AE-377 UDC 681.3.01

541.138 541.123.21.081

Studies of Redox Equilibria at Elevated

Temperatures I.

The Estimation of Equilibrium Constants and Standard

Potentials for Aqueous Systems up to 374° C

Derek Lewis

This report is intended for publication in a periodical. References may not be published prior to such publication without the consent of the author.

AKTIEBOLAGET ATOMENERGI

STUDSVIK, NYKOPING, SWEDEN 1969

AE-377

STUDIES O F REDOX EQUILIBRIA AT ELEVATED TEMPERATURES

I. THE ESTIMATION OF EQUILIBRIUM CONSTANTS AND STANDARD

POTENTIALS FOR AQUEOUS SYSTEMS UP TO 374°C

Derek Lewis

SUMMARY

A method is descr ibed for the est imat ion of equil ibrium con­

stants for aqueous sys tems a t t empe ra tu r e s up to 374°C from entropy

and free energy data for 25 C and data on the var ia t ion of heat capaci ty

with t e m p e r a t u r e . Pa r t i a l molal heat capaci t ies of aqueous ions a r e

es t imated on the bas is of the principle (C. M. C r i s s and J . W. Cobble)

that, with suitably chosen s tandard s t a t e s , the par t ia l molal entropies

of ions of a pa r t i cu la r c lass at any given t empera tu re a r e l inear ly r e ­

lated to the corresponding entropies at some reference t e m p e r a t u r e .

The method suggested is compared with other methods , based on the

Van't Hoff i sobar and on an extension (Naumov) of the conventional scale

of ionic free energy at 25 C, and the general dependence of aqueous

equil ibria on ionic heat capacity is considered.

This repor t is intended for publication in a

per iodical . References may not be published

pr ior to such publication without the consent

of the author.

- 2 -

LIST OF CONTENTS

Paffe

Introduction 3

1. Fundamental concepts 5

1.. 1. The descr ipt ion of e l ec t rochemica l equil ibria

in aqueous sys tems 5

1.2. The var ia t ion of the equil ibrium constant with

t empera tu re 6

2. The thermodynamic proper t i es of aqueous ions

at elevated t empera tu re s 10

2 . 1 . Relative ionic s tandard free energy 10

2 . 2 . Absolute ionic entropy and mean ionic heat capacity 12

3. An a s s e s s m e n t of methods for es t imat ing equil ibrium

constants for react ions in aqueous media at elevated

t empera tu re s 17

3. 1. Resul ts obtained using es t imates of ionic heat

capacity 17

3 . 1 . 1 . The formation of water 19

3 . 1 . 2 . The protolysis of ammonium ion 20

3 . 1 . 3 . The reduction of s i lver chloride 21

3 . 1 . 4 . The protolysis of water 22

4 . Fur the r analysis of aqueous equil ibria at elevated

t empera tu re s 23

4 . 1 . The free energy of solvation 23

4 . 2 . The effect of p r e s s u r e 26

Conclusion 27

Acknowledgements 28

References 29

Tables 33

F igures

- 3 -

INTRODUCTION

In connection with investigations of the cor ros ion of s t ruc tura l

m a t e r i a l s in var ious environments at high t e m p e r a t u r e s , being c a r r i e d

out by AB Atomenergi , i t has been n e c e s s a r y to study ways of e s t i m a ­

ting equil ibrium quantities from thermodynamic data and ways of p r e ­

senting large numbers of these quantities in easi ly comprehensible

f o r m s . Kinetic considerat ions may be of predominent importance in

cor ros ion p r o c e s s e s , pa r t i cu la r ly when appreciable m a s s - t r a n s p o r t

o c c u r s , but, as activation energy b a r r i e r s usually become smal l at

high t e m p e r a t u r e s , a knowledge of the thermodynamic p a r a m e t e r s r e ­

levant to the react ions (oxidation) accompanying i ts dissolution is essen­

tial for the definition of the stabil i ty of any solid phase . An exper imen­

tal study of each of the very many equil ibria involved in cor ros ion and

meta l lu rg ica l p r o c e s s e s is imprac t icable and thermodynamic methods

pe rmi t the predict ion of the r e su l t s of many react ions under a va r ie ty

of conditions from a l imited number of fundamental data .

For me ta l -wa te r - l igand sys tems mos t of the ve ry great number

of thermodynamic data that have been collected by Sillen [ l ] r e la te to

the reference t empera tu re 25.00 C (298.15 K). Tempera tu re s in the

water -cooled nuclear r e a c t o r s and the conventional s team plant now in

use a r e commonly as high as 250 C and in the future_this l imi t for the

liquid phase may be increased to the cr i t ica l t empera tu re (374 C).

Some information on the var ia t ion with t empera tu re of the s tandard

free energy of reac t ion for a number of meta l lurg ica l equil ibr ia has

been collected by, for example , Kubaschewsky and Evans [ 2 ] , and an

increas ing amount of data for aqueous sys tems at elevated t e m p e r a ­

tu res is now being obtained exper imental ly [ 3 ] . However, for m o s t

aqueous e lec t rochemica l r eac t ions , such as oxidation, e s t ima tes of the

equil ibrium constant at these t empera tu re s can still only be obtained

by extrapolation from data for about 25 C using the a rguments of c l a s ­

sical the rmodynamics . Relatively few at tempts have been made to do

this perhaps par t ly because the conventional sca les for the re la t ive

thermodynamic p roper t i e s of aqueous ions a r e not obviously suitable

for t empera tu re s other than the reference t e m p e r a t u r e . It i s only

- 4 -

recent ly that methods have been suggested, by Naumov and his co­

worke r s and by Cr i s s and Cobble, that resolve this difficulty.

The study presented here brings together and, to some extent,

further develops some aspec ts of previous work concerning ionic equi­

l ibr ia and the var ia t ion of thermodynamic proper t ies with t e m p e r a t u r e .

A method is descr ibed for es t imat ing the equil ibrium constants of r e ­

actions in dilute aqueous solutions at t empera tu re s up to the cr i t ica l

t empera tu re of wa te r . This method is used in a concurrent s e r i e s of

publications on equil ibrium d iagrams for meta l - water sys tems at

elevated t empera tu re s [4].

- 5 -

1. FUNDAMENTAL CONCEPTS

As some quantities that have hi therto only infrequently occur red

in e lec t rochemica l d iscuss ions will be used he re and in the publications

that follow, i t is convenient to define the notation in a recapitulat ion of

some fundamental concepts .

1 .1 . The descr ip t ion of e lec t rochemica l equil ibria in aqueous sys tems

Equi l ibr ia in aqueous media involving an oxidised spec ies , A,

and the conjugate reduced spec ies , B, may be descr ibed general ly by

the formula :

aA + hH+ + e" = bB + wHzO (r)

and the equil ibrium constant at T K:

T K r = {B} b {H z O} W {A} " a { H + } " h { e " } _ 1

For dilute solutions a reasonable approximation is obtained when con­

centra t ion, [ ] , is substi tuted for act ivi ty, { } , so that

l o g T k r = pe + hpH - log [ A ] a • [ B ] " b (1.1)

where p denotes the opera tor - log.

The equil ibr ium constant for any react ion r is re la ted to the

change in s tandard free energy accompanying the reac t ion , A T G , a c ­

cording to the Van't Hoff i so the rm,

- R T l n T K r = ATG° = Sv (i) • A T G ° (i) ( 1 . 2)

Here ATG. (i) denotes the s tandard par t ia l molal free energy of fo rma­

tion of the constituent i , v (i) moles of which par t ic ipate in the reac t ion .

Thus equil ibrium constants that may not be access ib le by d i rec t m e a s ­

u remen t can be calculated from the free energies of formation of the

reac tan ts or from the equil ibrium constants (multiplied by the appro ­

pr ia te coefficients) of a number of par t ia l react ions which together lead

to the overa l l reac t ion .

- 6 -

F o r l a r g e l y h i s t o r i c a l r e a s o n s the f r e e e n e r g y c h a n g e s a c c o m ­

pany ing r e a c t i o n s in e l e c t r o c h e m i c a l c e l l s have u s u a l l y b e e n e x p r e s s e d

in t e r m s of the N e r n s t r e l a t i o n . T h u s , for the h a l f - c e l l ( e l e c t r o d e ) r e -

r e a c t i o n ( r )

T e = T e ° + R T F - 1 In 1 0 . 1 o g [ H + 3 + R T F - 1 In 1 0 . l o g [ A ] a [ B ] " b

(1-3)

H e r e e r e p r e s e n t s e l e c t r o d e po t en t i a l (vo l t s ) , o t h e r w i s e the s y m b o l s

h a v e t h e i r conven t iona l m e a n i n g s [ l ] .

An often m o r e a d v a n t a g e o u s f o r m u l a t i o n of e l e c t r o c h e m i c a l p h e ­

n o m e n a , c o n s i s t e n t wi th the g e n e r a l t r e a t m e n t of c h e m i c a l e q u i l i b r i a

and c o m p a r a b l e wi th t h a t of the (hyd ra t ed ) p r o t o n , i s ob t a ined when the

e l e c t r o n i s t r e a t e d l ike any o t h e r an ion [ 1 , 5 , 6 , 7 ] . T h u s , f r o m (1 .1 )

pe = p e ° - hpH + l o g [ A ] a [ B ] " b (1 .4 )

w h e r e

pe = ( R T F - 1 . l n l O ) " 1 . T e (1 .5 )

p e ° = ( R T F - 1 . l n l O ) " 1 . ^ e° (1 .6 )

The v a l u e s of the f a c t o r ( R T F In 10) u s e d h e r e a r e

t ° C 50 100 150 200 250 300 350

( R T F _ 1 l n l 0 ) m V 6 4 . 1 2 7 4 . 0 4 8 3 . 9 6 9 3 . 8 8 1 0 3 . 8 1 1 3 . 7 1 2 3 . 6

As w e l l a s i m p r o v i n g l o g i c a l c o n s i s t e n c y the u s e of e l e c t r o n ac t i v i t y

i n s t e a d of e l e c t r o d e p o t e n t i a l s i m p l i f i e s c a l c u l a t i o n s and the c o n s t r u c ­

t ion of e q u i l i b r i u m d i a g r a m s by e l i m i n a t i n g the f a c t o r R T F In 10.

It a l s o e l i m i n a t e s the r i s k ' of t r e a t i n g s t a n d a r d e l e c t r o d e p o t e n t i a l s a s

i n d e p e n d e n t of t e m p e r a t u r e .

1 .2 . The v a r i a t i o n of the e q u i l i b r i u m c o n s t a n t wi th t e m p e r a t u r e

A n u m b e r of m e t h o d s have b e e n p r o p o s e d for t h e r m o d y n a m i c

c a l c u l a t i o n of e q u i l i b r i u m q u a n t i t i e s a t v a r i o u s t e m p e r a t u r e s . F o r the

p r e s e n t p u r p o s e of e x a m i n i n g r e a c t i o n s in a q u e o u s s y s t e m s a t e l e v a t e d

t e m p e r a t u r e s i t i s conven i en t to u s e e x p r e s s i o n s r e l a t i n g the m a g n i t u d e

of the e q u i l i b r i u m c o n s t a n t a t any g iven t e m p e r a t u r e to i t s m a g n i t u d e

- 7 -

at a reference t e m p e r a t u r e , 298.15 K, and to the corresponding

changes in enthalpy and entropy.

The change in s tandard free energy, A T G , is re la ted to the

change in s tandard enthalpy, A „H = E v ( i ) . A_.Hr (i), and in s tandard

entropy, A _S = £v ( i ) . S (i), by the Gibbs-Helmholtz equation

A T G ° = A T H ° - T A T S ° (1.7)

and, since 9(ATG°)/9T | p = - A T S ° ,

a ( A T G ° / T ) / 3 T | p = ( T 9 ( A T G ° ) / a T | p - A T G ° ) / T 2 = - A T H ° / T 2

which leads to the Van ' t Hoff i soba r :

8 ( l n T K ) / 3 T | p = A T H ° / R T 2 (1.8)

Thus , in a f i r s t approximation, AH may be supposed to be near ly

independent of T and then ln_,K can be es t imated using the expres s ion :

ln T K = l n 2 9 g K + ( A H ° / R ) ( T - 298)/298 T (1.9)

Exper ience has shown that the es t imates of equi l ibr ium con­

stants for aqueous sys tems at elevated t empera tu res formed using the

Van ' t Hoff i sobar may somet imes be in e r r o r by severa l logar i thmic

un i t s . E r r o r s might a r i s e from a var ie ty of causes such a s , for ex­

ample , unanticipated conjugate react ions like hydro lys i s , but it is c lear

that in o rde r to obtain be t te r e s t imates account m u s t be taken of the

var ia t ion of enthalpy and entropy with t e m p e r a t u r e .

The changes in s tandard enthalpy and s tandard entropy at t em­

pe ra tu re T a r e re la ted to these quantities at the re ference t empera tu re

and to the change in mola r heat capacity, A — Cp = Sv ( i ) T C (i), by

ATH° = A298H^ 1<> + i ' 2 9 8 A T C P * d T (1A°\

A T S° = A 2 9 8 S ° + ^ J 9 8 A T C p ' d In T (1.11)

These re la t ions , together with the Gibbs-Helmholtz equation and the

- 8 -

react ion i so the rm lead to the equation:

l n T K = ^ l n 2 9 8 K + ^ [ ( T - 298)A2 9 gS° + T\ ^ ATC° d in T

- . ^ 2 9 8 A T C p ' d T ] t 1 ' 1 3 )

Molar heat capacity may be expressed as a function of t empera tu re by

means of the empi r ica l formulae given by Kelley [8] and o the r s , e . g . ,

T C p ( i ) = a(i) + b(i)T + c( i )T" 2 (1 . 14)

where a(i) , b(i) and c(i) a r e constants pecul iar to the substance (i) in

quest ion. Thus , in so far as values for the Kelley coefficients of the

consti tuents can be obtained, a bet ter es t imate of In K may be formed

from the express ion :

l n T K = (298 /T ) ln 2 9 8 K + | - [2N> (i) . 2 9 8 S°( i ) ( l - 2 9 8 / T ) "

- S v(i) a(i) • ((1 - 298/T) + ln(298/T))

+ Sv(i)b(i) • ((T - 298) - (T 2 - 298 2 ) /2T)

- Ev( i )c ( i ) - ( ( T " 2 - 2 9 8 " 2 ) / 2 - ( T _ 1 - 2 9 8 _ 1 ) / T ] (1.15)

which may be wri t ten in the form

l o g T K r = f 1 ( T ) l o g 2 9 8 K r + f 2 (T)A 2 9 g S° + f 3(T)Aa +

+ f4(T)Ab + f (T)Ac (1-16)

The values of the coefficients f(T) in equation (1.16) for some t e m p e r a ­

tures between 50 and 350 C a r e given in table 1. An i l lus t ra t ion of the

use of equation (1 . 15) is the est imat ion of the equil ibrium constant for

the hemat i te -magnet i te react ion in water at elevated t e m p e r a t u r e s :

1 . 5 F e 2 0 3 ( s ) + H+ + e" = Fe3C>4(s) + 0 . 5 ^ 0 (Fe 12)

pe = l ° g T k F e l l " PH+ log { F e 2 0 3 ) i - 5 { F e 3 0 4 }

l o S 2 9 8 k F e l l = 3 - 7 4

- 9 -

t°C

f 1 ( T ) . l o g 2 9 8 k F e n

50

3 . 4 5

0 . 2 7

0 . 0 0

0 . 0 2

0 . 0 0

3 . 7 0

150

2 . 6 3

1.04

- 0 . 0 5

- 0 . 2 9

0 . 0 6

3 . 3 9

250

2 . 1 3

1.51

- 0 . 1 3

- 0 . 7 6

0 . 1 2

2 . 8 7

3 50

1.79

1.84

- 0 . 2 0

- 1 . 3 3

0 . 1 8

2 . 2 8

f 2 ( T ) . S v ( i ) . 2 9 8 S ° ( i )

f 3 ( T ) . S v ( i ) . a ( i )

f 4 ( T ) . E v ( i ) . b ( i )

f 5 ( T ) . S v ( i ) . c( i)

l o g T k 3

Since u s u a l l y v e r y m a n y e q u i l i b r i a m u s t be c o n s i d e r e d for e a c h m e t a l -

l i g a n d - w a t e r s y s t e m of i n t e r e s t , i t m a y often be conven i en t to u s e a com­

p u t e r for the c a l c u l a t i o n s . A s i m p l e p r o g r a m for t h i s p u r p o s e i s g iven

in ALGOL, in t ab l e 2 . A f a c s i m i l e of the ou tput (IBM 360-30) o b t a i n e d

fo r the h e m a t i t e - m a g n e t i t e r e a c t i o n i s g iven in t ab l e 3 . The q u a n t i t i e s

u n d e r the c o l u m n h e a d i n g s in t h i s t ab l e a r e :

1 0 E 3 = 1 0 3 T _ 1 ,

V H O F F K = e s t i m a t e of log k f o r m e d u s i n g the V a n ' t Hoff >r. i s o b a r , 1 . „ o , „ H E A T H = 1 0 " 3 . ^ 9 8 A

TC P * d T '

S I G T H = 10 - 3 (A 8 H ° + ^ A C ° d T ) , 298 J 298 T P '

H E A T S = ^ 2 9 8 A T C P d l n T »

TSIG TS = 1 0 " 3 T ( A 2 9 8 S ° + ^ 298 A T C P d l n T '

GIBBS K = e s t i m a t e of log k f o r m e d u s i n g equa t ion ( 1 . 15)

E Z E R O = R F " l n T k (GIBBS K) x n u m b e r of e l e c t r o n s i nvo lved

When the s t a n d a r d h e a t of f o r m a t i o n h a s no t been known for a l l the c o n ­

s t i t u e n t s the da t a for one c o n s t i t u e n t (usua l ly A_ q 8 H (e )) h a v e b e e n

ad ju s t ed so t h a t A _,H = 0. In such c a s e s a s i ng l e v a l u e , l o g 7 Q o k (

a p p e a r s r e p e a t e d l y u n d e r V H O F F K.

- 10 -

2. THE THERMODYNAMIC PROPERTIES OF AQUEOUS

IONS AT ELEVATED TEMPERATURES

Although the thermodynamic methods summar i sed in the p r e ­

vious section have been used extensively and for a long t ime in studies

of the effect of t empera tu re on many kinds of equil ibria such a s , for ex­

ample , meta l lu rg ica l react ions [2], re la t ively li t t le use has been made

of them in studies of react ions in aqueous media . In pa r t , at l eas t ,

this may have been due to a conceptual difficulty in the extension of the

conventional hydrogen sca les for the relat ive thermodynamic proper t i es

of ions to t empe ra tu r e s other than the re ference t empera tu re [9].

Recent ly, some success in t reat ing aqueous equil ibria has been

obtained by two quite different approaches to the thermodynamic p rope r ­

t ies of ions in solutions at elevated t e m p e r a t u r e s . In the f i r s t of these ,

proposed by Naumov and his co -worker s [10, 11] the a r b i t r a r y hydrogen

scale for ionic free energy is extended to elevated t empera tu re s on the

bas is of the exper imental ly determined var ia t ion of the free energy of

hydrogen g a s . In the second, proposed by Cr i s s and Cobble [12,13]

"abso lu te" ionic entropies and ionic heat capaci t ies a r e es t imated by

means of empi r ica l re la t ions based on a number of exper imenta l data

for aqueous equil ibria at elevated t e m p e r a t u r e s .

2 . 1 . Relative ionic s tandard free energy

The es tabl i shment of re la t ive values for the thermodynamic p r o ­

pe r t i e s of individual ions on general ly used conventional scales has lead

to the successful cor re la t ion and, to some extent, the in te rpre ta t ion of

a ve ry l a rge number of data on e lec t rochemical react ions in aqueous

med ia . A par t i cu la r ly a t t rac t ive aspec t of this conventional approach

has been that it has made possible widely accepted descr ip t ions of the

behaviour of e lectrolyte solutions r e g a r d l e s s of cont rovers ies about the

physical meaning of individual ionic p r o p e r t i e s .

The success and wide acceptance of the conventional approach

to e lec t rochemica l thermodynamics at t empe ra tu r e s near 25 C has lead

Naumov et a l . to propose that , as is the case at the reference t empera -

- 11 -

tu re , the s tandard free energy of formation of each aqueous ion at any

t empera tu re T is to be re la ted to the s tandard free energy of fo rma­

tion of hydrogen ion at the same t e m p e r a t u r e . It m a y thus be evalua­

ted from the exper imental ly determinable change of s tandard free

energy in reac t ions such as

A + H+ = B + + \ H zO

ATG°(B+) = A T G ° . * A-TG°(H+) + A TG°(A) - 0. 5ATG°(H20)

In turn , the s tandard free energy of formation of hydrogen ion is to be

evaluated by means of the react ion

H + + e" = | "H 2 (g) (HI)

for which the change in s tandard free energy is conventionally equated

to zero at all t empera tu re s so that

0.5ATG°(H2) - ATG°(H+) = A T G R 1 = 0

Thus , the s tandard free energy of formation of hydrogen ion at t empe­

ra tu re T is to be equated with half the s tandard free energy of fo rma­

tion of hydrogen gas at the same t empera tu re from hydrogen gas at the

reference t e m p e r a t u r e . In accordance with the a rguments of the p r e ­

ceding section this quantity i s given by

-ATG°(H2) = (T - 298). 2 9 g S ° ( H 2 ) + T j 2 9 8 T c £ ( H 2 ) d In T -

"J" 298 T ^ ) " dT fe'1) This express ion and the wel l -es tabl i shed exper imental values for the

entropy and Kelley coefficients of hydrogen gas lead to the following

values for the s tandard free energy of formation of hydrogen ion at

var ious t empera tu re s :-

T°K 323 373 423 473 523 573

A T G°(H + )kca l • m o l " 1 0.39 1.20 2.03 2 ,88 3.74 4 .63

- 12 -

On the bas is of this proposal and experimental ly determined

equil ibr ium constants for a few react ions at elevated t e m p e r a t u r e s ,

Naumov and his co -worker s have evaluated the relat ive s tandard free

energy of formation of a number of anions and cations in the t e m p e r a ­

ture range 25 to 300 C. These constants they have then employed in

studies of severa l other reac t ions , principally hydrothermal react ions

of geochemical i n t e r e s t .

Although the ag reement between experimental ly m e a s u r e d equi­

l ibr ium constants and those calculated using relat ive s tandard free

energies is likely to be as p rec i se as the determinat ions of these free

ene rg i e s , this conventional approach to equil ibrium analysis seems to

have some disadvantages . Thus , i t r equ i re s that for each and every

ion of i n t e r e s t as r ega rds react ions at elevated t e m p e r a t u r e s , at l eas t

one reac t ion in which that ion is a constituent m u s t have been studied

over the range of t empera tu re in question. Even if this may be possible

it s eems labor ious . Another disadvantage is that, like all a r b i t r a r y

approaches to general phenomena, i t might inhibit a t tempts to obtain

a m o r e detailed descr ipt ion and, pe rhaps , a deeper understanding of

the fundamental quantities involved. The continuation of efforts to r e ­

solve cont rovers ies about the proper t ies of individual ions seems de ­

s i r a b l e .

In the a l ternat ive approach suggested by Cr i s s and Cobble, in­

volving the evaluation of "absolute" ionic en t ropies , these disadvan­

tages a r e l ess m a r k e d .

2 . 2 . Absolute ionic entropy and heat capacity

The calculation of the free energies of aqueous ions from f i r s t

pr inciples continues to receive attention [14, 15, 16] but only l imited

success has been had so fa r . On the other hand, cons iderab le success

has been had recent ly in evaluating the s tandard par t ia l molal entropies

of ions at 25 C from m o r e or l e s s empir ica l re la t ions involving such

factors as ionic charge , m a s s , geometry , e t c . , [refs 17 to 2 2 ] .

Cr i s s and Cobble [12] have observed that the exper imental

values that have been obtained for the entropies of a number of ions at

- 13 -

elevated t empe ra tu r e s indicate that re la t ions hold between these quanti­

t ies and the p a r a m e t e r s ionic charge , m a s s , e t c . , like those holding

at 25 C. This leads them to suppose that there exis ts a s e r i e s of c o r ­

responding s ta tes for ionic entropies at different t empe ra tu r e s such

that the conventional s tandard par t ia l molal entropy of an ion at the o _

t empera tu re t C ai an express ion like

t empera tu re t C and at the reference t empera tu re 25 C a r e re la ted by

tS°(i) = ta + tb 2 5S°(i ) + t c ( 2 5 S°( i ) ) 2 +

If the e n t r o p i e s of a l l i o n s a r e r e l a t e d to tha t of the h y d r o g e n - i o n t h e n

the m a g n i t u d e s of the c o r r e s p o n d e n c e p r i n c i p l e coef f i c ien t s a, b , e t c .

fo r e a c h t e m p e r a t u r e a r e d e t e r m i n e d by the v a l u e of the e n t r o p y of the

h y d r o g e n - i o n a t t h a t t e m p e r a t u r e . F o r one , and only o n e , s e r i e s of

v a l u e s of t h i s quan t i ty for a r a n g e of t e m p e r a t u r e s , the c o r r e s p o n d e n c e

p r i n c i p l e i s found to l e a d to l i n e a r r e l a t i o n s h i p s of the f o r m :

t S ° ' ( i ) = t a + t b 2 5 S ° ' ( i ) ( 2 . 2 )

The c o r r e s p o n d e n c e p r i n c i p l e coef f ic ien t s a r e the s a m e for e a c h

ion of a c l a s s of s i m i l a r i o n s , s u c h a s the c l a s s of s i m p l e c a t i o n s M ,

d i f fe r ing on ly f r o m c l a s s to c l a s s . The l i n e a r c o r r e s p o n d e n c e r e l a t i o n ­

sh ip a c c u r a t e l y d e s c r i b e s the v a l u e s t ha t h a v e been ob ta ined e x p e r i m e n ­

t a l l y for the r e l a t i v e p a r t i a l m o l a l e n t r o p i e s of ions up to 200 C , a t

l e a s t . F o r s i m p l e ions up to 150 C the a c c u r a c y i s abou t 0 . 5 e . u .

The val,ue for _S (H ) wh ich l e a d s to the l i n e a r c o r r e s p o n d e n c e

r e l a t i o n for 25 C, n a m e l y - 5 . 0 e . u . , f a l l s wi th in the r a n g e of v a l u e s

t h a t h a v e b e e n s u g g e s t e d for the a b s o l u t e e n t r o p y of the H - ion a t 25 C

[ 2 3 , 2 1 , 15] . T h u s the s c a l e s of ion ic e n t r o p y def ined by the c h o s e n s e ­

r i e s of v a l u e s of the e n t r o p y of the h y d r o g e n - i o n a t v a r i o u s t e m p e r a ­

t u r e s , beg inn ing wi th __S (H )= - 5 . 0 , m a y b e r e g a r d e d a s s c a l e s of

" a b s o l u t e " e n t r o p y [ l l ] . The " a b s o l u t e " s t a n d a r d p a r t i a l m o l a l ion ic — o /

e n t r o p y a t the r e f e r e n c e t e m p e r a t u r e , _ ,.£! ( i ) , i s r e l a t e d to the " c o n ­v e n t i o n a l " ( 2 c S (H ) = 0) ion ic e n t r o p y , _§ (i) by the equa t i on

25§°'( i ) = 25§° ( i ) " 5*° Z < 2 ' 3 )

- 14 -

The following discussion will be concerned only with these "absolute"

ionic entropies which will be denoted by unprimed S .

In order that equations derived from the Gibbs-Helmholtz re­

lation, like equation (l. 13), can be applied to aqueous equilibria it is

desirable, and in some cases essential, that an estimate be formed of

the standard (partial) molal heat capacity of each of the species in­

volved. Criss and Cobble have shown [13] that estimates of this quan­

tity for ions in dilute aqueous solution (reliable data is available for

water and most solids and gases), can be obtained using the values for

the correspondence principle coefficients they have derived from ex­

perimental entropy data. The standard partial molal heat capacity of

an ion is defined by

t2S°(i) = t lS°(i) + ^ tC°(i)dlnT (2.4)

so that, if .C (i) is approximated with its average value between tl and

t2 C°] t2 P

t2S°(i) = tlSU(i) + Cp(i)]g ln(T2/Tl) (2.5)

Thus, an estimate of the mean value of the relative standard partial

molal heat capacity between two not too widely separated temperatures

may be obtained from values for the standard partial molal entropy at

the two temperatures using the equation

«.-> +->S°(i) - .S°(i) -o,,N-.t2 t2 w tl w (7 / \

V ; J t l " 2.303 log (T2/T1) { '

The values for the standard partial molal entropy, in turn, may be ob­

tained by means of the correspondence principle.

In their development of these ideas Criss and Cobble have chosen

to derive equations for the average heat capacity of ions of the various

classes, containing two empirical constants like those for ionic entro­

pies at various temperatures. They have also chosen to take the aver­

age between the (higher) temperature in question, here t2, and the re­

ference temperature. When applied to large intervals of temperature,

- 15 -

however , this usage m a y lead to unnecessar i ly la rge e r r o r s . In addi­

tion, it i s des i rab le that the var ia t ion with t empera tu re of the heat ca­

paci t ies of ions be descr ibed by equations like those used for other

spec ie s , i . e . , that Kelley coefficients be evaluated for ions! A simple

extension of C r i s s and Cobble ' s work makes this possible without any

significant dec rease in accuracy .

Cr i s s and Cobble have found that for t empe ra tu r e s up to 200 C.,

at l e a s t , the correspondence principle coefficients vary approximately

l inear ly -with t empera tu re so that for t C

a = et + f (2.7)

t b = gt + h (2.8)

Four sets of values of the constants e, f, g, and h, have been obtained

corresponding to the four c l a s ses of ions dist inguished. Using these

express ions for a and b the correspondence pr inciple (2.2) may be

rewr i t t en

£°(i) = (e + g- _ f S ° ( i ) ) ( T - 273.15) + (f + h- _ f S ° ( i ) ) T ~ V * / - \ - • 6 r e f " V - / 7 V * - • - . . . - , , . ^ • ~ r e r

i . e . ,

TS°(i) = (e + g. r e f S ° ( i ) ) . T - ( e + g r e f S ° ( i ) ) - 273.15

+ (f + h r e f S°( i ) ) .

F o r smal l t empera tu re in tervals the average s tandard par t ia l molal

heat capacity, C_j(i)]T J, is thus given by

G£(i)]£+J= ( T + j S°( i ) - T S°( i ) ) / ln ( (T + j ) / T )

so that , within the validity of (2. 7) and (2. 8) and of the approximation

l n ( l + j / T ) = j / T ,

T C ^ ( i ) = ( e + g r e f S ° ( i ) ) ' T (2.9)

Thus , the s tandard par t ia l molal heat capacit ies of aqueous ions m a y be descr ibed by the Kelley formula (1.14), the coefficients a and c

- 16 -

being z e r o , and

b = (e + g. 2 9 8 S ° ( i ) ) (2.10)

Values for the Kelley b-coefficient and other p roper t ies of a number of

common ions a r e collected in table 4 .

- 17 -

3. AN ASSESSMENT OF METHODS FOR ESTIMATING EQUILIBRIUM

CONSTANTS FOR REACTIONS IN AQUEOUS MEDIA AT ELEVATED

TEMPERATURES

The resu l t s obtained using the pr inciples descr ibed in sections

1.2 and 2 .2 can usefully be a s s e s s e d in connection with some general

observat ions regarding the effects of t empera tu re changes on aqueous

equi l ibr ia . As i t is des i rab le to at tempt to establ ish a theoret ica l

bas is for the empi r ica l re la t ions used in this work i t may also be u s e ­

ful to analyse further the factors l ikely to influence equil ibria on the

bas is of models of the p roper t i e s of ions .

3 . 1 . Resul ts obtained using es t imates of ionic heat capacity

It i s apparent from the quantities in table 1 that , depending on

the magnitudes of the Kelley coefficients, the l a rge s t contributions to

the equil ibrium constant a r e likely to be made by the proport ional t e r m

( 2 9 8 / T ) l o g 2 9 g k and the entropy t e r m (1 - 298/T) g S ° / R . Thus devia­

tions from a l inear dependence of log k on l / T , in accordance with

the Van ' t Hoff i soba r , a re to be expected only when the Kelley coeffi­

c ien ts , especia l ly the b-coeff icients , a r e la rge and when they a r e much

different for the consti tuents in the forward (reactants) and the r e v e r s e

(products) r eac t ions .

F o r many substances the a-coefficient is between 10 and 30,

only for a few does it exceed 40 . S imi lar ly , the b-coefficient seldom _3

exceeds about 20x10 . The c-coefficient is often close to unity. Fo r

aqueous ions , however , as seen in table 4, the b-coefficients vary be --3 -3

tween about 100x10 and 300x10 for cat ions, increas ing with charge, -3 -3

and between about -150x10 and -400x10 for mos t anions . Thus the

magnitude of the inc rement to the equil ibrium constant a r i s ing from the

heat capacity t e r m s will often be determined la rge ly by the contr ibu­

tions due to the ions taking pa r t in the reac t ion . The inc rements (log

units) for some typical ions , given by the product of f ,(T) in table 1

and the es t imates of the b-coefficients for the ions obtained by means

of the correspondence pr inc ip le , a r e given in table 11 .

- 18 -

Clear ly , the inc rement due to heat capacity can be expected to

be g rea te s t for react ions in which there a re m o r e ions among the r e a c -

tants than the products , or converse ly . The l a r g e r the number of un­

balanced ions , and the g rea te r the difference between unlike balanced

ions , the g rea te r will be the contribution of heat capacity to the equi­

l ibr ium constant and the e r r o r that would be introduced by neglecting

this contribution.

Some simple i l lus t ra t ions of this a r e given in the table below

which shows the e r r o r s (log units) that can be expected in the equil i ­

b r ium constants for some typical react ions at 350 C, es t imated in two

ways . In the f i r s t , e s t imate 1, log „ k has been calculated using equa­

tion (1.15) with the par t ia l molal heat capaci t ies of the ionic consti tu­

ents se t equal to z e r o . In the second, es t imate 2, log „ k has been ca l ­

culated using the Van ' t Hoff i soba r . The values obtained using equa­

tion (1.15) with ATC es t imated by means of the correspondence p r in -

ciple have been taken to be the c o r r e c t values of the constants and the

e r r o r s shown a re the differences from them.

Table 12. Typical e r r o r s in es t imates of equil ibrium constants

due to neglecting heat capacity t e r m s

Number of Reaction Es t imate Es t imate unbalanced 1 2

ions

0 | 0 2 ( g ) + H 2 ( g ) ^ H 2 0 ( l ) - 0.17

0 NH* ^ H+ + NH (aq) - 0.34

1 AgCl(s) + e~ ^ Ag(s) + Cl" 3.21 1.50

2 H zO # H+ + OH" 1.48 2.40

In figures 1, 3, 4 , and 6, the values obtained for the equil ibrium

constants of these reac t ions using equation (1.15), a re compared with

those der ived from data, repor ted in the l i t e r a t u r e , that have been ob­

tained by severa l different exper imental me thods . The data on which

these f igures a re based a re collected in tables 5 to 10.

- 19 -

3 . 1 . 1 . The formation of water

The formation or thermolyt ic dissociat ion of liquid water may­

be supposed to proceed via the two fundamental equil ibria

^ O z ( g ) + H+ + e " * | H 2 0 ( 1 ) (Ol)

H+ + e " * | H 2 ( g ) (HI)

so that

^ 0 2 ( g ) + i H 2 ( g ) ^ H 2 0 ( l ) (Wl)

l o § T k W l = l o 8 T k O l " l o 8 T k H l

Figure 1 i l lus t r a t e s the values for log k obtained on this bas i s from

es t imates of log _ k n and log k . , given in tables 6 and 7, formed on

the bas i s of the a rguments in sections 1.2 and 2 . 2 .

It has been shown [24] that the values for the free energy of

formation of water vapour at t empera tu re s between 298 and 2500 C,

obtained by ca lo r ime t r i c exper imen t s , can be r ep resen ted by the equa­

tion

| 0 2 ( g ) + H 2 ( g ) ^ H 2 0 ( g )

ATG(H zO(g)) = - 58900 + 1 3 . 4 T + 1000 (3.1)

Taken with values obtained from s team tables [25] for the equil ibrium

constant of the p roces s

HzO(l) * H2<D(g) (W2)

l o § TkW2 = l o g TP ( H 2 ° )

equation (3.1) leads to values for log T k 1 according to

log T k w l = -A T G°(H 2 0(g)) /2RT In 10 - log - p P ^ O ) (3 . 2)

Some "exper imenta l" point values for log _,k . obtained using

equation (3.2) a r e indicated in figure 1. As is to be expected from the

- 20 -

general observat ions above, these points lie close to the curve defined

by the theore t ica l e s t imates of log^k^ . . and l o g ^ k . .

Although it has not hi therto been stated explicit ly, it is c lear

that the Cr i s s and Cobble re la t ions define the potential of the s tandard

hydrogen e lect rode at t empera tu re T K, relat ive to the potential of

the same elect rode at the reference t empera tu re which continues to be

ass igned the value z e r o . The p re fe r r ed pa rame te r he re is the c o r r e ­

sponding equil ibrium constant l o g T k 1 but as values of the s tandard

potential T e (H ) may be of i n t e r e s t in some connections the v a r i a ­

tion of this quantity with t empera tu re is i l lus t ra ted in figure 2.

Genera l ly , corresponding values of log T k and e (r) will be given

in TEMCON outputs, as in table 7.

3 . 1 . 2 . The protolysis of ammonium ion

The acid - base dissociat ion or protolysis of the ammonium ion

m a y be descr ibed by the formula

NH* ^ H+ + NH (aq) (N2)

and for dilute solut ions,

l o g T k N 2 = log[H+] /[NH+] + logNH3(aq)

F igure 3 i l lus t ra tes the es t imates of log k obtained using equation

+ + 1.15 with the b-coefficients for the H - and NH^-ions given in table 4 ,

the hea t capacity of NH„(aq) being approximated with that of the gas [2].

The exper imenta l values indicated on the figure were obtained from

m e a s u r e m e n t s of e lec t r ica l conductance [26 ,27 ] .

In accordance with the expectation that the effect on the equil i ­

b r ium constant of the hea t capacity of the reac tant ion will be nullified

by that of a s imi la r ion among the products , equation 1.15 and the

Van ' t Hoff i sobar lead to s imi la r values for log _k . The exper imen­

tal values for this constant seem to lie close to the curve defined by

equation 1.15.

- 21 -

3 . 1 . 3 . The reduction of s i lver chloride

At p resen t the bes t cha rac t e r i s ed e lec t rochemica l p rocess is

the reduction of s i lver chloride in the s i lver - s i lver chloride e lect rode

reac t ion :

AgCl(s) + e" = Ag(s) + CI" (Ag2)

for which, in dilute solut ions,

pe = l ° g T k A g 2 " log [CI"]

This e lect rode has been studied between 25 and 275 C by

Greeley et a l . [28] in an extensive s e r i e s of m e a s u r e m e n t s of the emf

of the cell

Pt - H 2 H + , Cl" |AgCl - Ag

AgCl(s) + | H2(g) ^ Ag(s) + H+ + CI" (Agl)

The exper imenta l r e su l t s obtained by Greeley et a l . , h e r e ex­p r e s s e d as log ^ k , at a number of t e m p e r a t u r e s , a r e indicated in

i Agl figure 4 , which also i l lus t r a t e s the values given by

l o S Tk A g l = l o g T

k A g 2 " l o S Tk H l

es t ima tes of log—k. ? (and log._,k 1 ) being obtained from equation

(1.15) and the data in table 4 as previously descr ibed . F igure 5 i l lu­

s t r a t e s the same r e su l t s expres sed as T s (AgCl), the s tandard poten­

tial of the s i lver - s i lver chloride e lect rode at T K re la t ive to the po­

tential of the s tandard hydrogen electrode at the same t e m p e r a t u r e .

There is good ag reemen t between the exper imenta l r esu l t s and

the theore t ica l e s t ima tes over the whole range of t e m p e r a t u r e s . How­

eve r , Cobble has found in a "third law" analysis of the exper imenta l

r e su l t s [29] that above about 125 C there is a slowly increas ing s y s t e ­

mat ic deviation between these resu l t s and the corresponding es t imates

formed on the bas is of the pr inciple of entropy cor respondence .

- 22 -

3 . 1 . 4 . The proteolysis of water

Figure 6 i l lus t ra tes the resu l t s obtained by applying equation

(1.15) and the data in table 4 to the protolysis of water

H z O % H + + OH~ (W3)

l o g T k w 3 = log [H+] + log [OH"]

The exper imenta l values for log k , indicated on the figure a r e those

obtained by Noyes et a l . [27] from conductance m e a s u r e m e n t s . In the

calculation of l o g ^ k the cur rent ly accepted value - 13.997 at 25 C

has been used instead of that found by Noyes, - 14. 086.

Up to 218 C, at l eas t , there is acceptable agreement between

the theore t ica l e s t ima tes of l o g m k and the exper imental va lues . It 1 WJ

is not yet c lear whether the relat ively large deviation between the theo­

re t ica l curve and the exper imental value for 306 C reflects an e r r o r in

the es t imates of the par t ia l molal heat capacit ies of the H and OH

ions or an e r r o r in the exper imental data. However, despite this d i s ­

crepancy, it i s seen that the resu l t s for the protolysis of wa te r , like

those for the other equil ibria examined, confirm the validity of the

method descr ibed he re for es t imat ing equil ibrium constants , and the

general observat ions made at the beginning of this sect ion.

- 23 -

4. FURTHER ANALYSIS OF AQUEOUS EQUILIBRIA AT ELEVATED

TEMPERATURES

It seems likely that it will be possible to obtain much improved

estimates of equilibrium constants for aqueous systems at elevated

temperatures, better than those formed using Criss and Cobble's empi­

rical relations, only when extensive experimental determinations of

ionic heat capacity have been carried out. However, a better under­

standing of the factors effecting ionic reactions and, perhaps, some­

what improved estimates of equilibrium constants, might be obtained

by an approach based on some model of ion - solvent interactions. One

such quasi-thermodynamic analysis of aqueous ionic equilibria, based

on the separation of thermodynamic quantities into hypothetical electro­

static and non-electrostatic terms, has been presented by Helgeson

[30]. In a complete analysis the effects of changes of pressure on ionic

equilibria must also be taken into account.

4 .1 . The free energy of solvation

Helgeson supposes that the entropy of dissociation of aqueous

complexes, i_S , is made up of two terms, AmS/ \ and A—S/ N, which r T r r T (e) T (nj

respectively account for electrostatic and non-electrostatic interactions.

Thus,

ATS°r = ATS(e) + ATS(n) ( 4 ^

The first term is evaluated from the electrostatic free energy of solva­

tion of the complex using a form of the Born equation such that

*TSto=-WlLTG°(e))\p:S-AWil/TD)\l> ( 4 ' 2 )

where _D is the (bulk) dielectric constant of water and A is a constant

(A = - A .S, \/g(Tl)). The non-electrostatic term is evaluated from

the non-electrostatic contribution to the heat capacity of dissociation:

-T ATS7 , = A. r lS?*+ \ ATC° . d l n T (4.3)

T J W U T l g ( n ) T J T ] uT~P(n)

- 24 -

On this bas is the free energy of dissociat ion and the equil ibrium

constant a r e obtained by an argument which may be reduced to the fol­

lowing, T

ATG°r =A T 1 G° r - J ' T i A T S 0r dT

= A T 1 H ° r - T l A T 1 S ° r - y ^ A T S ° r d T

= A T 1 H ° r - T l A T 1 S ° r + A / T D

T

" ( A T l S ° r " A T l S ( e ) ^ T " T 1> " \]T1 A T C P(n) d l n T

= A T 1 H ° r . - T A T 1 S ° r + A / T D + A T 1 S ° e ) ( T - T l )

JJ T 1 A T C P ( n ) d l n T

, V A T l H ° r , A T l S ° r , *Tl S °e) T r ~ " RT R g ( T l ) R T T D

R < 1 - T T ' + 5 ? f f T 1 * T c ^ n ) d l n T <4-4>

In the application of equation (4.4) to any par t icu la r react ion

A T , H and A T , S may be expected to be known, the d ie lec t r ic con­

stant i s to be evaluated by any one of the severa l empi r ica l express ions -1 f(T)

that have been proposed for this quantity, for example , _D = D e ,

and the non-e lec t ros ta t i c heat capacity is to be expressed by the empi ­

r ica l equation

A T C P ( n ) = a + P T ( 4 ' 5 )

The constants A_,S/ \, a, and (3, which a r e cha rac te r i s t i c for the r e ­

action in question, a r e to be obtained by a l e a s t - s q u a r e s procedure fit­

ting equations (4.4) and (4. 5) to such exper imental values as may be

known for log k at different t empera tu res .

- 25 -

For each of the several dissociation equilibria examined by

Helgeson, equations (4.4) and (4.5) together lead to a curve which fits

the experimental data over the whole range of temperatures. Other

assumptions for A^C . . than (4.5), such as A —Cn/ \ = 0 an<i 0 T P(n) 1 ^{p-j

hrrC—), % = a constant, do not lead to a good fit. Helgeson concludes

that the assumptions in the argument-leading to equation (4.4) are valid

and that equation (4. 5) describes the non-electrostatic part of the heat

capacity of dissociation.

Continuing his analysis, Helgeson considers the variation with

temperature of the total heat capacity of dissociation, made up of elec­

trostatic and non-electrostatic contributions:

,o

ATCP:r - T 8 T ( A T S r - , | p - a + T L ? . + g ( T l ) ^ 2 < e ) (4.6)

2 Because the differential in equation (4.6) contains terms in T and T ,

as do the corresponding differentials obtained with other empirical ex­

pressions for TD , A Cp cannot vary linearly with T but must

pass through one or more turning points. Helgeson concludes that al­

though A^Cp/ ^ will usually increase with temperature, the total heat

capacity of dissociation will usually pass through a maximum and then

rapidly decrease because of the decrease in the dielectric constant

(A^S/ \ is usually negative). Whether or not this will be the case de­

pends on the relative magnitudes of the linear and non-linear terms in

equation (4.6). The data for TD reported by Akerlof and Oshry [32]

indicate that 8 ( l / D)/3T [ varies only slowly with temperature up

to about 200 C, when it is about five times as large as at 25 C. Above

about 250 C the differential increases very rapidly until at 330 C it is

ten times as large as at 200 C. The corresponding change in the elec­

trostatic contribution to the heat capacity of dissociation can be expec­

ted to be significant in at least some reactions. It might be the cause

of the discrepancy between the experimental values for the dissociation

constant of water and the estimates formed on the basis of the corre­

spondence principle.

- 26 -

Even if He lgeson ' s approach to aqueous equil ibria at elevated

t empe ra tu r e s is valid, which, because of the inadequacy of the Born

model [16, 31, and the re ferences t h e r e i n ] , is not c lear ly the case , in

p rac t ica l applications it r equ i re s at l eas t a par t ia l study of each r e a c ­

tion of i n t e r e s t and so is even m o r e disadvantageous than the approach

suggested by Naumov. However, whatever the m e r i t s of this par t i cu la r

t r ea tmen t , i t i s l ikely that a good understanding of the heat capacity of

aqueous r eac t ions , and so bet ter e s t imates of log—k from l imited num­

be r s of data, will eventually be obtained by a detailed study of the seve­

ra l components of the free energy of solvation of ions .

4 . 2 . The effect of p r e s s u r e

In the p resen t study, as in other studies of aqueous equil ibria at

elevated t empera tu re s under the ambient p r e s s u r e of water [13 , 28, 30],

the effect of p r e s s u r e changes has been neglected. This var iab le , which

affects the activity of wa te r , the par t ia l molal volumes of the substances

involved, and the activity coefficients of dissolved spec ies , has been

d i scussed recent ly by Cobble [29] and by Hills and Ovenden [33] who

conclude that in mos t cases it will be of secondary impor tance . Data

given by Owen and Brinkley [34] for the effect of p r e s s u r e on a number

of aqueous equil ibria support this conclusion and suggest that the effect

of p r e s s u r e dec rease s with increas ing t e m p e r a t u r e . F igure 7 i l l u s t r a ­

tes the data for the var ia t ion with p r e s s u r e and t empera tu re of the ioni-

sation constant for w a t e r .

- 27 -

CONCLUSION

At p resen t , es t imates of equil ibrium constants for react ions in

aqueous media at elevated t e m p e r a t u r e s , useful in studies of cor ros ion

and m a s s - t r a n s p o r t in water -cooled power plants can bes t be obtained

from free energy and entropy data for 2 5 C and empi r ica l express ions

for the heat capaci t ies of the react ing spec ies . The resu l t s obtained

by the method descr ibed he re for some typical equil ibr ia a r e in r e a s o n ­

able agreement with the exper imenta l data . For some equil ibria above

about 250 C the ag reement may be l e s s sa t is factory, but there does

not yet seem to be any simple bas i s for improving the e s t i m a t e s . How­

ever , a study of the severa l components of the free energy of hydrat ion

of ions might provide such a b a s i s .

- 28 -

A CKNOWLEDGEMENTS

The work repor ted he re formed par t of a joint r e s e a r c h p r o ­

g ram of the Depar tment of Inorganic Chemis t ry , KTH, Stockholm 70,

( thermodynamics) and the Mater ia l s and Fuels Department , AB Atom-

energ i , Stockholm 43 , (corros ion) . I gratefully acknowledge the inval­

uable support and advice given me at these institutions by Professor

L a r s Gunnar Sillen and Docent Gustav Ostberg . I thank Dr O Kuba-

scheski and P ro fe s so r G Wranglen for thei r constructive comments

on this work in i ts ear ly s tages , and Dr M Pourbaix for his helpful

i n t e r e s t in it and for bringing to my attention s imi la r work being

c a r r i e d out concurrent ly by other w o r k e r s . It is a p leasure to a c ­

knowledge the useful exchanges of views with Dr H E Towns end that

have followed Dr Pourba ix ' introduction. I also thank fil l ie George

Neuman and tekn l ie Tom Wallin for many helpful d i scuss ions , and

fil mag Bengt Tollander for ass i s tance with computer work, includ­

ing coding a FORTRAN vers ion of TEMCON.

This work has been financed by The Swedish Board for Tech­

nical Development (STU).

-29-

REFERENCES

1. SILLEN L a r s Gunnar.

Stability constants of meta l - ion complexes. Section I.

The Chemical Society, London 1964.

2. KUBASCHEWSKY O. and EVANS E. LI.

Metal lurgical Thermochemis t ry , 2nd ed.

Pergamon, London 1956.

3. MARSHALL William L.

Conductances and equil ibria of aqueous e lect rolytes over ex t reme

ranges of t empe ra tu r e and p r e s s u r e .

Rev. P u r e Appl. Chem. 18 (1968) p. 167.

4. LEWIS Derek,

Equil ibr ium d iagrams for aqueous sys tems up to 350 C.

I. Water and the sys tem iron - water . 1970.

(AE - 378).

5. CLARK W. Mansfield.

A lit t le of the perspect ive of acid - base and oxidation - reduction

equil ibria.

Ind. Eng. Chem. 28 (1936) p. 620.

6. BRADLEY R. S.

Note on the symmet ry between electron and proton t r ans fe r .

J. Chem. Educ. 27 (1950) p. 208.

7. JOHANSSON Stig.

Elektronens sarstSllning i kemin. I. Redoxreakt ioner och

e lekt rokemi i ny belysning.

Elementa 49 (1966) p. 3, 95 (in Swedish).

8. KELLEY K. K.

Data on theore t ica l meta l lurgy. X. High- tempera tu re heat-content ,

heat -capaci ty , and entropy data for inorganic compounds.

U.S . Bur. Mines Bull. No. 476, 1949.

9. I V E S D . J . G . and JANZ G. J.

Reference e lec t rodes . General and theore t ica l introduction, p. 14.

Academic P r e s s , New York 1961.

- 3 0 -

10. NAUMOV G. B. and KHODAKOVSKII I. L.

Thermodynamic potentials of ions in aqueous solutions at

elevated t e m p e r a t u r e s .

Dokl. Akad. Nauk. S. S. S. R. , 1 70(1966) p. 886 (in russ ian) .

11. NAUMOV G. B. , RYZHENKO B. N. and KHODAKOVSKII I. L. ,

Thermodynamics of aqueous solutions of e lect rolytes at heightened «

t e m p e r a t u r e s . (Thermodynamic calculations in a single hydrogen

scale of m i n e r a l equil ibria with part icipation of the hydrous phase).

Geokhimiya 1968:7 p. 795 (in russ ian) .

12. CRISS Cecil M. and COBBLE J. W.

The thermodynamic proper t ies of high t empera tu re aqueous

solutions. IV. Entropies of the ions up to 2 00 and the

correspondence principle .

J. Am. Chem. Soc. 86 (1964) p. 5385.

13. CRISS Cecil M. and COBBLE J. W.

The thermodynamic proper t ies of high t empera tu re aqueous

solutions. V. The calculation of ionic heat capaci t ies up to

200 . Entropies and heat capacit ies above 200 C.

Ibid, p. 5390.

14. NOYES Richard M.

Assignment of individual ionic contributions to proper t ies of

aqueous ions.

J. Am. Chem. Soc. 86 (1964) p. 971.

15. de LIGNY C. L. , ALFENAAR M. , and Van der VEEN N. G.

The standard chemical free enthalpy, enthalpy, entropy and

heat capacity of hydration of the hydrogen ion, and the surface

potential of water at 25 C.

Rec. Trav . Chim. 87 (1968) p. 585.

16. IRVING H. M. N. H. and LEWIS Derek.

The extraction of indium halides into organic solvents . VIII.

A theore t ica l approach to the part i t ion of solvated ion-pa i r s .

Arkiv Kemi (in p re s s ) .

17. LATIMER Wendell M.

The oxidation s tates of the elements and thei r potentials in aqueous

solutions. 2nd Edn.

Pren t ice -Hal l Inc. , Englewood Cliffs, N. J. 1952.

- 31 -

18. COBBLE J. W.

Empi r i ca l considerat ions of entropy. I. The entropies of the

oxyanions and re la ted spec ies .

J. Chem. Phys. 21 (1953) p. 1443.

19. COBBLE J. W.

Empi r i ca l considerat ions of entropy. II. The entropies of inorganic

complex ions.

Ibid, p. 1446.

20. COBBLE J. W.

Empi r i ca l considerat ions of entropy. III. A s t ruc tu ra l approach

to the entropies of aqueous organic solutes and complex ions.

Ibid, p. 1451.

21 . LAIDLER K. J.

The entropies of ions in aqueous solution. I. Dependence on

charge and rad ius .

Can. J. Chem. 34 (1956) p. 1107.

22. COUTURE A. M and LAIDLER K. J.

The entropies of ions in aqueous solution. II. An empi r i ca l

equation for oxy-anions.

Can. J. Chem. 35 (1957) p. 202.

23. GURNEY Ronald W. •

Ionic p roces se s in solution.

McGraw Hill, London 1953.

24. RICHARDSON F . D. and J E F F E S J. H. E.

The thermodynamics of substances of in te res t in iron and s tee l

making from 0°C to 2400°C.

J. Iron Steel Inst. 160(1948)261.

25. WUKA.LOWITSCH M. P.

Termodynamische Eigenschaften des Wassers und des Wasse r -

dampf es .

VEB Verlag Technik, Berl in 1958.

26. WRIGHT J. M. , LINDSAY W. T, and DRUGA T, R.

The behaviour of e lectrolyt ic solutions at elevated t e m p e r a t u r e s

as derived from conductance m e a s u r e m e n t s . 1961.

(WAPD-TM-204).

- 3 2 -

27. NO YES Arthur A.

The e lec t r i ca l conductivity of aqueous solutions.

Carnegie hist. Washington, Publ. No:63, 1907.

28. GREELEY Richard S. , SMITH William T. , STOUGHTON Raymond

W. , and LIETZKE M. H.

Elec t romot ive force studies in aqueous solutions at elevated

t e m p e r a t u r e s . I. The standard potential of the s i lver - s i lver

chloride e lec t rode .

J. Phys . Chem. 64 (i960) p. 652.

29. COBBLE J. W.

The thermodynamic proper t ies of high t empera tu re aqueous solutions.

VI. Applications of entropy correspondence to thermodynamics and

k inet ics .

J. Am. Chem. Soc. 86 (1964) p. 5394.

30. HELGESON Harold C.

Thermodynamics of complex dissociat ion in aqueous solution at

elevated t e m p e r a t u r e s .

J. Phys. Chem. 71 (1 967) p. 3121.

31. IRVING H. M. N. H. and LEWIS Derek,

The extract ion of indium halides into organic solvents . IX. The

re la t ive efficiencies of different organic solvents .

Arkiv Kemi (in p re s s ) .

32. AKERLOF G. C. and OSHRY H. I.

The d ie lec t r ic constant of water at high t empe ra tu r e s and in

equil ibrium with its vapor.

J. Am. Chem. Soc. 72 (1950) p. 2844.

33. HILLS G. J. and OVENDEN P. J.

E l ec t rochemis t ry at high p r e s s u r e s .

Advances in E lec t rochemis t ry and Elec t rochemica l Engineering.

Vol. 4. p. 185.

In tersc ience, New York 1966.

34. OWEN Benton Brooks and BRINKLEY Stuart R. J r .

Calculation of the effect of p r e s s u r e upon ionic equil ibria in pure

water and in salt solutions.

Chem. Rev. 29 (1941) p. 461.

- 33 -

Table 1. Coefficients for calculat ions of equil ibrium constants

at var ious t e m p e r a t u r e s according to equation (1.15)

t°c

T°Kelvin

fj(T)

f 2 (T ) .10 3

f 3 (T ) . 10 3

f4(T) :

f 5 (T ) . 10 6

50

323

0.923

16.8

0.83

0.219

0.007

100

373

0.799

43 .9

5.20

1.639

0.049

150

423

0.704

64.7

11.95

4 .042

0.107

200

473

0.630

80.8

20.15

7.079

0.168

250

523

0.570

94.0

28.93

10.58

0.228

300

573

0.520

104.9

38.04

14.42

0.283

350

623

0.478

114.1

47 .13

18.53

0.335

- 34 -

Table 2. TEMCON - A p rog ram for the calculation of equil ibrium

constants and s tandard potentials at var ious t empera tu re s

begin comment temcon;

r ea l fak 1, fak 2, fak 3, teminc , ce l r , corefk, narefk,

coef, r e f s , s igs , refh, sigh, aion, siga, bion,

sigb, cion, s igc , ke l r , kelt , fun 1, fun 2, fun 3,

hoffk 1, heath, delt, hea t s , de ls , natemk, gibbsk,

charge , tenoll , gradk, s t o r e ;

integer maxinc , numeqa, sa t s , i , j , ;

fak l : = l . / l . 9872; fak 2:=1. / 2 . 3026; fak 3:=1. 984x10+-4;

teminc :=r_ead; maxinc :=read; celr ;=read;

numeqa:= read ; sats:=0

n y s a t s : eqtext :=read; newline; print text eqtext; newlinej

eqform:=read; newline; print text eqform; newline;

charge :=r_ea_d;

s a t s : = s a t s + l . ;

s igs:=0; sigh:=0; siga:=0; sigb:=0; sigc:=0;

corefk :=read; narefk :=corefkx2. 3026;

for i:=l step 1 until 5 do_ begin comment s igprop;

coef :=read;

refs :=read; sigs :=sigs+coefx r e f s ;

refh := read ; sigh:=sigh+coef x refh;

aion:=re_ad; siga:=siga+coefx aion;

bion:=r_e_ad; sigb:=sigb+coefxbion;

cion:= r_ead_; sigc :=sigc+coef x cion; end s igprop;

newline;

- 35 -

Table 2 . contd.

pr int text 'LOG 298 K = ' ; pr int corefk (2 ,3) ;

pr int text 'SIGMA 298 S ='j pr in t sigs (4 ,2) ;

pr int text 'SIGMA 298 H ='; pr in t sigh (6 ,2) ; newline;

newline;

print text ' TEMP C ' ; pr int text ' TEMP K' ;

pr int text ' 1 0 E 3 / T ' ; pr int text ' VHOFF K< ;

pr int text 'HEAT H ' ; pr int text 'SIG T H ' ;

pr int text 'HEAT S ' ; pr int text ' T » S I G T S ' ;

pr int text 'GIBBS K ' ; pr int text ' E Z E R O ' ; newline;

kel r :=273. 15+celr;

for j :=l s tep 1 until maxinc do_ begin comment t e m p e r a t u r e ;

ce l t :=ce l t+ jx teminc ; kelt:= 273.15+celt ;

fun 1 :=cel t /kel t ; fun 2:=l . - fun 1; fun 3:=l . - fun l x f u n 1;

hoffk 1: =(narefk+sighxfun 2xfak l / k e l r ) x f a k 2;

heath:=sigaxfun 2xke l t+s igbxfun 3 x k e l t x k e l t x 0. 5

+s igcxfun 2 / k e l r ;

delt:= (sigh+heath)x 0 . 0 0 1 ;

heats :=sigbx fun 2 x k e l t - s igax ln( fun 1)

+s igcxfun 3/(kelr x k e l r x 2 ) ;

dels :=(s igs+heats) .xkel tx 0. 001;

natemk:=narefkxfun l+(s igsxfun 2 - hea th /ke l t

+heats )xfak 1;

gibbsk:=natemkxfak 2;

tenoll :=gibbskxfak 3 x k e l t x charge ;

gradk:=1000. /ke l t ; s torc :=heathx 0. 001;

pr in t celt (3 ,2) ; p r in t kelt (3, 2); pr int gradk (1 ,4) ;

pr int hoffk 1 (3, 3); pr int s tore (3, 3); pr in t delt (3, 3);

pr int hea ts (3 ,3) ; pr in t dels (3 ,3) ; pr int gibbsk (3,3) ;

pr int tenoll (2 ,4) ; end t e m p e r a t u r e ;

if sats <numeqa then goto nysats

end temcon;

- 36 -

Table 2. contd.

comment the format for the data input is as follows;

t empera tu re inc rement ; number of i n c r e m e n t s ; reference

t empe ra tu r e C; number of equil ibria to be t r ea ted ;

comment he re follow data for each equil ibrium sa t s := 1 to nu-

meqa ;

name of equi l ibr ium;

symbolic descr ip t ion;

number of e lec t rons involved comment 0 or 1. ;

equi l ibr ium constant at the reference t e m p e r a t u r e ;

comment he re follow data for each constituent par t ic ipat ing in

the equi l ibr ium i:= 1 to 5j

s to ichiometr ic coefficient;

r e f S ° ( i ) ; A r e f H°( i ) ; a(i); b(i); c(i);

Table 3. TEMCON output. Es t imates of the equil ibrium constant and standard potential for the hemat i te ». magnet i te

react ion at t empera tu res up to 350 C.

REDN IRON 3 OXIDE

1.5FE203(S) + H+l + E-l = FE304(S) + 0.5H20

L0G298K =

TEMP C

50.00 75.00 100.00 125.00 150.00 175.00 200.00 225.00 250.00 275.00 300.00 325.00 350.00 375*00

3.740

TEMP K

323.15 348.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 598.15 623.15 648.15

SIGMA298S

10E3/T

3.0945 2.8723 2.6799 2.5116 2.3632 2.2314 2.1135 2.0074 1.9115 1.8243 1.7447 1.6718 1.6047 1.5429

16,

VH0FF K

3.320 2.960 2.648 2.376 2.136 1.922 1.731 1.559 1.404 1.263 1.134 1.016 0.907 0.807

,11 SIGMA298H =

HEAT H

-0.529 -1.124 -1.779 -2.492 -3.260 -4.083 -4.957 -5.883 -6.860 -7.886 -8.961

-10.084 -11.256 -12.475

SIG TH

-7.939 -8.534 -9.189 -9.902

-10.670 -11.493 -12.367 -13.293 -14.270 -15.296 -16.371 -17.494 -18.666 -19.885

-7410.00

HEAT S

-1.704 -3.474 -5.290 -7.139 -9.010

-10.898 -12.797 -14.703 -16.615 -18.530 -20.448 -22.366 -24.285 -26.203

T*SIGTS

4.655 4.399 4.037 3.572 3.004 2.336 1.568 0.701

-0.264 -1.327 -2.486 -3.742 -5.094 -6.542

GIBBS K

3.709 3.655 3.582 3.493 3.390 3.276 3.152 3.020 2.880 2.734 2.583 2.426 2.266 2.101

E ZERO

0.2378 0.2525 0.2652 0.2759 0.2846 0.2913 0.2959 0.2985 0.2990 0.2974 0.2937 0.2880 0.2801 0.2702

- 3 8 -

T a b l e 4 . T h e r m o d y n a m i c c o n s t a n t s for c o m m o n a q u e o u s ions

ION

G r o u p 1.

298 conv . a 2 9 8 r t f 298 abs

c a l / d e g k c a l / d e g x 10

The h y d r o g e n i o n . e = 0 .09225; f=0. 00; g=0 .00 ; h=1.47

0 . 0 0 0 . 0 0 - 5 . 0 0 9 2 . 2 5

_3 G r o u p 2 . S i m p l e c a t i o n s . e = 0. 133 ; f=-3 . 32 ; g = - l . 6 5 x 1 0 ; h = l . 0413

97

112

112

117

135

141

152

158

159

171

183

188

189

194

194

196

217

273

279

NH+

A g +

H g 2

N a +

L i +

P b 2 +

r 2 + C u 2

ZJ 2 +

Hg

S n 2 +

C a 2 +

•KX 2 +

Mn r 2+ Cu TVT-2 +

N i

C o 2 +

F e 2 +

^ 2+ Mg

u 3 +

F e 3 +

C r 3 +

2 6 . 9 7

1 7 . 6 7

1 7 . 7 0

1 4 . 4

3 . 4

5 .1

- 6 . 3

- 5 . 4

- 5 . 9

- 1 3 . 2

- 2 0 . 0

- 2 3 . 6

( - 2 4 . 0 )

- 2 7 . 0

- 2 7 . 1

- 2 8 . 2

( - 3 6 . 0 )

- 7 0 . 1

( - 7 3 . 5 )

- 3 1 . 7 4

2 5 . 3 1

- -

- 5 7 . 2 8

- 6 6 . 5 5

+ 0 . 3 9

+ 1 2 . 4

+ 4 1 . 5 9

- 2 . 3 9

- 1 2 9 . 8

- 5 3 . 3

+ 1 5 . 3 9

- 1 5 . 3

- 1 4 . 2

- 2 1 . 0

- 1 1 0 . 4

- 1 2 3 . 0

- 1 1 . 4

- 3 3 . 2

2 1 . 9 7

1 2 . 6 7

12 .70

9 .4

- 1 . 6

- 4 . 9

- 1 1 . 3

- 1 5 . 4

- 1 5 . 9

- 2 3 . 2

- 3 0 . 0

- 3 3 . 6

- 3 4 . 0

- 3 7 . 0

- 3 7 . 1

- 3 8 . 2

- 5 1 . 0

- 8 5 . 1

- 8 8 . 5

- 3 9 -

Table 4 . contd.

298Sconv. A298Hf 298Sabs b

ca l /deg kca l /deg x 10

Group 2.

A l 3 +

u4+

Group 3 .

r B r "

HS"

C l "

s2"

OH"

Group 4 .

N Q 3 -

NG 2"

so42"

co32"

P O 43 "

Group 5.

HSO." 4

H C 0 3 "

H 2 P ° 4 "

H P Q 42 "

contd.

- 7 4 . 9

-78 .0

Simple anions .

26.14

19.29

(14. ;9)

13.20

- 6 . 4

-2 .52

Oxy-anions . e =

35 .0

29 .9

4 . 1

-12 .7

-52 .0

Acid oxy-anions

30.32

22 .7

21 .3

- 8 . 6

-125.4

-146.7

e=-0.1726;

-13 .37

-28 .90

-4 .22

-40 .02

8.56

-54.96

-0.4366; f=

-49 .37

-25 .40

-216 .9

-161.6

-306 .9

;. e=-0. 399

-211 .7

-165 .2

-311 .3

-310.4

-89 .9

-98 .0

f=4.30; g=-4.

31.14

24.29

19.9

18.2

3 . 6

2.48

10.92; g=7.25

40 .0

34.9

14.1

- 2 . 7

-37 .0

i ;f=10.10;g=:

(31.6)

27.7

26 .3

1.4

281

295

7 3 x l 0 " 5 ; h=0.999

-174 .1

-174.0

-173 .5

-173 .5

-172 .8

-172 .7

x l 0 " 3 ; h = 0 . 8 1 8 8

-147

-184

-334

-456

-705

L1.25xl0~ 3 ; h=0.710

- 4 3 . 5

-87 .4

-103

-383

- 4 0 -

Table 5 • Equi l ibr ium constants for some react ions at infinite dilution in water at 25 C

Reaction

3 F e 2 0 3 ( s ) + 2H+ + 2e" = 2 F e 3 0 4 ( s ) + H 2 0

Oz(g) + 4H+ + 4e" = HzO(l)

NH 4+ = H+ + NH3(aq)

AgCl(s) + e" = Ag(s) + CI"

H O = H+ + OH"

h . Es t imated from Sv(i). A?QgGf (i)

l o § 2 9 8 k

7 . 4 8 h

83.11

-9 .25

3.76

-13 .997

Rei ierence

2

17

26

28

29

T a b l e 6. TEMCON output . E s t i m a t e s of the e q u i l i b r i u m c o n s t a n t and s t a n d a r d po t en t i a l for the r e d u c t i o n

of oxygen.

REDN OXYGEN

502(G)

298K =

TEMP C

50.00 75.00 100.00 125.00 150.00 175.00 200.00 225.00 250.00 275.00 300.00 325.00 350.CO 375.00

+ H + l +

20.788

TEMP K

323.15 348.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 598.15 623.15 64 8.15

IN OXYGEN, CP(I )=0

50.CO 75.CO

100.00 125.CO 150.CO 175.00 200.00 225.CO 250.00 275.CO 3CC.C0 325.00 35C.C0 375.00

323.15 348.15 373.15 398.15 423.15 448.15 47 3.15 -498.15 523.15 548.15 573.15 598.15 623.15 648. 15

E-l =

SIGMA298S

10E3/T

3.0945 2.8723 2.6799 2.5116 2.3632 2.2314 2.1135 2.0074 1.9115 1.8243 1.7447 1.6718 1.6047 1.5429

3.0945 2.8723 2.6799 2.5116 2.3632 2.2314 2.1135 2.0074 1.9115 1.8243 1.7447 1.6718 1.6047 1.5429

0.5H20

; = i .

VHCFF K

18.851 17.192 15.755 14.499 13.391 12.407 11.527 10.735 10.019 9.368 8.774 8.230 7.729 7.267

18.851 17.192 15.755 14.499 13.391 12.407 11.527 10.735 10.019 9.368 8.774 8.230 7.729 7.267

,10 SIGMA298H = -

HEAT H

-0.535 -1.128 -1.780 -2.489 -3.257 -4.082 -4.966 -5.907 -6.907 -7.964 -9.079

-10.252 -11.483 -12.771

0.181 0.362 0.542 0.722 0.902 1.081 1.260 1.439 1.617 1.795 1.973 2.151 2.328 2.505

SIG TH

-34.695 -35.288 -35.940 -36.649 -37.417 -38.242 -39.126 -40.067 -41.067 -42.124 -43.239 -44.412 -45.643 -46.931

-33.979 -33.798 -33.618 -33.438 -33.258 -33.079 -32.900 -32.721 -32.543 -32.365 -32.187 -32.009 -31.832 -31.655

-34160.00

HEAT S

-1.722 -3.490 -5.296 -7.136 -9.004

-10.899 -12.817 -14.755 -16.712 -18.686 -20.675 -22.677 -24.693 -26.720

0.584 1.123 1.623 2.089 2.527 2.938 3.327 3.695 4.044 4.377 4.694 4.998 5.288 5.567

T*SIGTS

-0.200 -0.830 -1.564 -2.401 -3.343 -4.389 -5.542 -6.800 -8.165 -9.637

-11.216 -12.903 -14.699 -16.602

0.546 0.776 1.018 1.272 1.537 1.812 2.097 2.391 2.694 3.005 3.324 3.650 3.984 4.325

GIBBS K

19.184 17.783 16.543 15.435 14.433 13.520 12.681 11.906 11.184 10.509 9.873 9.273 8.703 8.160

19.203 17.855 16.695 15.688 14.805 14.026 13.334 12.715 12.160 11.658 11.203 10.789 10.411 10.065

E ZERO

1.2300 1.2284 1.2248 1.2193 1.2117 1.2021 1.19C5 1.1767 1.1609 1.1429 1.1228 1.1005 1.0760 1.0493

1.2312 1.2334 1.2361 1.2393 1.2430 1.2471 1.2517 1.2567 1.2621 1.2679 1.27^0 1.2805 1.2872 1.29^3

T a b l e 7. T E M C O N output . E s t i m a t e s of the e q u i l i b r i u m c o n s t a n t and s t a n d a r d p o t e n t i a l for the r e d u c t i o n

of h y d r o g e n ion ,

REDN HYDROGEN ION

H+l + E-l

L0G298K =

TEMP C

50.00 75.CO 100.00 125.00 150.00 175.00 200.00 225.00 250.00 275.00 300.00 325.00 350.00 375.CO

= 0.5H2(9)

0.0

TEMP K

323.15 348.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 598.15 623.15 648.15

SIGMA298S

10E3/T

3.0945 2.8723 2.6799 2.5116 2.3632 2.2314 2.1135 2.0074 1.9115 1.8243 1.7447 1.6718 1.6047 1.5429

=

VHCFF

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

20.60 S

K HEAT H

-0.630 -1.318 -2.064 -2.867 -3.728 -4.646 -5.622 -6.655 -7.745 -8.893

-10.099 -11.362 -12.682 -14.060

IA298H *

SIG TF

-0.630 -1.318 -2.064 -2.867 -3.728 -4.646 -5.622 -6.655 -7.745 -8.893 -10.099 -11.362 -12.682 -14.060

0.0

HEAT S

-2.029 -4.079 -6.146 -8.228

-10.324 -12.432 -14.550 -16.677 -18.813 -20.956 -23.106 -25.263 -27.425 -29.593

T*SIGTS

6.003 5.754 5.395 4.928 4.350 3.663 2.865 1.957 0.938

-0.192 -1.434 -2.786 -4.250 -5.825

GIBBS K

0.331 0.583 0.771 0.906 0.999 1.056 1.082 1.083 1.061 1.020 0.962 0.889 0.803 0.705

E ZERO

0.0212 0.0403 0.0571 0.0716 0.0839 0.0939 0.1016 0.1070 0.1101 0.1109 0.1094 0.1055 0.0993 0.0907

I J T 2 2 3 I

Table 8. TEMCON output. Es t imates of the equil ibrium constant for the protolysis of the ammonium ion.

ACID AfPCNIlP

NH4+1 = NH3CAQ) + H + l

L0G298K =

TEMP C

50.00 75.00

100.CO 125.00 150.00 175.00 200.00 225.00 250.CO 275.00 3C0.00 325.00 350.00 375.CO

-9.250

TE^P K

323.15 348.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 598.15 623.15 648. 15

SIGMA298S

10E3/T

3.0945 2.8723 2.6799 2.5116 2.3632 2.2314 2.1135 2.0074 1.9115 1.8243 1.7447 1.6718 1.6047 1.5429

-0,

VH0FF K

-8.546 -7.943 -7.420 -6.963 -6.561 -6.203 -5.883 -5.595 -5.335 -5.098 -4.882 -4,684 -4.502 -4.334

,67 SIGMA298H =

HEAT H

0.174 0.350 0.527 0.706 0.886 1.067 1.249 1.432 1.616 1.800 1.986 2.172 2.358 2.546

SIG TH

12.594 12.770 12.947 13.126 13.306 13.487 13.669 13.852 14.036 14.220 14.406 14.592 14.778 14.966

12420.00

HEAT S

0.560 1.084 1.576 2.040 2.478 2.894 3.289 3.666 4.026 4.371 4.701 5.019 5.325 5.620

T*SIGTS

-0.035 0.144 0.338 0.545 0.765 0.997 1.239 1.492 1.756 2.028 2.310 2.601 2.901 3.208

GIBBS K

-8.541 -7.925 -7.385 -6.905 -6.477 -6.091 -5.741 -5.422 -5.130 -4.861 -4.612 -4.381 -4.165 -3.964

E ZERO

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

T a b l e 9. T E M C O N output . E s t i m a t e s of t h e e q u i l i b r i u m c o n s t a n t and s t a n d a r d po t en t i a l for t h e r e d u c t i o n

of s i l v e r c h l o r i d e .

REDN SILVER CHLORIDE

AGCL(S) + E - l = AG(S) + C L ~ l

REDN

298K =

TEMP C

50.00 75.00 100.00 125.00 150.00 175.00 200.00 225.00 250.00 275.00 300.00 325.00 350.00 375.00

N SILVER

50.00 75.CO

ICC.CO 125.CO 15C.C0 175.CO 200.CO 225.00 25C.C0 275.CO 30C.C0 325.CO 35C.C0 375.CO

3.760

TEMP K

323.15 348.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 598.15 623.15 648.15

CHLORIDE

323.15 348.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 598.15 623.15 648.15

SIGMA298S

10E3/T

3.0945 2.8723 2.6799 2.5116 2.3632 2.2314 2.1135 2.C074 1.9115 1.8243 1.7447 1.6718 1.6047 1.5429

, CP(I)=0

3.0945 2.8723 2.6799 2.5116 2.3632 2.2314 2.1135 2.0074 1.9115 1.8243 1.7447 1.6718 1.6047 1.5429

_ c

VH0FF K

3.209 2.737 2.328 1.971 1.655 1.375 1.125 0.900 0.696 0.511 0.341 0.187 0.044

-0.087

3.209 2.737 2.328 1.971 1.655 1.375 1.125 0.900 0.696 0.511 0.341 0.187 0.044

-0.087

i.41 SIGMA298H =

HEAT H

-1.505 -3.129 -4.869 -6.725 -8.695

-10.778 -12.973 -15.279 -17.696 -20.223 -22.861 -25.609 -28.466 -31.432

-0.157 -0.325 -0.502 -0.685 -0.874 -1.067 -1.263 -1.463 -1.665 -1.869 -2.075 -2.282 -2.491 -2.700

SIG TH

-11.225 -12.849 -14.589 -16.445 -18.415 -20.498 -22.693 -24.999 -27.416 -29.943 -32.581 -35.329 -38.186 -41.152

-9.877 -10.045 -10.222 -10.405 -10.594 -10.787 -10.983 -11.183 -11.385 -11.589 -11.795 -12.002 -12.211 -12.420

-9720.00

HEAT S

-4.844 -9.682

-14.509 -19.322 -24.119 -28.899 -33.664 -38.413 -43.146 -47.865 -52.569 -57.261 -61.939 -66.606

-0.506 -1.007 -1.496 -1.972 -2.431 -2.874 -3.301 -3.713 -4.109 -4.490 -4.857 -5.211 -5.552 -5.881

T*SIGTS

0.183 -1.487 -3.395 -5.539 -7.917

-10.527 -13.368 -16.440 -19.742 -23.271 -27.029 -31.014 -35.226 -39.664

1.585 1.533 1.46C 1.369 1.261 1.136 0.998 0.846 0.681 0.504 0.317 0.119

-0.088 -0.305

GIBBS K

3.520 3.238 .2.923 2.582 2.218 1.837 1.442 1.033 0.615 0.187

-0.248 -0.690 -1.138 -1.590

3.556 3.374 3.209 3.058 2.918 2.789 2.669 2.556 2.449 2.348 2.253 2.162 2.076 1.993

E ZERO

0.2257 0.2237 0.2164 0.2039 0.1863 0.1634 0.1353 0.1021 0.0638 0.0203

-0.0283 -0.0819 -0.14C7 -0.2045

0.2280 0.2331 0.2376 0.2415 0.2450 0.2480 0.2505 0.2526 0.2542 0.2554 0.2562 0.2566 0.2567 0.2563

i

4*-*-i

I J T 2 2 3 I

Tab le 10. TEMCON output . E s t i m a t e s of t h e e q u i l i b r i u m c o n s t a n t for the p r o t o l y s i s of w a t e r .

ACID WATER

H20 = H + l OH-1

L0G298K - 1 3 . 9 9 7 SIGMA298S - 1 9 . 2 4 SIGMA298H = 1 3 3 7 0 . 0 0

TEMP C TEMP K 10E3 /T VHOFF K HEAT H SIG TH HEAT S T*SIGTS GIBBS K E ZERO

50.00 75.00 100.00 125.00 150.00 175.00 200.00 225.00 250.00 275.00 300.00 325.00 350.CO 375.00

323.15 348.15 373.15 398.15 423.15 448.15 473.15 498.15 523.15 548.15 573.15 598.15 623.15 648.15

2. 2, 2,

3.0945 2.8723 2.6799

5116 3632 2314

2.1135 2.0074 1.9115 1.8243 1.7447 1.6718 1.6C47 1,5429

-13.239 -12.590 -12.027 -11.536 -11.102 -10.717 -10.372 -10.062 -9.782 -9.527 -9.295 -9.082 -8.886 -8.705

-1. -2, -3, -4, -5. -7. -8. -10, -11, -13, -14, -16, -17.

076 201 377 604 881 207 585 012 490 018 596 225 904

12.294 11.169 9.993 8.766 7.489 6.163 4.785 3 . 1 , 0,

358 880 352

- 1 9 . 6 3 3

- 1 . 2 2 6 - 2 . 8 5 5 - 4 . 5 3 4 - 6 . 2 6 3

- 3 . 4 6 3 - 6 . 8 1 8

- 1 0 . 0 7 9 - 1 3 . 2 6 0 - 1 6 . 3 6 9 •19 -22 -25 -28 - 3 1 -33 -36

.415

. 4 0 5

. 345

.239

. 0 9 2

. 9 0 7

.688 - 3 9 . 4 3 8 - 4 2 . 1 5 8

- 7 . 3 3 6 - 9 . 0 7 2

- 1 0 . 9 4 1 - 1 2 . 9 4 0 - 1 5 . 0 6 8 - 1 7 . 3 2 3 - 1 9 . 7 0 4 - 2 2 . 2 1 0 - 2 4 . 8 3 9 - 2 7 . 5 8 9 - 3 0 . 4 6 1 - 3 3 . 4 5 3 - 3 6 . 5 6 5 - 3 9 . 7 9 5

- 1 3 . 2 6 9 - 1 2 . 6 9 9 - 1 2 . 2 5 4 - 1 1 . 9 0 8 - 1 1 . 6 4 5 - 1 1 . 4 4 6 - 1 1 . 3 0 7 - 1 1 . 2 1 2 - 1 1 . 1 5 7 - 1 1 . 1 3 6 - 1 1 . 1 4 3 - 1 1 . 1 7 6 - 1 1 . 2 3 0 - 1 1 . 3 0 3

0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0

IT.

ACI0 WATER, C P U )=0

5 0 . 0 0 75.CO

1 0 0 . 0 0 1 2 5 . 0 0 1 5 0 . 0 0 1 7 5 . 0 0 2 0 0 . 0 0 2 2 5 , 0 0 2 5 0 . 0 0 275.CO 3 0 0 . 0 0 325.CO 3 5 0 . 0 0 3 7 5 . 0 0

3 2 3 . 1 5 3 4 8 . 1 5 3 7 3 . 1 5 3 9 8 . 1 5 4 2 3 . 1 5 4 4 8 . 1 5 4 7 3 . 1 5 4 9 8 . 15 5 2 3 . 1 5 5 4 8 . 15 5 7 3 . 1 5 5 9 8 . 1 5 6 2 ? . 3 5 6 4 8 . 15

3 . 0 9 ^ 5 2 . 8 7 2 3 2 . 6 7 9 9 2 . 5 1 1 6 2 . 3 6 3 2 2 . 2 3 1 4 2 . 1 1 3 5 2 . 0 0 7 4 1 . 9 1 1 5 1 . 8 2 4 3 1 . 7 4 4 7 1 . 6 7 1 8 1.6C47 1 . 5 4 2 9

- 1 3 . 2 3 9 - 1 2 . 5 9 0 - 1 2 . 0 2 7 - 1 1 . 5 3 6 - 1 1 . 1 0 2 - 1 0 . 7 1 7 - 1 0 . 3 7 2 - 1 0 . 0 6 2

- 9 . 7 8 2 - 9 . 5 2 7 - 9 . 2 9 5 - 9 . 0 8 2 - 8 . 8 8 6 - 8 . 7 0 5

- 0 . 4 5 1 - 0 . 9 0 1 - 1 . 3 5 2 - 1 . 8 0 3 - 2 . 2 5 4 - 2 . 7 0 4 - 3 . 1 5 5 - 3 . 6 0 6 - 4 . 0 5 7 - 4 . 5 0 7 - 4 . 9 5 8 - 5 . 4 0 9 - 5 . 8 6 0 - 6 . 3 1 0

1 2 . 9 1 9 1 2 . 4 6 8 1 2 . 0 1 8 1 1 . 5 6 7 1 1 . 1 1 6 1 0 . 6 6 5 1 0 . 2 1 5

9 . 7 6 4 9 . 3 1 3 8 . 8 6 3 8 . 4 1 2 7 . 9 6 1 7 . 5 1 0 7 . 0 6 0

- 1 . 4 5 2 - 2 . 7 9 5 - 4 . 0 4 6 - 5 . 2 1 5 - 6 . 3 1 3 - 7 . 3 4 8 - 8 . 3 2 7 - 9 . 2 5 5

- 1 0 . 1 3 8 - 1 0 . 9 7 9 - 1 1 . 7 3 4 - 1 2 . 5 5 3 - 1 3 . 2 9 2 - 1 4 . 0 0 1

- 6 . 6 8 7 - 7 . 6 7 2 - 8 - 9

- 1 0 . - 1 1 - 1 3 - 1 4 - 1 5 - 1 6 - 1 7 - 1 9 - 2 0 - 2 1

,689 ,737 ,813 ,915 ,043 ,195 ,369 ,565 , 7 8 1 ,017 ,272 ,545

- 1 3 . 2 5 2 - 1 2 . 6 3 6 - 1 2 . 1 2 1 - 1 1 . 6 8 8 - 1 1 . 3 2 0 - 1 1 . 0 0 6 - 1 0 . 7 3 8 - 1 0 . 5 0 6 - 1 0 . 3 0 6 - 1 0 . 1 3 3

- 9 , - 9 ,

983 853

0, 0 . 0, 0 . 0 . 0, 0 . 0 . 0, 0 , 0 ,

c, - 9 . 7 4 0 - 9 . 6 4 1

0 .C 0 . 0

- 4 6 -

Tab le 1 1 . I n c r e m e n t s to e q u i l i b r i u m c o n s t a n t s a t v a r i o u s t e m p e r a

t u r e s a r i s i n g f r o m the h e a t c a p a c i t y of ions

t°c

ION

H +

N a +

F e 2 +

C r 3 +

u 4 +

H S 0 4 "

OH"

so.2" 4 3_

po„

1 0 3 b

0 .092

0 .117

0 . 1 9 4

0 . 2 7 9

0 . 2 9 5

- 0 . 0 4 4

- 0 . 1 7 2

- 0 . 3 3 4

- 0 . 7 0 5

50

0 . 0 2

0 .02

0 . 0 4

0 . 0 6

0 . 0 6

- 0 . 0 1

- 0 . 0 3

- 0 . 0 7

- 0 . 1 4

100

0 . 1 5

0 . 1 9

0 . 3 1

0 . 4 5

0 . 4 7

- 0 . 0 7

- 0 . 2 8

- 0 . 5 3

- 1 . 1 3

150

0 . 3 7

0 . 4 7

0 . 7 8

1.12

1.18

- 0 . 1 8

- 0 . 6 9

- 1 . 3 4

- 2 . 8 2

200

f 4 (T)b

0 . 6 5

0 . 8 3

1.38

1.98

2 . 0 9

- 0 . 3 1

- 1 . 2 2

- 2 . 3 7

- 5 . 0 1

250

0 . 9 8

1.24

2 . 0 6

2 . 9 6

3 . 1 3

- 0 . 4 7

- 1 . 8 2

- 3 . 5 4

- 7 . 4 7

300

1.33

1.68

2 . 7 9

4 . 0 2

4 . 2 5

- 0 . 6 3

- 2 . 4 8

- 4 . 8 1

- 1 0 . 1 5

350

1.71

2 . 1 6

3 . 5 9

5 .16

5 . 4 6

- 0 . 8 2

- 3 . 1 8

- 6 . 1 8

- 1 3 . 0 4 4

- 4 7 -

FIGURES.

The curves in the following figures i l lus t ra te the resu l t s obtained on

the basis of :-

1. The Van ' t Hoff i sobar .

2. Equation (1. 15) with the heat capacit ies of ionic species taken to be ze ro .

3. Equation ( l . 15) with heat capacit ies of ions according to equation (2. 10)

and the data in table 4.

F i g u r e 1 , The v a r i a t i o n with t e m p e r a t u r e of the f o r m a t i o n c o n s t a n t for l iquid w a t e r

l o g T k w l

40 0 .

35 0 .

30 0 -

25 0 -

20. 0

10 3 / T d e g " 1 K

2. 0 2. 5 3. 0

Figure 2. The var ia t ion with t empera tu re of the potential of the

s tandard hydrogen e lect rode.

100 .

?5 -

50 -

25 -

300 400 500 600

Figure 3. The variat ion with t empera tu re of the dissociat ion constant of the ammonium ion.

(Full c i rc les indicate the exper imental resu l t s of NoyesL274, open c i rc les those of Wright [263).

log T k N 3

- 5. 0 -

6. 0

7 0 -

0 -

9 0 -

10 / T deg *K

2. 0 2 . 5 3. 0

Figure 4. The variat ion with t empera tu re of the reduction (electrochemical) constant

for s i lver chloride

J i i 2. 0 2. 5 3. 0

Figure 5. The s tandard potential of the s i l v e r - s i lver chloride electrode

,*(Ag2) mV

at elevated t empe ra tu r e s re la t ive to the standard hydrogen

electrode at 25 C

200 *

100"

100

•200

T°K

300 400 500 6 00

Figure 6, The variat ion with t empera tu re of the dissociation constant of water .

Figure 7. The variation with p r e s s u r e of the dissociat ion constant of water .

200 400 600 800 1000

LIST OF PUBLISHED AE-REPORTS

1-300 (See the back cover earlier reports.)

301. The present status of the half-life measuring equipment and technique at Studsvik. By S. G. Malmskog. 19G7. 2S p. Sw. cr. 10:- .

302. Determination of oxygen in aluminum by means of 14 MeV neutrons with an account of flux attenuation in the sample. By D. Brune and K. Jirlow. 1967. 16 p. Sw. cr. 10:- .

303. Neutron elastic scattering cross sections of the elements Ni , Co, and Cu between 1.S and 8.0 mev. By B. Holmqvist and T. Wiedling. 1967. 17 p. Sw. cr. 10:—.

304. A study of the energy dependence of the Th232 capture cross section in the energy region O.I to 3.4 eV. By G. Lundgren. 1967. 25 p. Sw. cr. 10:-.

305 Studies of the reactivity effect of polythene in the fast reactor FRO. By L. I. Tiren and R. Hakansson. 1967. 25 p. Sw. cr. 10:- .

306. Final report on IFA-10, the first Swedish instrumented fuel assembly irra­diated in HBWR, Norway. By J-A. Gyllander. 1967. 35 p. Sw. cr. 10:- .

307. Solution of large systems of linear equations with quadratic or non-qua­dratic matrices and deconvolution of spectra. By K. Nygaard. 1967. 15 p. Sw. cr. 10:- .

308. Irradiation of superheater test fuel elements In the steam loop of the R2 reactor. By F. Ravndal. 1967. 94 p. Sw. cr. 10:- .

309. Measurement of the decay of thermal neutrons in water poisoned with the non-1/v neutron absorber cadmium. By. L. G. Larsson and E. Moller. 1967. 20 p. Sw. cr. 10:- .

310. Calculated absolute detection efficiencies of cylindrical Nal (Tl) scintill­ation crystals for aqueous spherical sources. By. O. Strindehag and B. Tollander. 196S. 18 p. Sw. cr. 10:- .

311. Spectroscopic study of recombination in the early afterglow of a helium plasma. By J. Stevefelt. 1968. 49 p. Sw. cr. 10:-.

312. Report on the personnel dosimetry at AB Atomenergi during 1966. By J. Carlsson and T. Wahlberg. 1968. 10 p. Sw. cr. 10:- .

313. The electron temperature of a partially ionized gas In an electric field. By F. Robben. 1968. 1$ p. Sw. cr. 10:-.

314. Activation Doppler measurements on U238 and U235 in some fast reactor spectra. By L. I. Tiren and I. Gustafsson. 1968. 40 p. Sw. cr. 10: - .

315. Transient temperature distribution In a reactor core with cylindrical fuel rods and compressible coolant. By H. Vollmer. 1968. 38 p. Sw. cr. 10:- .

316. Linear dynamics model for steam cooled fast power reactors. By H. Voll­mer. 1968. 40 p. Sw. cr. 10:- .

317. A low level radioactivity monitor for aqueous waste. By E. J. M. Quirk. 1968. 35 p. Sw. cr. 10: - .

318. A study of the temperature distribution in UOi reactor fuel elements. By I. Devoid. 1968. 82 p. Sw. cr. 10:- .

319. An on-line water monitor for low level ^-radioactivity measurements. By E. J. M. Quirk. 1968. 26 p. Sw. cr. 10: - .

320. Special cryostats for lithium compensated germanium detectors. By A. Lauber, B. Malmsten and B. Rosencrantz. 1968 14 p. Sw. cr. 10:—.

321. Stability of a steam cooled fast power reactor, its transients due to mode­rate perturbations and accidents. By H. Vollmer. 1968. 36 p. Sw. cr. 10:—.

322. Progress report 1967. Nuclear chemistry. 1968. 30 p. Sw. cr. 10:- . 323. Noise in the measurement of light with photomultipllers. By F. Robben.

1968. 74 p. Sw. cr. 10:- . 324. Theoretical investigation of an electrogasdynamic generator. By S. Palm-

gren. 1968. 36 p. Sw. cr. 10:- . 325. Some comparisons of measured and predicted primary radiation levels in

the Agesta power plant. By E. Aalto, R Sandlin and A. Krell. 1968. 44 p. Sw. cr. 10:-.

326. An investigation of an irradiated fuel pin by measurement of the production of fast neutrons in a thermal column and by pile oscillation technique. By Veine Gustavsson. 1968 24 p. Sw. cr. 10:- .

327. Phytoplankton from Tvaren, a bay of the Baltic, 1961-1963. By Torbjorn Willen. 1968. 76 p. Sw. 10:- .

328. Electronic contributions to the phonon damping in metals. By Rune Jonson. 1968. 38 p. Sw cr. 10:- .

329. Calculation of resonance interaction effects using a rational approximation to the symmetric resonance line shape function. By H. Haggblom. 1968. 48 p. Sw. cr 10:- .

330. Studies of the effect of heavy water in the fast reactor FRO. By L. I. Tiren, R. HSkansson and B. Karmhag. 1968. 26 p. Sw. cr. 10:-.

331. A comparison of theoretical and experimental values of the activation Dop­pler effect in some fast reactor spectra. By H. Haggblom and L. I. Tiren. 1968. 28 p. Sw. cr. 10:- .

332. Aspects of low temperature irradiation in neutron activation analysis. By D. Brune. 1968. 12 p. Sw. cr. 10:- .

333. Application of a betatron in photonuclear activation analysis. By D. Brune, S. Mattsson and K. Liden. 1968. 13 p. Sw. cr. 10: - .

334. Computation of resonance-screened cross section by the Dorix-Speng system. By H. Haggblom. 1968. 34 p. Sw. cr. 10:- .

335. Solution of large systems of linear equations in the presence of errors. A constructive criticism of the least squares method. By K. Nygaard. 1968. 28 p. Sw. cr. 10:- .

336. Calculation of void volume fraction in the subcooled and quality boiling regions. By S. Z. Rouhani and E. Axelsson. 1968. 26 p. Sw. cr. 10:- .

337. Neutron elastic scattering cross sections of iron and zinc in the energy region 2.5 to 8.1 MeV. By B. Holmqvist, S. G. Johansson, A. Kiss, G. Lo-din and T. Wiedling. 1968. 30 p. Sw. cr. 10:- .

338. Calibration experiments with a DISA hot-wire anemometer. By B. Kjell-strom and S. Hedberg. 1968. 112 p. Sw. cr. 10:- .

339. Silicon diode dosimeter for fast neutrons. By L. Svansson, P. Swedberg, C-O. Widell and M. Wik. 1968. 42 p. Sw. cr. 10:- .

340. Phase diagrams of some sodium and potassium salts in light and heavy water. By K. E. Holmberg. 1968 48 p. Sw. cr. 10:-.

341. Nonlinear dynamic model of power plants with single-phase coolant reac­tors. By H. Vollmer. 1968. 26 p. Sw. cr. 10:- .

342. Report on the personnel dosimetry at AB Atomenergi during 1967. By J. Carlsson and T. Wahlberg. 1968. 10 p. Sw. cr. 10:- .

343. Friction factors in rough rod bundles estimated from experiments in parti­ally rough annuli - effects of dissimilarities in the shear stress and tur­bulence distributions. By B. Kjellstrom. 1968. 22 p. Sw. cr. 10:-.

344. A study of the resonance interaction effect between a * U and u*Pu In the lower energy region. By H. Haggblom. 1968. 48 p Sw. cr. 10:—.

345. Application of the microwave discharge modification of the Wilzbach tech­nique for the tritium labelling of some organics of biological interest. By T. Gosztonyi. 1968. 12 p. Sw. cr. 10:-.

346 A comparison between effective cross section calculations using the Inter­mediate resonance approximation and more exact methods. By H. Ha'afl-blom. 1969. 64 p. Sw. cr. 10:- .

347. A parameter study of large fast reactor nuclear explosion accidents. By J. R. Wiesel. 1969. 34 p. Sw. cr. 10:-.

348. Computer program for inelastic neutron scattering by an anharmonic crystal. By L. Bohlin, I. Ebbsjo and T. Hogberg. 1969. 52 p. Sw. cr. 10:- .

349. On low energy levels in <"W. By S G. Malmskog, M. Hojeberg and V. Berg. 1969. 18 p. Sw. cr. 10:-.

350. Formation of negative metal ions in a field-free plasma. By E. Larsson. 1969. 32 p. Sw. cr 10:-.

351. A determination of the 2 200 m/s absorption cross section and resonance integral of arsenic by pile oscillator technique. By E. K. Sokolowski and R. Bladh. 1969. 14 p. Sw. cr. 10:- .

352. The decay of " 'Os. By S. G, Malmskog and A. Backlin. 1969. 24 p. Sw. cr. 10:-.

353. Diffusion from a ground level point source experiment with thermolumine-scence dosimeters and Kr 85 as tracer substance. By Ch. Gyllander, S. • Hollman and U. Widemo. 1969. 23 p. Sw. cr. 10:- .

354 Progress report, FFN, October 1, 1967 - September 30, 1968. By T. Wied­ling. 1969. 35 p. Sw. cr. 10:- .

355. Thermodynamic analysis of a supercritical mercury power cycle. By A. S. Roberts, Jr., 1969. 25 p. Sw. cr. 10:-.

356. On the theory of compensation in lithium drifted semiconductor detectors. By A. Lauber. 1969. 45 p. Sw. cr. 10:-.

357 Half-life measurements of levels in "As. By M. Hojeberg and S. G. Malmskog. 1969. 14 p. Sw. cr. 10:-.

358. A non-linear digital computer model requiring short computation time for studies concerning the hydrodynamics of the BWR. By F. Reisch and G. Vayssier. 1969. 38 p. Sw. cr. 1 0 : - ,

359. Vanadium beta emission detectors for reactor in-core neutron monitoring. I. 0 . Andersson and B. Sbderlund. 1969. 26 p. Sw. cr. 10:—.

360. Progress report 1968 nuclear chemistry. 1969. 38 p. Sw. cr. 10:- . 361. A half-life measurement of the 343.4 keV level in "'Lu. By M. Hojeberg

and S. G. Malmskog. 1969. 10 p. Sw. cr. 10:-. 362. The application of thermoluminescence dosimeters to studies of released

activity distributions. By B-l. Ruden. 1969. 36 p. Sw. cr. 10:- . 363. Transition rates in '"Dy. By V. Berg and S. G. Malmskog. 1969. 32 p.

Sw. cr. 10:- . 364. Control rod reactivity measurements in the Agesta reactor with the pulsed

neutron method. By K. Bjoreus. 1969. 44 p. Sw. cr. 10:- . 365. On phonons in simple metals I I . Calculated dispersion curves in aluminium.

By R. Johnson and A. Westin. 1969. 124 p. Sw. cr. 10:- . 366. Neutron elastic scattering cross sections. Experimental data and optical

model cross section calculations. A compilation of neutron data from the Studsvik neutron physics laboratory. By B. Holmqvist and T. Wiedling. 1969. 212 p. Sw. cr 10.- .

367. Gamma radiation from fission fragments. Experimental apparatus — mass spectrum resolution. By J. Higbie. 1969. 50 p. Sw. cr. 10: - .

368. Scandinavian radiation chemistry meeting Studsvik and Stockholm, Sep­tember 17-19, 1969. By H. Christensen. 1969. 34 p. Sw. cr. 10:- .

369. Report on the personnel dosimetry at AB Atomenergi during 1968. By J. Carlsson and T Wahlberg. 1969. 10 p. Sw. cr 10:-.

370. Absolute transition rates in "Mr. By S- G. Malmskog and V. Berg. 1969. 16 p. Sw. cr. 10:-.

371. Transition probabilities in the 1/2+(631) Band in 2«U. By M. Hojeberg and S. G. Malmskog. 1969. 18 p. Sw. cr. 10:- .

372. E2 and M1 transition probabilities in odd mass Hg nuclei. By V. Berg, A. Backlin, B. Fogelberg and S. G. Malmskog. 1969. 19 p. Sw. cr. 10: - .

373. An experimental study of the accuracy of compensation in lithium drifted germanium detectors. By A. Lauber and B. Malmsten. 1969. 25 p. Sw. cr. 10.- .

374. Gamma radiation from fission fragments. By J. Higbie. 1969. 22 p. Sw. cr. 10:- .

375 Fast Neutron Elastic and Inelastic Scattering of Vanadium. By B. Holm­qvist, S. G. Johansson, G. Lodin and T. Wiedling. 1969. 48 p. Sw. cr. 10:- .

376. Experimental and Theoretical Dynamic Study of the Agesta Nuclear Power Station. By P.-A. Bliselius, H. Vollmer and F. Akerhielm. 1969. 39 p. Sw. cr. 1 0 : -

377. Studies of Redox Equilibria at Elevated Temperatures 1. The Estimation of Equilibrium Constants and Standard Potentials for Aqueous Systems up to 374°C. By Derek Lewis. Sw. cr. 10:-

List of published AES-reports (In Swedish)

1. Analysis be means of gamma spectrometry. By D. Brune. 1961. 10 p. Sw. cr. 6:-.

2. Irradiation changes and neutron atmosphere in reactor pressure vessels-some points of view. By M. Grounes. 1962. 33 p. Sw cr. 6:—.

3. Study of the elongation limit in mild steel. By G. Dstberg and R. Atter-mo. 1963 17 p. Sw. cr. 6:- .

4. Technical purchasing in the reactor field. By Erik Jonson. 1963. 64 p. Sw. er. 8:—.

5. Agesta nuclear power station. Summary of technical data, descriptions, etc. for the reactor. By B. Lilliehook. 1964. 336 p. Sw. cr. 15:- .

6. Atom Day 1965. Summary of lectures and discussions. By S. Sandstrom. 1966. 321 p. Sw. cr. 15:-.

7. Building materials containing radium considered from the radiation pro­tection point of view. By Stig O. W. Bergstrom and Tor Wablberg. 1967. 26 p. Sw. cr. 10:-.

Additional copies available from the library of AB Atomenergi, Fack, S-611 01 Nykoping, Sweden.

EOS-tryckerierna, Stockholm 1970