Dicky Dermawan www.dickydermawan.net78.net dickydermawan@gmail.com ITK-234 Termodinamika Teknik Kimia II Nonideal Behavior Dicky Dermawan www.dickydermawan.net78.net dickydermawan@gmail.com

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) 30oC 1 atm P-x-y diagram t-x-y diagram

Effect of Nonideality: Chloroform(1)/Tetrahydrofuran(2) 30oC 1 atm P-x-y diagram t-x-y diagram

Effect of Nonideality: Furan(1)/Carbontetrachloride(2) 30oC 1 atm P-x-y diagram t-x-y diagram

Effect of Nonideality: Ethanol(1)/Toluene(2) 65oC 1 atm P-x-y diagram t-x-y diagram

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

Partial Molar Properties Pure-species Properties: Solution Properties: NOT: Partial Properties: ….are properties of component i in the state of mixtures, which, in general different from that in the state of pure species 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/mol Water (2) : V2 = 18.068 cm3/mol What 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

More on Partial Molar Properties NOT:

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 Property If we set M = G: The definition of chemical potential: Thus:

Evaluation of Partial Molar Properties Methanol – Water Mixture Example

Exercise A 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, f At constant T Ideal gas : Real gas : Residual Gibbs energy : Residual Property Fugacity coefficient :

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

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

Evaluation of Pure Component Fugacity, fi From 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 State Virial :

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, Example Using virial equation of state, calculate the fugacity and fugacity coefficient of: Pure methyl-ethyl-ketone Pure toluene at 50oC and 25 kPa. The required data:

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

Evaluation of Pure Component Fugacity, fi from Redlich-Kwong Equation of State Using Redlich - Kwong equation of state, calculate the fugacity and fugacity coefficient of: Pure methyl-ethyl-ketone Pure toluene at 50oC and 25 kPa. The required data:

Evaluation of Pure Component Fugacity, fi : Pitzer’s Generalized Correlation

Evaluation of Pure Component Fugacity, fi : Pitzer’s Generalized Correlation

Evaluation of Pure Component Fugacity, fi : Pitzer’s Generalized Correlation

Evaluation of Pure Component Fugacity, fi : Pitzer’s Generalized Correlation

Evaluation of Pure Component Fugacity, fi : Pitzer’s Generalized Correlation

Evaluation of Pure Component Fugacity, fi : Pitzer Correlation Using Pitzer Correlation, calculate the fugacity and fugacity coefficient of: Pure methyl-ethyl-ketone Pure toluene at 50oC and 25 kPa. The required data:

Evaluation of Liquid Pure Component Fugacity, fi Since Vl is a weak function of P at temperatures well below Tc: Poynting factor Fugasity of saturated vapor, calculated exactly as calculating gas phase fugacity

Estimation of Liquid Density Rackett Equation:

Examples of Evaluation of Liquid Pure Component Fugacity, fi 11.5 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 11.6 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 of Evaluation of Liquid Pure Component Fugacity, fi 11.10 The normal boiling point of n-butane is 0.5oC. Estimate the fugacity of liquid n-butane at this temperature and 200 bar. 11.11 The normal boiling point of 1-pentene is 30.0oC. Estimate the fugacity of liquid 1-pentene at this temperature and 350 bar. 11.12 The normal boiling point of isobutane is -11.8oC. Estimate the fugacity of liquid isobutane at this temperature and 150 bar.

Examples of Evaluation of Gas & Liquid Pure Component Fugacity, fi 11.13 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 of Evaluation of Gas & Liquid Pure Component Fugacity, fi 11.14 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 Up to Pisat, i.e. gas phase water (steam): P* : lowest value of P in steam table At P >= Pisat, i.e. liquid phase water:

Example of Steam and Water Fugacity Calculation Using Steam Table 11.7 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. 11.8 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 state 11.9 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 state

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

Example of Calculation for Fugacity of Mixtures Using Virial Equation Estimate 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:

Fugacity of Components in Mixture is partial molar property of Thus: 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: 11.18 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 Mixing Rules : For ternary mixtures, i = 1,2,3 and j = 1,2,3

More on Virial: Fugacity of Ternary & Multicomponent Mixtures Example 11.19 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 State Redlich-Kwong: }to be solved simultaneously

Evaluation of Mixture Fugacity, f , using 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 State Redlich-Kwong:

Evaluation of Mixture Fugacity, f , using 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:

UTS 1

Excess Gibbs Energy Pure-species Properties: Solution Properties: Partial Properties: Residual Property Partial Property of the Excess Property Excess Property Partial Property of the Excess Property

Excess Gibbs Energy Pure-species Properties: Solution Properties: Partial Properties: Residual Property Partial Property of the Excess Property Excess Property Partial Property of the Excess Property

Activity Coefficient Definition of fugacity: Integration (Ideal solution) The definition of activity coefficient gi

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 Mixtures Activity Coefficient: Wilson

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

Models for Multicomponent Mixtures Activity Coefficient: UNIquac Functional- group Activity 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 & Qk Example

Models for Multicomponent Mixtures Activity Coefficient: UNIFAC: amk