(2)

Partial Molar PropertiesSolution Properties:.are properties of component i in the state of mixtures, which, in general different from that in the state of pure speciesPartial Properties:Pure-species Properties:What physical interpretation can be given for, viz. partial molar volume ?

Methanol Water Mixture, An ExampleFor 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 molesMol of water: (1-0.3) x 10 moles = 7 molesVolume of methanol: 3 moles x 40.727 = 122.181 cm3Volume of water: 7 moles x 18.068 = 126.476 cm3Thus, the total volume: 122.181 + 126.476= 248.657 cm3

Wrong answer!The correct answer is 240.251 cm3Thus there is 240.251 248.657 = -8.406 cm3 deviation from expected value

More on Partial Molar Properties

Chemical Potential as Partial Molar Property Criteria for Vapor - Liquid Equilibria

The chemical potential of i-th component is defined as:

Chemical Potential as Partial Molar PropertyIf we set M = G:Thus:The definition of chemical potential:

Evaluation of Partial Molar Properties Methanol Water Mixture Example

Sheet1

Methanol mol fractionMolar volume, mL/mol

018.1

0.11420.3

0.19721.9

0.24923.0

0.49528.3

0.69232.9

0.78535.2

0.89237.9

140.7

Sheet2

Sheet3

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?

Fugacity, fIdeal gas:Real gas:Residual Gibbs energy:Fugacity coefficient:At constant TResidual Property

Evaluation of Pure Component Fugacity, fiReal gas:Pure Component Fugacity Coefficient:The fugacity :At constant T:

Evaluation of Pure Component Fugacity, fiFrom the following compressibility data for hydrogen at 0oC, determine the fugacity of hydrogen at 950 atm

Evaluation of Pure Component Fugacity, fiFrom the following compressibility data for isobutane,determine the fugacity of butane at various temperature and pressure

Evaluation of Pure Component Fugacity, fi from Equation of StateVirial:

Critical Constants & Accentric Factors:Paraffins

Critical Constants & Accentric Factors:Olefin & Miscellaneous Organics

Critical Constants & Accentric Factors:Miscellaneous Organic Compounds

Critical Constants & Accentric Factors:Elementary Gases

Critical Constants & Accentric Factors:Miscellaneous Inorganic Compounds

Evaluation of Pure Component Fugacity, fi from Virial Equation of State, ExampleUsing virial equation of state,calculate the fugacity and fugacity coefficient of:Pure methyl-ethyl-ketonePure tolueneat 50oC and 25 kPa.

The required data:

Evaluation of Pure Component Fugacity, fi from Equation of StateRedlich-Kwong:}to be solved simultaneously

Evaluation of Pure Component Fugacity, fi from Redlich-Kwong Equation of StateUsing Redlich - Kwong equation of state,calculate the fugacity and fugacity coefficient of:Pure methyl-ethyl-ketonePure tolueneat 50oC and 25 kPa.

The required data:

Evaluation of Pure Component Fugacity, fi :Pitzers Generalized Correlation

Evaluation of Pure Component Fugacity, fi :

Pitzers Generalized Correlation

Evaluation of Pure Component Fugacity, fi : Pitzer CorrelationUsing Pitzer Correlation,calculate the fugacity and fugacity coefficient of:Pure methyl-ethyl-ketonePure tolueneat 50oC and 25 kPa.

The required data:

Evaluation of LiquidPure Component Fugacity, fiPoynting factorFugasity of saturated vapor,calculated exactly as calculating gas phase fugacitySince Vl is a weak function of P at temperatures well below Tc:

Estimation of Liquid Density

Rackett Equation:

Examples ofEvaluation of Liquid Pure Component Fugacity, fi11.5Estimate 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-111.6Estimate 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, fi11.10The normal boiling point of n-butane is 0.5oC.Estimate the fugacity of liquid n-butane at this temperature and 200 bar.11.11The normal boiling point of 1-pentene is 30.0oC.Estimate the fugacity of liquid 1-pentene at this temperature and 350 bar.

11.12The 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, fi11.13Prepare 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:

Examples ofEvaluation of Gas & Liquid Pure Component Fugacity, fi11.14Prepare 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 TableP*: lowest value of P in steam tableAt P >= Pisat, i.e. liquid phase water:Up to Pisat, i.e. gas phase water (steam):

Example of Steam and Water Fugacity Calculation Using Steam Table11.7From 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.11.8Steam 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 state11.9Steam 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 state

Fugacity of MixturesAre formulated exactly as calculation for pure component, but we use Mixing Rules to obtain the parametersVirial:For binary mixtures, i = 1,2 and j = 1,2

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 kPaThe required data are as follows:

Fugacity of Components in MixtureThus:Virial, binary mixtures:

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:11.18Estimate 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 MixturesMixing Rules :For ternary mixtures, i = 1,2,3 and j = 1,2,3

More on Virial: Fugacity ofTernary & Multicomponent Mixtures Example11.19Estimate 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% ethaneSet all kij = 0

Evaluation of Mixture Fugacity, f, from Equation of StateRedlich-Kwong:}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:

Evaluation of Component Fugacity in Mixture Fugacity, f, from Equation of StateRedlich-Kwong:

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:

Excess Gibbs EnergySolution Properties:Partial Properties:Pure-species Properties:Residual PropertyExcess PropertyPartial Property of the Excess PropertyPartial Property of the Excess Property

Activity CoefficientDefinition of fugacity:IntegrationThe definition of activity coefficient gi(Ideal solution)

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

Models for Binary Mixtures Activity Coefficient:van Laar

Models for Binary Mixtures Activity Coefficient:Wilson

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

Models for Multicomponent MixturesActivity Coefficient:Wilson

Models for Multicomponent Mixtures Activity Coefficient:UNIversal QUAsi Chemical (UNIQUAC)(Abrams & Prausnitz)

UNIquac Functional-groupActivity Coefficient (UNIFAC)(Aa Fredenslund,Rl Jones & JM Prausnitz)Models for Multicomponent Mixtures Activity Coefficient:

UNIFAC: Rk & Qk

Models for Multicomponent Mixtures Activity Coefficient:

UNIFAC: Rk & QkExampleModels for Multicomponent Mixtures Activity Coefficient:

UNIFAC: amk

Models for Multicomponent Mixtures Activity Coefficient:

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Nonideal Behavior