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The First Law

PVT relationships

The Second Law

Energy for process

Prediction of equilibrium state and properties and engineering analysis of system

(physical, chemical, or biological)

Mathematical formalism and generalization

Path forward from two great laws of nature

Laws

Property data, models correlations

Solution Thermodynamics

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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M in relation to G

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Summary

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Learning Objectives

 

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Excess Gibbs Energy and Activity Coefficients

 

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Excess Gibbs Energy and Activity Coefficients

 

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liquid

vapor

 

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CODE

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Question

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Question

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Question

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Question

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Getting Activity Coefficients from Expt.

  • Activity coefficients are functions of temperature and liquid-phase composition, and correlations

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Getting Activity Coefficients from Expt. .

Solid line is species fugacities in liquid, the

Dashed lines is Lewis/Randall rule (ideal solution)

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Getting Activity Coefficients from Expt. .

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Henry’s Law for low soluble molecules in liquid

 

Composition dependence of the�fugacity of acetone in two binary liquid�solutions at 50°C. �

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Question Assuming that carbonated water contains only CO2(1) and H2O(2), determine the compositions of the vapor and liquid phases in a sealed can of “soda” at 25ºC if the pressure inside the can is 5 bar.

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Henry’s law applies to a species as it approaches infinite dilution in a binary solution whereas the Gibbs/Duhem equation insures validity of the Lewis/Randall rule for the other species as it approaches purity

 

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Henry’s law applies to a species as it approaches infinite dilution in a binary solution whereas the Gibbs/Duhem equation insures validity of the Lewis/Randall rule for the other species as it approaches purity……

 

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VLE Recap

 

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Real gas and non ideal solution

 

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Chloroform/1,4-dioxane System at 50 ℃

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Fitting Activity Coefficient similar for negative deviations

 

 

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Correlations For Liquid-Phase Activity Coefficients

 

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Redlich/Kister Expansion

 

It Capital Y not activity coefficient

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Redlich/Kister Expansion..

 

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Redlich/Kister Expansion….

 

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The van Laar Equation

 

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Local Composition Models

  • Based on molecular thermodynamics of liqluid-solution behavior
  • In the liquid solution,

local compositions (different from the overall mixture composition)

In order to get the short-range order and nonrandom molecular orientations based on inter and intra molecular forces

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Most common models are

    • Wilson Equation like Margules and van Laar eqn’s
    • NRTL (Non-Random-Two-Liquid) by Renon and Prausinitiz
    • UNIQUAC (Universal Quasi-Chemical) – by Abrams and Prausinitiz App. G
    • UNIFAC (UNIQUAC Functional-group Activity Coefficients) – App. G

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Local composition model Wilson Equation

 

 

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Local composition model NRTL Equation

 

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Local composition model

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Local composition model UNIFAC

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Local composition model Multicomponent Systems

 

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Getting Activity Coefficients from Expt.

  • Activity coefficients are functions of temperature and liquid-phase composition, and correlations

P (kPA)

x1

y1

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GE/RT

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12.3 (P2sat)

0

0

0.0000

12.3000

nan

1.0000

Nan

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0.0000

nan

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15.51

0.0895

0.2716

4.2125

11.2975

1.3042

1.0088

0.2656

0.0087

0.0317

0.3893

18.61

0.1981

0.4565

8.4955

10.1145

1.1883

1.0255

0.1725

0.0251

0.0543

0.3420

21.63

0.3193

0.5934

12.8352

8.7948

1.1138

1.0504

0.1078

0.0492

0.0679

0.3124

24.01

0.4232

0.6815

16.3628

7.6472

1.0713

1.0779

0.0689

0.0750

0.0724

0.2967

25.92

0.5119

0.744

19.2845

6.6355

1.0438

1.1053

0.0429

0.1001

0.0708

0.2834

27.96

0.6096

0.805

22.5078

5.4522

1.0231

1.1354

0.0228

0.1270

0.0635

0.2667

30.12

0.7135

0.8639

26.0207

4.0993

1.0105

1.1633

0.0104

0.1512

0.0508

0.2484

31.75

0.7934

0.9048

28.7274

3.0226

1.0033

1.1894

0.0033

0.1735

0.0384

0.2345

34.15

0.9102

0.959

32.7498

1.4002

0.9970

1.2676

-0.0030

0.2372

0.0185

0.2268

36.09(P1sat)

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1

1

36.0900

0.0000

1.0000

nan

0.0000

nan

nan

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VLE Data for Methyl Ethyl Ketone(l)/Toluene(2) at 50°C �

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Fitting Activity Coefficient similar for negative deviations

 

 

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Chloroform/1,4-dioxane System at 50 ℃

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Thermodynamic Consistency

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Thermodynamic Consistency

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Pxy diagram for ethanol(1)/water(2). The lines represent predicted values; the points are experimental values. �

Consistency test of data for diethyl ketone(l)/ n-hexane(2) at 65°C. �

Thermodynamic Consistency �

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Henry’s law applies to a species as it approaches infinite dilution in a binary solution whereas the Gibbs/Duhem equation insures validity of the Lewis/Randall rule for the other species as it approaches purity

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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Henry’s law applies to a species as it approaches infinite dilution in a binary solution whereas the Gibbs/Duhem equation insures validity of the Lewis/Randall rule for the other species as it approaches purity……

 

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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VLE Recap

 

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Real gas and non ideal solution

 

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PT Flash using Raoult’s Law

 

https://drive.google.com/drive/folders/1xQ29Mih7DCSi6wPdQXGKNTGca-0eR_camDPf87HdieTqvQCcCeLPnkq4PN0EkfcPG2agp_s3?usp=sharing

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PT Flash using Raoult’s Law

1 Mol feed

 

 

 

Link

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General solution procedure of Flash Calculation

Rice/Rachford equation

 

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Pbubble and Pdew significance

 

https://chemicals.readthedocs.io/chemicals.flash_basic.html?

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Question

A binary mixture of mole fraction z1 is flashed to conditions T and P. For one of the�following, determine the equilibrium mole fractions x1 and y1 of the liquid and vapor�phases formed, the molar fraction of the vapor formed, and the fractional recovery�R of species 1 in the vapor phase (defined as the ratio for species 1 of moles in the�vapor to moles in the feed). Assume that Raoult’s law applies. �

1-Chlorobutane(1)/chlorobenzene(2), z1 = 0.50, T = 125°C, P = 1.75 bar �

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A

B

C

Chlorobenzene

C6H5Cl

13.8635

3174.78

211.700

1-Chlorobutane

C4H9Cl

13.7965

2723.73

218.265

ln Psat∕kPa = A – B/( t∕°C + C)��

a=-1*(k1-1)*(k2-1);

b=(k1*k2-z1*k1-z2*k2-k1-k2+2);

c=z1*k1+z2*k2-1;

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Revisit Cubic EoS

 

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Residual property from Cubic EoS

 

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Residual property from Cubic EoS

Pure Species in VLE …

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Residual property from Cubic EoS

Pure Species in VLE

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Residual property from Cubic EoS

Pure Species in VLE …

 

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Residual property from Cubic EoS

Pure Species in VLE …Numerical Scheme

 

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Residual property from Cubic EoS for Mixture in VLE

 

 

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Residual property from Cubic EoS for Mixture in VLE

 

 

 

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Residual property from Cubic EoS for Mixture in VLE

Numerical Scheme

 

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Define T range, P range, EoS Parameter, Substance parameter, Feed composition

Use Wilson correlation for initial guess equilibrium constant K-Value

Get vapor fraction using Rice/Rachford equation using K Value V should not infinity

Get guessed y1, y2, x1, x2 based on K value and vapor fraction

Get interaction variable using compositions

Apply suitable cubic EoS for vapor and liquid separately get Zv and Zl using Newton’s method Zn+1​=Zn​−f′(Zn​)/f(Zn​)​, iterate till Converge

Calculate Fugacity coefficient and fugacity using Zv and Zl

 

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Matlab files and data

13.1. Assuming the validity of Raoult’s law, do the following calculations for the benzene(1)/toluene(2) system ...

13.2. Assuming Raoult’s law to be valid, prepare a Pxy ..

.13.9. A mixture containing equimolar amounts of benzene(1), toluene(2), and ethylbenzene(3) ....

13.13. A concentrated binary solution containing mostly species 2 (but x2 ≠ 1) is...

13.11. A binary mixture of mole fraction z1 is flashed to conditions T and P. ...

13.24. Flash calculations are simpler for binary systems than for the general multi-component...

13.34. The following is a set of VLE data for the system acetone(1)/methanol(2) ...

13.35. The excess Gibbs energy for binary systems consisting of ...

13.37. VLE data for methyl tert-butyl ether(1)/dichloromethane(2) at 308.15 K ...

13.43. For one of the binary systems listed in Table 13.10, WILSON... Pxy diagram for t = 60°C.

13.44. Wilson.... txy diagram for P = 101.33 kPa

13.45. NRTL...Pxy diagram for t = 60°C.

13.46. NRTL... txy diagram for P = 101.33 kPa.

13.67. A system formed of methane(1) and a light oil(2) at 200 K

13.76. Generate P-x1-y1 diagrams at 100°C for one of the systems identified below

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Thermodynamic Consistency

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Thermodynamic Consistency

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The excess Gibbs energy for binary systems consisting of liquids not too dissimilar in chemical nature is represented to a reasonable approximation by the equation:

GE ∕RT = A x1 x2

where A is a function of temperature only. For such systems, it is often observed that the ratio of the vapor pressures of the pure species is nearly constant over a considerable temperature range. Let this ratio be r, and determine the range of values of A, expressed as a function of r, for which no azeotrope can exist. Assume the vapor phase to be an ideal gas.

 

 

 

Note: Solutions to some of the problems of this chapter require vapor pressures as a function of tem­perature. Table B.2, Appendix B, lists parameter values for the Antoine equation, from which these can be computed.

Dr. Nilesh Choudhary, Department of Chemical Engineering, IIT Tirupati

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