BFAQUEOUS ELECTROLYTE

Theory & Application

Joseph E Zemaitis,Jr. Chem Solve, Inc.

Diane M. Clark OLI Systems, Inc.

Marshall Rafal OLI Svstems. Inc.

Noel C. Scrivner E.I. dubnt de Nemours & Co., Inc.

WILEY- INTERSCIENCE

A JOHN WILEY & SONS, INC., PUBLICATION

A publication of the Design Institute for Physical Property Data (DIPPR)

Sponsored by the American Institute of Chemical Engineers

345 East 47th Street New York, New York 10017

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MlDBB@@K @FA UEOUS

THERMODYNAMICS ELEC 9 ROLYTE

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BFAQUEOUS ELECTROLYTE

Theory & Application

Joseph E Zemaitis,Jr. Chem Solve, Inc.

Diane M. Clark OLI Systems, Inc.

Marshall Rafal OLI Svstems. Inc.

Noel C. Scrivner E.I. dubnt de Nemours & Co., Inc.

WILEY- INTERSCIENCE

A JOHN WILEY & SONS, INC., PUBLICATION

A publication of the Design Institute for Physical Property Data (DIPPR)

Sponsored by the American Institute of Chemical Engineers

345 East 47th Street New York, New York 10017

No part. of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otheiwise, except as permitted under Scctions 107 or 108 of thc 1976 United Statcs Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923. (978) 750-8400, fax (978) 750-4470. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., I 1 1 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008.

0 Copyright 1986 American Institute of Chemical Engineers, Inc. 345 East Forty-Seventh Street New York, New York 10017

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner.

ISBN 978-0-8 169-0350-4 AlChE shall not be responsible for statements or opinions advanced in papers or printed in its publications.

Dedication: 1 his book is dedicated to the mem- ory of Dr. Joseph F. Zemaitis, Jr. Dr. Zemaitis, a colleague and friend for many years, was responsible for the outline of this book and the writing of the first three chapters. In a larger sense, he provided for the synthesis of a very diverse body of work into a coherent frame- work for problem solving. We dearly hope that our dedication to and respect for his memory is reflected in the content of this work.

Diane M. Clark Marshall Rafal Noel C. Scrivner

Acknowledgment: T h e authors wish to express their gratitude to Lisa Perkalis. This book could not have been completed without her word processing skills, patience and dedication in the face of never-ending “small” changes to the manuscript.

vi

Sponsors: T h e DlPPR sponsors of this project, and the technical representatives who served on the steering com- mittee are listed below. Stars indicate those companies which sup- ported the project throughout its three year duration.

Sponsors of DIPPR Project 811 (1 981 -1 983)

Partlclpant Technical Representative

*Air Products & Chemicals, Inc. Allied Corporation

*Amoco Chemicals Corporation Chevron Research Company

*Chiyoda Chemical Engineering & Construction Co., Ltd.

*E.I. du Pont de Nemours & Company, Inc.

'El Paso Products Company

'Hatcon SD Group, Inc. Exxon Research and Engineering Co.

Hoff mann-LaRoche, Inc. Hooker Chemical Company lnstitut Francais du Petrole

*Institution of Chemical Engineers M.W. Kellogg Company Kennecott Copper Corporation

*Kerf--McGee Chemical Corporation *Olin Chemicals Group 'Phillips Petroleum Company *Shell Development Company *Simulation Sciences, Inc. *The Standard Oil Company (SOHIO) *Texaco, Inc. 'Texasgulf, Inc. Union Carbide Corporation

Dr. M.S. Benson Mr. W.B. Fisher Dr. D.A. Palmer Dr. W.M. Bollen Mr. T. Maejima

Dr. N.C. Scrivner

Mr. K. Claiborne Dr. C. Tsonopoulos Dr. C.EChueh Dr. R. Schefflan Dr. W.L. Sutor Dr. J. Vidal Dr. 6. Edmonds Mr. H. Ozkardesh Mr. D.S. Davies Dr. D.S Arnold Mr. W.M. Clarke Mr. M.A. Albright Dr. R.R. Wood Dr. C. Black Mr. TB. Selover Dr. C. Wu Mr. S.H. DeYoung Mr. E. Buck

Federal Grantor

*National Bureau of Standards Dr. H.J. White, Jr.

'Supported Project for 3 year life

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Foreword: A n international conference on the ‘Ther- modynamics of Aqueous Systems” sponsored by the American Institute of Chemical Engineers (AIChE), the National Science Foundation (NSF), and the National Bureau of Standards (NBS), was held in Warrenton, Virginia, on October 22-25,1979. The papers presented reflected a great deal of research on electrolyte solutions. However, it was apparent that there was no fundamental document to tie all of the different information together and so to form a framework for solving real problems.

Therefore, AIChE’s Design Institute for Physical Property Data (DIPPR) decided to publish this book to meet such a need. Through a cooperative effort by participating corporations, different correlations have been compiled and objectively compared to experimental data, in regions of industrial interest. Effective methods of finding and using data are also described. The Handbook incorporates and extends previous work in a well-organized, easy to understand format, with a focus on applications to serious industrial problems. It will become a cornerstone in the study of aqueous electrolyte thermodynamics.

Electrolyte mixtures come in various forms and add another dimension to the normal complexities of nonelectrolyte solutions: entirely new species can form in water, some of which are not obvious; components can precipitate; soluble components can affect the vapor pressure of the solution very significantly. In industrial applications, the solutions are often highly concentrated and encounter high pressures and temperatures. There- fore expertise in electrolyte systems has become increasingly critical in oil and gas exploration and production, as well as in the more traditional chemical industry opera- tions. A variety of correlations are available that can solve the problems that are encountered in industry, but which ones work best? This comprehensive handbook not only provides easy access to available data but also presents comparative studies of various correlations up to extreme conditions.

As the Chairman of the Technical Committee of AIChE’s Design Institute for Physical Property Data, I conceived this cooperative research project and chose as its leader, Dr. Noel C. Scrivner of the E.I. duPont de Nemours Company, one of the leading practi- tioners of electrolyte thermodynamics. With his expertise and enthusiasm, Dr. Scrivner defined the work that needed to be accomplished, promoted the project until it was funded, and directed its completion. He was elected to head the steering committee of representatives from the supporting companies.

The initial work was carried out in 1981 by the Electrolyte Data Center of the National Bureau of Standards, under the direction of Dr. B.R. Staples. That work continued throughout the project, generating the bibliographies for electrolyte systems. One of these bibliographies, developed by R.N. Goldberg, is included in this volume.

A significant portion of the project funding came from the Office of Standard Refer- ence Data of the NBS (Dr. David R. Lide, Jr., Director). The NBS liaison to DIPPR was Dr. Howard J. White, Jr. DIPPR provided additional funding along with administrative and technical assistance.

The task of creating the actual handbook was given to the late Dr. Joseph F. Zemaitis,

Jr., owner of Chem Solve, Inc. His intellectual contribution to this project will remain as his legacy. He wrote the first few chapters and carefully outlined the remainder of the book. His principal colleague in this work, Ms. Diane M. Clark, dedicated several years of creative effort to take the outline and complete the project. Another colleague of Or. Zemaitis, Dr. Marshall Rafal, owner of OLI Systems, Inc., assumed the contractor’s responsibility for execution of the handbook and contributed some of the writing. Dr. Scrivner gave technical direction and technical contributions to assure that the work would meet the standards set by the steering committee.

This book is dedicated to Dr. J.F.Zemaitis. Dr. David W.H. Roth, Jr., the administrative committee chairman of DIPPR, and I would like to express sincere appreciation to the other authors, the steering committee members, the corporate sponsors, and the National Bureau of Standards.

David A. Palmer, Chairman DIPPR Technical Executive Committee and DIPPR Technical Committee

X

TABLE OF CONTENTS

I

I1

111

IV

INTRODUCTION

THERMODYNAMICS OF SOLUTIONS Basic Thermodynamic Functions Solutions - Basic Definitions and Concepts Equilibrium - Necessary Conditions Activities, Activity Coefficients and Standard States

EQUILIBRIUM CONSTANTS Ionic andlor Reaction Equilibrium in Aqueous Solutions Solubility Equilibria Between Crystals and Saturated Solutions Vapor-Liquid Equilibria in Aqueous Solutions Temperature Effects on the Equilibrium Constant Estimating Temperature Effects on Heat Capacity and Other

Equilibrium Constants from Tabulated Data Pressure Effects on the Equilibrium Constant Appendix 3.1 - C r i s s and Cobble Parameters

ACTIVITY COEFFICIENTS OF SINGLE STRONG ELECTROLYTES

Thermodynamic Properties

History Limitations and Improvements to the Debye-Huckel Limiting Law Further Refinements

Bromley's Method Meissner's Method Pitzer's Method Chen's Method

Short Range Interaction Model Long Range Interaction Model

Temperature Effects Bromley's Method Meissner's Method Pitzer's Method Chen's Method

Bromley's Method Meissner's Method Pitzer's Method Chen's Method NBS Smoothed Experimental Data Test Cases:

Application

HC1 K C1 KOH NaCl NaOH CaCl2 Na2SO4 MgSOO,

Bromley's Extended Equation MgS04 Test Case

1

11 13 14 16 17

25 27 30 31 32

33 36 36 39

45 48 55 56 64 67 71 76 76 82 84 84 84 86 89 90 91 93 94 96 98

99 103 106 110 113 117 121 124 127 128

Comparison of Temperature Effect Methods B romley Meiss ner Pitzer and Chen Experimental Data Test Cases :

HC1 at 50' Celsius KC1 a t 80' Celsius KOH a t 80° Celsius NaCl at 100 and 300' Celsius NaOH at 35O Celsius CaClz a t 108.85 and 201.85' Celsius Na2S04 a t 80° Celsius MgS04 at 80' Celsius

Appendix 4.1 - Values for Guggenheim's 0 Parameter Table 1 : B Values for Uni-univalent Electrolytes Table 2: 0 and B Values of Ri-univalent and Uni-bivalent

Methods for Calculating 8

Table 1 : B Values at 25'C Determined by the Method of Least Squares on Log Y to 1=6.0 (or less if limited data)

Table 2: Individual Ion Values of B and 6 in Aqueous Solutions a t 25OC

Table 3: Bivalent Metal Sulfates at 25OC

Table: Average Values of Parameter q in Equation (4.46)

Electrolytes from Freezing Points

Appendix 4.2 - Bromley Interaction Parameters

Appendix 4.3 - Meissner Parameters

for Selected Electrolytes

Table 1: Inorganic Acids. Bases and Salts of 1-1 Type Table 2: Salts of Carboxylic Acids (1-1 Type) Table 3 : Tetraalkylammonium Halides Table 4: Sulfonic Acids and Salts (1-1 Type) Table 5: Additional 1-1 Type Organic Salts Table 6: Inorganic Compounds of 2-1 Type Table 7: Table 8: 3-1 Electrolytes Table 9: 4-1 Electrolytes Table 10: 5-1 Electrolytes Table 11: 2-2 Electrolytes

Table 1: Temperature Derivatives of Parameters for 1-1 Electrolytes Evaluated from Calorimetric Data

Table 2: Temperature Derivatives of Parameters for 2-1 and 1-2 Electrolytes Evaluated from Calorimetric Data

Table 3 : Temperature Derivatives of Parameters for 3-1 and 2-2 Electrolytes from Calorimetric Parameters

T Values Fit for 5:olality Mean Ionic Activity Coefficient Data of Aqueous Electrolytes at 298.15 K

Appendix 4.4 - Pitzer Parameters

Organic Electrolytes of 2-1 Type

Appendix 4.5 - Pitzer Parameter Derivatives

Appendix 4.6 - Chen Parameters Table:

V A CT IV IT Y CO E FF ICIE NTS 0 F M U LT 1 CO hlP ON E N T ST RO NG ELECTROLYTES

Guggenheim's Method for Multicomponent Solutions

130 130 131 131 132

133 136 140 144 150 153 159 162

165 165

166 167 170

170

173 174 175

175 179 179 131 181 182 183 183 185 185 18t1 18 7 187 188

188

189

190 19 1

191

205 209

xii

Bromley's Method for Multicornponent Solutions Activity Coefficients of Trace Components

Meissner's Method for hlulticoinponent Solutions Pitzer's Method for Multicomponent Solutions Chen's Method fo r Multicomponent Solutions Application

Guggenheiin's Method Broinley's Method Meissner's Method Pitzer's Method Water Activities

B romley's Water Activity Pdeissner's Water Activity Pitzer's Water Activity

Phase Diagram Calculations Basic flow of t he testing program Program block descriptions H:O - NaCl - KC1 H 2 0 - NaCl - HC1 H 2 0 - NaCl - NaOH Hz0 - KC1 - HC1 H z 0 - NaCl - CaC12 H$I - NaCl - MgC12 I 1 2 0 - NaCl - NaeSOs H z O - KC1 - CaC12 I 1 2 0 - NaOH - Na2S04 H z 0 - NaCl - CaSOs H 2 0 - HCI - CaS04 H 2 0 - CaC12 - CaS04 H 2 0 - Na2S04-CaSOk I i 2 0 - MgS04 - CaSOb

Appendix 5.1 - Values for Pitzer's 0 and J, Parameters Table 1: Parameters fo r mixed electrolytes with virial

Table 2:

Effects of Higher-order Electrostatic Terms Table 3: Parameters for binary mixtures with a common

coefficient equations ( a t 25OC:) Parameters for the virial coefficient equations a t 25OC

ion at 25OC

V I ACTIVITY COEFFICIENTS OF S'TKONGLY COMPLEXING COMPOUNDS Identification of Complexing Electrolytes

Literature Review U s e of Meissner's Curves Comparison of Osmotic Coefficients

Phosphoric A c i d Sulfuric Acid Zinc Chloride Ferr ic Chloride Cuprous Chloride Calcium Sulfate Sodium Sulfate Other Chloride Complexes

Manganous Chloride Cobalt Chloride

211 212 214 2 19 223 23 1 232 234 235 236 238 238 240 24 1 242 243 245 250 261 268 278 29 0 299 315 326 335 347 357 363 369 377 384

394

385 386

389

39 9 406 407 407 407 409 415 419 424 428 43 1 436 440 440 443

xiii

Nickel Chloride Cupric Chloride

Activity Coefficient Met hods Summary Appendix 6.1 - Cuprous Chloride

Table la: Interaction Parameters Table l b : Three Parameter Set Table 2 : Equilibrium Constants and Heats of Reaction Table 3a: Equilibrium Constants and Changes in Thermodynamic

Properties for Formatiog-of CuC1; and c'uC1;- from CuCl(s) + nC1- = CuC1,+1

Table 3b: Equilibrium Constants and Changes in ThermodynRmic Properties for Formtttio of CuCI; and CuC1:- from cu+ t nC1- = c u c l y - l f

V I I ACTIVITY COEFFICIENTS OF WEAK ELECTROLYTES A N D MOLECULAR SPECIES

Setschihow Equation Salting Out Parameter Determination by Randall and Pailey Salting Out Parameter Determination by Long and McDevit Salting Out Parameter Determination by Other Authors

Edwards, Maurer, Newman and Prausnitz Pitzer Based Method Beutier and Renon's Pitzer Based Method Chen's Pitzer Based Method

Predictions Based upon Theoretical Equations Ammonia - Water Carbon Dioxide - Water Ammonia - Carbon Dioxide - Water Sulfur Dioxide - Water Oxygen - Sodium Chloride - Water Conclusions

Pitzer Based Equations

Appendix 7 .1 - Salting Out Parameters for Phenol in Aqueous Salt Appendix 7.2 - Salting Out Parameters from Pawlikowski and Prausnitz

Solutions at 2 5 O Celsius

for Nonpolar Gases in Common Salt Solutions at Moderate Temperatures

Lennard - Jones Parameters for Nonpolar Gases as Reported by Liabastre (S14) Salting Out Parameters for Strong Electrolytes in Equation (7.18) at 25OC Temperature Dependence of the Salting Out Parameters for Equation (7.19) Salting Out Parameters for Individual Ions for Equation (7.20) Temperature Dependence of the Salting Out Constants for Individual Ions

Table 1:

Table 2:

Table 3:

Table 4 :

Table 5 :

VIII THERMODYNAMIC FUNCTIONS D E R I V E D FROM ACTIVITY C 0 E F F I C I E N T S

Density Binary Density Multicomponent Density Strong Electrolytes Which Complex Weak Electrolytes

447 449 453 455 457 457 457 458

458

459

479

485 486 491 496 5 03 503 505 512 517 517 524 524 524 524 524

538

540

540

540

541

542

542

551

554 554 558 558 5 59

xiv

Temperature Effects Illustrative Example

Heat of Formation at Infinite Dilution Enthalpy

Molecular Species Ionic Species Range of Applicability

Excess Enthalpy Example

IX WORKED EXAMPLES Model Formulation Obtaining Coefficients Model Solution Specific Examples

Sodium Chloride Solubility Water - Chlorine Water - Ammonia - Carbon Dioxide Water - Sulfur Dioxide Chrome Hydroxides Gypsum Solubility Water - Phosphoric Acid Table -1 : Table 2 : Table 3 : Table 4 : Table 5 :

Appendix 9 . 1 - Parameters for Beutier and Renon's Method Temperature fit parameters for equilibrium constants Temperature fit parameters for Henry's constants Pitzer ion-ion interaction parameters Temperature fit molecule self interaction parameters Dielectric effect parameters

Appendix 9 .2 - Parameters for Edwards, Maurer, Newman and Prausnitz Method

Table 1 : Table 2 : Table 3 : Table 4 : Table 5 : Molecule-ion interaction parameters

Table 1 : Pure component parameters Table 2:

Table 3 : Interaction parameter a92 for polar-nonpolar mixtures Table 4: Table 5 :

Temperature fit parameters for equilibrium constants Temperature fit parameters for Henry's constants Ion-ion interaction parameters Temperature fit molecule self interaction parameters

Appendix 9.3 - Fugacity Coefficient Calculation

Nonpolar and polar contribution to parameters a and B for four polar gases

Parameter a12 for binary mixtures of nonpolar gases Interaction parameter a L for polar-polar mixtures

Appendix 9.4 - Brelvi and O'Connell Correlation for Partial Molar Volumes

Table 1 : Characteristic volumes Appendix 9.5 - Gypsum Solubility Study Parameters at 25OC

Table 1: Binary solution partimeters for the Pitzer equations Table 2 : Mixed electrolyte solution parameters for the Pitzer

equations Table 3: Gypsum solubility product a t 25OC

560 560 563 564 564 566 567 568 568

575 577 584 586 588 589 595 606 6 4 1 650 663 675 683 683 683 684 685 685

69 1 691 691 692 692 693 699 700 701

7 0 1 702 703

704 705 706 706 706

706

X . AP P EN D1 CES ?ll

APPENDIX A - COMPUTER PROGRAMS FOR SOLVING EQUILIBRIA 713 PROBLEMS

APPENDIX B - SELECTED THERMODYNAMIC DATA 721

APPENDIX C - COMPILED THERMODYNAMIC DATA SOURCES FOR 737 AQUEOUS AND BIOCHEMICAL SYSTEMS: A n Annotated Bibliography (1930 - 1983)

INDEX 843

xvi

N O M E N C L A T U R E

A - Debye-Huckel constant, log base 10, equation ( 4 . 3 1 )

A+ - Debye-huckel constant for osmotic coefficients, log base e,

A' - Debye-Huckel constant for activity coefficients, log base e,

equation ( 4 . 6 4 )

equation

a i - activity of species i. equation ( 2 . 2 1 ) at - parameter used by Criss and Cobble's correspondence

principle, equation ( 3 . 3 2 )

aW - water activity a - distance of closest approach or core size. equation ( 4 . 3 3 )

n - parameter for Guggenheim's activity coefficient equation, log

B - interaction parameter for Bromley's activity coefficient

B Y - parameter in Pi tzer's activity coefficient equation,

1 0 basis. equation ( 4 . 3 9 )

equation, equation ( 4 . 4 4 )

equations ( 4 . 6 3 ) . ( 4 . 6 6 )

bt - parameter used by Criss and Cobble's correspondence

C 9

,Cp - heat capacity Cpo - partial molal heat capacity C - molarity

C - salt concentration in the Setschgnow equation (7.1)

D - dielectric constant. equations ( 4 . 1 1 , ( 4 . 9 8 )

d - solution density, equation ( 2 . 3 4 1 , Chapter V l l l

dL - solvent density

dW - pure water density, equation ( 4 . 9 8 ) E - intrinsic energy e - electronic charge. equation ( 4 . 2 )

principle, equation (3.32)

- Pitzer parameter, equation ( 4 . 6 5 )

-

xvii

F

f

f Y

f V

gi

G - Gi

gi j

H

H - Hi

I

K

Ka q

KS P

KT - ko

k

k

L

M

MS

m

NA

"i

P

- NRTL parameter of equations ( 4 . 7 0 1 ,

- rational activity ( 2 . 3 3 ~ )

- Pitzer electrosta - fugacity of vapor

Chen's activity ( 4 . 7 1 )

coefficient (mo

coefficient equation,

e fraction based), equation

ic function, eq ation ( 4 . 5 2 )

species V . equation ( 3 . 2 0 )

- number of grams of i , i=O for solvent - Gibbs free energy

- partial molar Gibbs free energy, equation ( 2 . 1 4 )

- radial distribution function, equation ( 4 . 5 1 ) - enthalpy - Henry' s constant - partial molar enthalpy, equation ( 2 . 1 5 )

- ionic strength, equation ( 4 . 2 7 ) - equilibrium constant, dissociation constant - equilibrium constant. equation ( 3 . 1 8 ) - solubility product, equation (3.13) - thermodynamic equilibrium constant, equation ( 3 . 6 ) - partial molal compressibility, equation ( 3 . 4 0 ) - Boltzmann's constant, equation ( 4 . 2 ) - Setschhnow salt coefficient, equation (7.1) - Ostwald coefficient

- solute molecular weight. equation ( 2 . 3 4 ) - solvent molecular weight, equation ( 2 . 3 4 )

- molality - Avagadro' s number, equation ( 4 . 2 ) - number of moles of i - pressure, total vapor pressure

- p a r t i a l p r e s s u r e = - log K

- Meissne r ' s i n t e r a c t i o n p a r a m e t e r , e q u a t i o n (4.46) - g a s law c o n s t a n t - r a d i u s of t h e f i e l d a r o u n d a n ion , e q u a t i o n ( 4 . l a ) - e n t r o p y - g a s s o l u b i l i t y i n p u r e w a t e r , Se t schenow e q u a t i o n (7.1) - g a s s o l u b i l i t y i n s a l t so lu t ion . S e t s c h e n o w e q u a t i o n ( 7 . 1 ) - t e m p e r a t u r e , Ke lv ins - t e m p e r a t u r e , C e l s i u s - volume

- p a r t i a l molar volume, e q u a t i o n (2 .16) - l i q u i d mole f r a c t i o n - v a p o r mole f r a c t i o n - a n y e x t e n s i v e the rmodynamic p r o p e r t y , e q u a t i o n ( 2 . 8 )

- molar a c t i v i t y c o e f f i c i e n t , equa t ion (2.3313) - n u m b e r of c h a r g e s on ion i - Debye-Hucke l c o n s t a n t , log b a s e e

- n o n r a n d o m n e s s f a c t o r in Chen ' s e q u a t i o n f o r act c i e n t s , e q u a t i o n (4.70)

- p a r a m e t e r i n c o r r e s p o n d e n c e p r i n c i p l e e q u a t i o n , (3 .36a)

v i t y coe f f i -

equa t ion

- p a r a m e t e r for Gugyenheim's a c t i v i t y c o e f f i c i e n t e q u a t i o n . e q u a t i o n ( 4 . 3 8 )

- p a r a m e t e r i n c o r r e s p o n d e n c e p r i n c i p l e e q u a t i o n , e q u a t i o n

- P i t z e r i n t e r a c t i o n coe f f i c i en t ( 3 . 3 6 b )

- Y i t z e r i n t e r a c t i o n coe f f i c i en t - P i t z e r i n t e r a c t i o n coe f f i c i en t

r - reduced activity coefficient, equation ( 4 . 4 5 ) Y - molal activity coefficient, equation ( 2 . 2 2 ) 6 - Bromley parameter for the additive quality of ion interac-

tion, equation ( 4 . 4 5 )

€gas - Lennard-Jones energy interaction, equation ( 7 . 1 8 ) O i j - Pitzer's coefficient for like charged ion interactions,

v i - partial molar Gibbs free energy or chemical potential, equations ( 5 . 3 2 1 , ( 5 . 3 3 )

equation ( 2 . 1 7 )

u i O - reference state chemical potential. equation ( 2 . 2 1 ) V - sum of cation and anion stoichiometric numbers V - harmonic mean of v + and v-, equation ( 4 . 3 8 ) - vi - stoichiometric number of ion i

n - osmotic pressure, equation ( 4 . 5 1 ) P - charge density, equation ( 4 . 1 ) T - NWTL binary interaction parameter of Chen's activity

coefficient equation. equations ( 4 . 7 0 ) . ( 4 . 7 1 )

,4 - osmotic coefficient, equation ( 2 . 3 0 ) $a - ionic atmosphere potential, equation ( 4 . 1 4 ) J'ijk - Pitzer triple ion interaction parameter, equation ( 5 . 3 2 )

J l r - ionic potential $t - total electric field potential, equation ( 4 . 1 ) Q - apparent molal volume

Subscripts :

A - anion a - anion

C - cation C - cation g - gas

1 - any species j - any species

L - liquid

m - molecular species

S - sal t

U - molecular (undissociated species

V - vapor

W - water

1,3,5... . - cations 2 . 4 , 6 , . . . - anions * - molecular species

Superscripts :

el - electrostatic

ex - excess

lc - local composition

P - Pitzer long range contribution of Chen's equation, equation ( 4 . 8 7 )

tr - trace amount

0 - indicates reference state of pure (single solute) solutions

u - infinite dilution

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I nt rod uction

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INT RODU CT ION

In the past several years, interest in electrolyte phase equilibria has grown significantly. This growth in interest can be attributed to a number of evolving application areas and factors among which are:

o Recognition of the necessity to reduce pollutant levels in process waste The removal of sulfur by formation of gypsum is an example water streams.

of such an application. o Development of new flue gas scruhbing systems using regenerative processes.

Scrubbing of C1, from incinerator streams and SO2 from flue gases a re specific application examples.

o Recent escalation of the prices of oil and gas leading to the study and development of synthetic fuel processes i n which ammonia. carbon dioxide, and hydrogen sulfide a re produced as by-products which usually condense to form aqueous solutions. Sour water strippers and amine scrubbers are specific processes developed in this area.

Most of the application areas mentioned above concern the vapor-liquid phase equilibria of weak electrolytes. However, in the past several years, consider- able interest has also developed in the liquid-solid equilibria of both weak and strong electrolytes. Application areas and factors that have affected this growth in interest include:

o Hydrometallurgical processes. which involve the treating of a raw ore or concentrate with an aqueous solution of a chemical reagent.

o The need of corrosion engineers to predict the scale formation capabilities of various brines associated with oil production or geothermal energy production.

o The need of petroleum engineers to predict the freezing or crystallization point of clear brines containing sodium, calcium, and zinc chlorides and bromides to high concentrations.

o The need for waste water clean up customarily done by precipitation of heavy metals.

o Sea water desalination. o Crystallization from solution in the manufacture of inorganic chemicals.

3

AQUEOUS ELECTROLYTE THERMODYNAMICS

o Specific ion electrolytes o Ion exchange

Specific processes which typify these application areas are:

o Treatment of gypsum which is formed in waste water cleanup. o Several processes involving formation of Cr(OH)3. These processes include:

- cooling tower blowdown - plating processes - manufacture of chrome pigment U s e of a simple solubility product (e.g. Lange's Handbook) for Cr(OH), is invalid since precipitation involves intermediate complexes which f a r m to a significant degree.

These are just a few of the application areas of electrolyte phase equilibria which have generated an interest in developing a better understanding of aqueous chemistry. In contrast to other systems, in particular hydrocarbon systems, design-oriented calculation methods are not generally available for electrolyte systems. In the undergraduate education of chemical engineers, little if any mention of electrolyte thermodynamics is made and most chemical engineering thermodynamic texts ignore the subject completely. If an engineer is exposed to electrolyte thermodynamics a t all during undergraduate education, the subject is taught on a rudimentary level so that many misconceptions may arise. For example, in manufacturing chrome pigment, noted above, use of the solubility product in order to determine solubility leads to very large errors since the solubility product approach totally ignores formation of complexes and their attendant effect on system state. Ry contrast. for hydrocarbon systems, most engineers are presented with a basic groundwork that includes design-oriented guidelines for the calculation of vapor-liquid equilibria of simple a s well a s complex mixtures of hydrocarbons. In addition, during the last decade, the education of a chemical engineer has usually included the introduction to various computer techniques and software packages for the calculation of phase equilibria of hydrocarbon systems. This has not been the case for electrolyte systems and even now it is generally not possible for the engineer to predict phase equilibria of aqueous systems using available design tools.

I . .Introduction

For processes involving electrolytes, the techniques used in the past and even some still in use today at times rely heavily on correlations of limited data which a r e imbedded into design calculation methods oriented towards hydrocarbon systems. Worse yet , until recently, limited use of the limited data available has occasionally led to serious oversights. For example, in the C1, scrubbing system noted earlier, the basic data published in Perry's Chemical Engineers' Handbook which has been used for years is actually in error. Hampering the improvement of the design tools or calculative techniques have been several restrictions including :

o A lack of understanding of electrolyte thermodynamics and aqueous chemistry. Without this understanding, the basic equations which describe such systems cannot be written.

o The lack of a suitable thermodynamic framework for electrolytes over a wide range of concentrations and conditions.

o The lack of good data for simple mixtures of strong andlor weak electro- lytes with which to test or develop new frameworks.

o The diversity in data gathering because of the lack of a suitable thermody- namic framework. A s a result of different thermodynamic approaches, experimental measurements to develop fundamental parameters have often led to the results being specific to the system studied and not generally useful for applications where the species studied are present with other species.

Fortunately, in the last decade, because of the renewed interest in electrolyte thermodynamics for the reasons described earlier, a considerable amount of work in the field of electrolyte thermodynamics has been undertaken. Techniques for the calculation of the vapor-liquid equilibria of aqueous solutions of weak electrolytes a re being published. New, improved thermodynamic frameworks for strong electrolyte systems are being developed on a systematic basis. With these developments. DIPPR established, in 1980, Research Project No. 811. The objective of this project i s to produce a "data book" containing recommended calculation procedures and serving as a source of thermodynamic data either through recommended tabulated values or through annotated bibliographies which point t o suitable sources.

5

AQUEOUS ELECTROLYTE THERMODYNAMICS

In order to meet the objectives of this project, several phases were established. The specific phases involved:

1) Definition of the project scope.

2) Gathering available data and literature references for the preparation of test data sets and data tables contained in the report.

3) Review of thermodynamics, techniques and recent developments in order to select those techniques to be evaluated in the final report.

4) Testing and comparison of the various techniques against selected tes t data sets.

5) Development of the handbook in order to present the results of the project in a useful and readable form.

This book is a result of DIPPR Research Project No. 811. In it, the reader and user will find a systematic presentation of electrolyte thermodynamics, from the basic definitions of equilibrium constants of ionic reactions. to the prediction of activity coefficients of various species in rnulticornponent aqueous solutions of strong andlor weak electrolytes and the resulting phase equilibria calculative techniques. For several systems, data are presented and calculative techniques are illustrated. The goal of this book is for the engineer, faced with the need for solving industrially important problems involving aqueous solutions of electrolytes, to be able to understand t h e possible alternatives available and apply them to the problem at hand, either with available data or through available data prediction and analysis techniques. Several examples will be used to illustrate the calculative techniques necessary for different types of problems. The examples chosen are of a size that can be solved with limited computer facilities. The techniques can be expanded for more complex problems.

In order to better understand the basis for the chapters which follow. let us consider the formulation of a predictive model for a particular aqueous based electrolyte system. The example chosen involves water-chlorine. The reactions to be considered are: