handbook of aqueous electrolyte thermodynamics theory amp application

Basic Thermodynamic Functions Solutions - Basic Definitions and Concepts Equilibrium - Necessary Conditions Activities, Activity Coefficients and Standard States EQUILIBRIUM CONSTANTS Io

This page intentionally left blank

MlDBB@@K

This page intentionally left blank

BFAQUEOUS ELECTROLYTE

Theory & Application

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-

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

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

This page intentionally left blank

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-

ported the project throughout its three year duration

(1 981 -1 983)

*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)

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

'Supported Project for 3 year life

This page intentionally left blank

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

DIPPR Technical Executive Committee and DIPPR Technical Committee

X

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

Short Range Interaction Model

Long Range Interaction Model

Comparison of Temperature Effect Methods

KOH at 80° Celsius NaCl at 100 and 300' Celsius NaOH at 35O Celsius

CaClz at 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

at 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 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

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 f o r Multicomponent Solutions

B romley's Water Activity

Pdeissner's Water Activity

Pitzer's Water Activity

Phase Diagram Calculations

Basic flow of t h e testing program

Program block descriptions

Appendix 5.1 - Values for Pitzer's 0 and J, Parameters

Table 1: Parameters f o 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

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

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 - Solutions at Salting Out Parameters from Pawlikowski and Prausnitz 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

Water - Ammonia - Carbon Dioxide

Water - Sulfur Dioxide

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

Table 5 : Molecule-ion interaction parameters

Table 1 : Pure component 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 aL 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 at 25OC

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)

xvi

NOMENCLATURE

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,

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

- 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 )

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 )

-

v i - stoichiometric number of ion i

n - osmotic pressure, equation ( 4 5 1 )

P - charge density, equation ( 4 1 )

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 l r - ionic potential

$t - total electric field potential, equation ( 4 1 )

Q - apparent molal volume

This page intentionally left blank

I nt rod uction

This page intentionally left blank

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 are 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 are produced as by-products which usually condense to

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

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

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 at 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 as 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'

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-

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

electrolytes are being published New, improved thermodynamic frameworks for strong electrolyte systems are being developed on a systematic basis With these

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 test 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

electrolytes, to be able to understand t h e possible alternatives available and

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:

I Introduction

Cl,(vap) = Cl,(aq)

Cl,(aq) + H,O = H(ion) + Cl(ion) + HClO(aq1

HClO(aq) = H(ion) + ClO(ion)

H,O(aq) = H(ion) + OH(ion)

The problem is to predict the resulting phase distribution and phase compositions

Or, in other words:

Given: Temperature (T), Pressure (PI and inflow quantities H,O(in) and Cl,(in)

Determine:

1) Total vapor rate V

2) Rate of HzO(aq)

3) Vapor phase partial pressures, pHzO and pClz

Liquid phase concentrations, usually expressed in molality (gm moles solute per 1000 gms solvent-Hz O(aq)), mHCIO(aq), mC12 (aq) , "H(ion), mOH(ion), mCl(ion), mClO(ion)

involving electrolytes

For the water-chlorine system above, a set of ten equations is required in order to

solve for the ten unknowns just described These equations are:

Equilibrium K equations are written, one for each reaction

equations are of the form:

As we shall see these 'ip

AQUEOUS ELECTROLYTE THERMODYNAMICS

yip, yiR = Activity coefficient or, for vapors, fugacity coefficient of the

ith product and reactant respectively; a function of T, P and canposi t ion

vip, viR = Stochianetric coefficient of the ith product and reactant

mip, miR = Molality or, for vapors, partial pressure of ith product and

respectively

reactant respectively

For our H20-Cl2 system (using y for activity coefficient, a for activity, f for fugacity coefficient and p for vapor partial pressure) w e thus have five such equations :

- - ‘H(ion) % ( i o n ) ‘Cl(ion) mCl(ion) YHCIO(aq) %ClO<aq)

K ~ 1 2 ( a s ) yC12 ( a q ) m C12 (aq) ‘H20(aq)

- YH( ion) “‘HC ion) ‘OH( ion) “‘OH( ion)

Electroneutrality Equation: Equation 6

The electroneutrality equation states that the solution is a t equilibrium, electrically neutral Generally stated, the equation is:

total molality of cations = total molality of anions

or, for our H20-C12 system:

% ( i o n ) = OH(ion) + C l ( i o n ) + CIO(ion)

1 introduction

Material Balances: Equations 7-10

The requisite material balances In this case, four such balances are needed to make the number of equations equal to the number of unknowns The equations are:

Vapor Phase

= %,avap) + P c ~ (vap)

These ten equations can, with a reasonable computer, be solved for the ten

unknowns in question Alternatively, by carefully organizing the calculations and

making some simplifying assumptions, for a simple system such a s CL,-H,O trial and

error using a calculator is also feasible What has been understated thus far is that, embedded in equations 1-5, the K equations, is the essential complexity of

the electrolyte calculations The variables, K(T,P) and y(T,P.m) are often highly nonlinear functions of the state variables shown The purpose of this book is

thus to describe:

1) The underlying physical chemistry theory which governs determination of

2) Practical methods for calculation, estimation or extrapolation of these values

K and y

9

This page intentionally left blank

I I:

Solutions

This page intentionally left blank

THERMODYNAMICS OF SOLUTIONS

In order to calculate the equilibrium composition of a system consisting of one

or more phases in equilibrium with an aqueous solution of electrolytes, a review

of the basic thermodynamic functions and the conditions of equilibrium is impor- tant This is particularly true inasmuch as the study of aqueous solutions requires consideration of chemical and/or ionic reactions in the aqueous phase

as well as a thermodynamic framework which is, for the most part, quite different from those definitions associated with nonelectrolytes Therefore, in this section we will review the definition of the basic thermodynamic functions the partial molar quantities, chemical potentials, conditions of equilibrium, activities, activity coefficients, standard states, and composition scales encountered in describing aqueous solutions

Basic Thermodynamic Functions

The thermodynamic properties of a system at equilibrium consists of two types of

properties, intensive and extensive properties The most common intensive properties encountered are the temperature, T and pressure, P, which are independent of the size of a measurement sample and are constant throughout the system In fact, our definition of true equilibrium, to be described later requires T and P to be uniform throughout the system and the constituent phases

The most common extensive properties are volume, V and mass As one would

suspect, these extensive properties are proportional to the size of a measurement sample

The thermodynamic properties most often encountered in describing phase equilibria

of a system are functions of the state of the system This is important since the calculation of these thermodynamic properties depends only on the existing state

of the system and not the route by which this state has been reached The following energy and energy related properties are extensive properties if they refer to the system as a whole:

The intrinsic energy E

The enthalpy H = E + P V

AQUEOUS ELECTROLYTE THERMODYNAMICS

definition of the Gibbs free energy,

can be arranged to give the Gibbs-Helmholtz equation, an expression very useful in calculating the effect of temperature on equilibrium

is given by:

-H

- Solutions - Basic Definitions and Concepts

The pure substances from which a solution can be made are called the components,

or constituents of a solution The extensive properties of a solution are deter-

intensive properties of a solution are determined by the pressure, temperature and

the relative amounts of each constituent or in other words b y the pressure,

commonly used measurement of composition of the solution is the molality, m

Molality is defined as the number of moles of a solute in one kilogram of the solvent, and for aqueous solutions the solvent is water One of the advantages of

using the molality scale for concentration is that it is independent of temperature

11 Thermodynamics of Solutions

and thus, the density of the solution does not need to be known in order to determine the composition on a mole basis as would be required with the unit of

of solute and solvent, M is the solute mo!ecule weight and ni is the number of gm-moles of solute

The thermodynamic analysis of solutions is facilitated by the introduction of

quantities that measure how the extensive thermodynamic quantities (V, E, HI) G ,

I of the system depend on the state variab!es T , P, and ni This leads to the definition of partial molar quantities where, i f , w e let Y be any extensive thermodynamic property, we can define the partial molar value of Y for the ith component as:

where nj stands for all the mole quantities except ni It is important to note that the partial molar (or partial mold, which has the same meaning) quantities pertain to the individual components of the system and are also properties of the system as a whole Furthermore

Partial molar quantities are intensive properties of the solution since they

depend only on the composition of the solution, not upon the total amount of each component If w e add the several components simultaneously, keeping their ratios constant, the partial molal quantities remain the same W e can thus integrate the above expression keeping “1, “2, in constant proportions and find, while holding temperature and pressure constant, that