Approach to Equilibrium in Solid Solution-Aqueous Solution Systems

Jul 23, 2009 - Solid solutions containing less than 19 and more than 73 mole percent KBr ... established in other low-temperature solid solution-aqueo...
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26 Approach to Equilibrium in Solid Solution-Aqueous Solution Systems: The K C l - K B r - H O System at 25°C 2

L. Niel Plummer U.S. Geological Survey, Reston, VA 22092 Thermodynamic calculations based on the compositional dependence of the equilibrium constant are applied to solubility data in the KCl-KBr-HO system at 25°C. The experimental distribution coefficient and activity ratio of Br /Cl in solution is within a factor of two of the calculated equilibrium values for compositions containing 19 to 73 mole percent KBr, but based on an assessment of uncertainties in the data, the solid solution system is clearly not at equilibrium after 3-4 weeks of recrystallization. Solid solutions containing less than 19 and more than 73 mole percent KBr are significantly farther from equilibrium. As the highly soluble salts are expected to reach equilibrium most easily, considerable caution should be exercised before reaching the conclusion that equilibrium is established in other low-temperature solid solution-aqueous solution systems. 2

-

Equilibrium relatively

between easily

composition

of

no l o n g e r

the is

i s added

the chemical

and

aqueous rarely

that

component

such

path

that

as o c c u r s

to

requires

in

and s o l i d .

solution

coefficients

was e s t a b l i s h e d

used have

(1-3).

shifts

Equilibrium is

homogeneous

between

As a r e s u l t , been

which

composition

may b e r e q u i r e d

o f a l l components

have

often

i n the

component

composition

a solid

is

when t h e

the solid

times

the s o l i d

with

activity

equilibrium

long

are equivalent.

studies

solutions

an a d d i t i o n a l

the solution

until

demonstrated

Laboratory solid

Very

potentials

phases

invariant,

when

the reaction

of both

not established

and is

when

and aqueous

i n the laboratory

to the system,

invariant.

equilibrium

composition

salts

is

However,

coprecipitates is

simple

demonstrated

the s o l i d

KCI-H2O s y s t e m .

reach

-

solid

equilibrium

series. to evaluate

made

Using

the

the assumption more

T h i s chapter not subject t o U . S . c o p y r i g h t . P u b l i s h e d 1986, A m e r i c a n C h e m i c a l Society

recent

562

G E O C H E M I C A L P R O C E S S E S AT M I N E R A L S U R F A C E S

thermodynamic shown

that

periods

data

o f 8 weeks

Schmeling did

not reach

earth

sulfate

reactions

the

solid

study

o f 3 weeks

coefficient,

to attain

Stoessell

not established

The

present

paper

to

and there

equilibrium

(6-8)

(3,8).

thermodynamic

greater

of

By e x a m i n i n g

equilibrium

trace

criteria

i n the

and has

distribution

concluded

coprecipitation

salt is

Solubility

at 25°C

(9)

alkaline-

equilibrium

Soluble

the experimental

and Carpenter

during

uses

of

Recrystalli­ with

temperature.

rapid

studied

by

solutions

batch

days

the approach

well

over

solid in

t o be e s t a b l i s h e d .

dependence

was

a t room

t o be r e l a t i v e l y

previously

hundred

2

system has been

assumed

(5)

i t c a n be

studied

(4).

system K C l - K B r - H 0 .

for equilibrium

compositional

a t 76°C

several

examines

salt

(aragonite)

by r e c r y s t a l l i z a t i o n

solutions

soluble

KCl-KBr-H20 been

SrCC>3-CaC03

periods

a r e known

likelihood

system

2

for at least

present

the very

compositions,

not established

i n t h e SrC03-BaC03-H 0

equilibrium

after

continued

The in

was p r o b a b l y

a t 25°C.

experiments zation

f o r t h e end-member

equilibrium

Br i n KC1.

to test

for

equilibrium. KCl-KBr-H?0 In

this

System

study

KCl-KBr-H 0

solution amounts

(Table

solution,

an i n i t i a l

total

number

composition approached The

containing For to

four

of

were

K B r was

pair

of

identical.

solution

was,

The tubes

rotated

runs

nearly

observed

compared (6,7).

were

favorably

Table

I

paths. each at

ground.

identical after

the

therefore,

reaction

marbles.

finely

added

runs

The f i n a l

tubes"

were

reported

solid

in "solubility

of

which

In the

conducted

compositions weeks,

out i n

t o an i n i t i a l KBr

compositional

the material

and

solid

identical.

o f KC1 and K B r were

t o keep pair

this

carried

F o r each

and aqueous

the e n d -

(A and Β ) , t h e t o t a l

runs,

KC1 s o l u t i o n .

of

oversaturation of

were

K C 1 was a d d e d

two d i f f e r e n t

two g l a s s

solid-aqueous

periods

to

of

three

compositions

summarizes

the o r i g i n a l

(8). Although

compositions

nearly

identical

are observed

directions

under

this

is insufficient

alone

equilibrium. solution compare the

experiments

of experiments

solid

the s o l i d

from

each

previously data

both

the s o l u b i l i t y

and i n t h e B-type

o f moles

± 0.02°C

solution

I),

aqueous

experiments

25.00

from

o f KC1 and K B r i n t h e s y s t e m were runs

aqueous to

pair

i n the

The s o l u b i l i t i e s

determined

solubility

F o r each

recrystallization

(8).

In studying

system,

(8).

A-type

examined

at 25°C

KC1 and K B r were

undersaturation. pairs

25°C

we h a v e

system

2

members

at

conditions

In order

activity observed

appropriate

of

values

total

proof

to test

coefficients solid

solid-aqueous

solution

in recrystallization of

constant

f r o m two composition,

the establishment

for equilibrium, must

be d e t e r m i n e d

and aqueous

solution

expected

equilibrium.

at

of

the solid and used

compositions

to

with

26.

Approach

PLUMMER

Table

I.

Original

to Equilibrium

solubility

KCl-KBr-H 0 Total No.

Composition

563

System

2

data

a t 25°C

2

in the KCl-KBr-H 0

f o r t h e system

(8) Liquid

Phase

KBr

KC1

KBr

KC1

Wt.%

Wt.%

Wt.%

Wt.%

Solid Br

Br+Cl

Solution

KBr

Mole

Wt.%

Fraction KBr

Moles 0.00

...

10.00

25.00

1 2A

0.00

26.42

10.01

20.91

0.000 .231

0.00 7.89

0.000 .051

2B

10.00

25.00

10.28

20.69

.237

6.87

.044

3A

21.00

22.00

20.21

15.31

.453

26.95

.188

3B

21.00

22.00

20.13

15.39

.450

26.99

.188

4A

25.00

21.00

22.85

13.83

.509

37.78

.276

4B

25.00

21.00

22.75

13.92

37.29

.271

5A

34.00

18.00

26.62

11.56

.506 .591

60.0

.485

5B

34.00

18.00

26.42

11.71

.586

59.9

.483

6A

37.00

10.00

30.46

8.74

.686

81.1

.729

6B

37.00

10.00

30.50

8.70

.687

81.0

.728

7A

39.00

5.00

35.09

4.89

.818

92.9

.891

7B

39.00

5.00

35.21

4.75

.823

92.9

.891

0.00

40.57

0.00

1.000

100.0

1.000

8 Theory The

final

Table either (3)

solid

I will

solution-aqueous

fall

into

be a t e q u i l i b r i u m ,

correspond If

(2)

will

at stoichiometric

to solution

(1)

they

will

saturation,

or

state.

are at equilibrium,

be r e l a t e d

compositions of

catagories:

t o some n o n - e q u i l i b r i u m

the solutions

activities

solution

one o f three

the solid

composition

component by t h e

equations

a

KCl(s) KCl

=

a

KBr(s) KBr

=

K

a

K

+

a

C l ~

and

where

K

a^ci( ) s

a

n

a

"

a

a

K

+

a

KBr(s)

Br~

i n the s o l i d ,

K ,

CI"" and B r ~ i n aqueous

+

a £ + , açy-

constants

KC1 = K

+

+ CI"

2

denote

KBr

equilibrium

the a c t i v i t i e s

and a g

r

solution,

o f KC1 and

- are the activities of and K^ci*

f o r t h e end-member

Kj^g

r

are the

reactions (3)

and KBr

= K+ + B r "

(4)

G E O C H E M I C A L PROCESSES AT M I N E R A L

564 Furthermore, with

the

if

the

aqueous

solid

solution

solution,

the

salt

is

at

equilibrium

SURFACES

equilibrium

constant

for

the

reaction K B r will

be

C l

x

1

-

defined

=

(x)

K

where

(

the

x

= K

)

+

+

xBr~

+

(1-x)

Cl~

(5)

by

v-

a

B r -

X

activity

of

41:

>

x)

the

(6

solid

KBr Cl(i_ ) x

is

x

unity

by

definition. Stoichiometric aqueous fixed

solution

composition

composition is

part

this

of

a

case,

solid

may

is

the

no

longer

of

(10).

the

the

as

restrictions, free

component The

equilibrium If

the

the

are

at

This

for

(discussed

the

are

to

if

without of

the

at the

provisional

of

of

the

such

as

may

determination

not

been

the

with

the The

to

from

provisional

observed those

data

true

dependence

the

calculated

defined

possible

established

provided

Using

compare

then

activity

is

compositional

experimental

are

and

be

of

coefficients

it

has

would

compositions between

solution.

compositional

activity

saturation

equilibrium.

is

no

agreement

properties

established.

The

depends

that

stoichiometric

data

for

the

and

(8),

solids

solid

calculated and

observed

uncertainties,

solid be

solution

equal

to

the

values.

there

coefficients

phase

all

aqueous

the

measurements.

the

properties

solid-solution not

the of

because

Agreement

establishment

with

constant

within

both

system

2

provisional

we

for

stoichiometric

that

equilibrium

data

solution.

applicable.

KCl-KBr-H 0

constant

solid

knowledge

individual

aqueous

nor

not

assumes

calculation

solution

confirms,

If

saturation

are

The

coefficient

thermodynamic

was

the

thermodynamic

equilibrium.

values

in

initially

constant,

compositions of

identically

equilibrium

stoichiometric

solution-aqueous

and

termed

independent

activity

defined

6

the

solution

2

to

saturation. or

of

equilibrium

independent

solid

6

1 and

owing

equivalence

equilibrium

equilibrium

below).

coefficients determine

is

the

Equation

because,

saturated

2,

1,

and

mineral in

Equations

saturation an

the

invariant,

applicable.

between

x

follows

values

is

an

of

the

Since,

phase

at

provisional

of

provisional

solid

and

K( ),

though

series.

establishing

neither

stoichiometric

dependence

solid

in

potentials

is

that

permits

criteria

Equations

testing

analysis

the

stoichiometric

solid

the

of

between

solid

saturation

even

one-component

constant,

and

saturation, In

a

the

change

chemical

equilibrium

fixed

stoichiometric

are

to

stoichiometric

compositional

equilibrium at

equilibrium

multi-component

remains

composition

kinetic not

At

solid

treated

apply

defines

homogeneous

continuous

be

only

saturation

and

on

we

in can

validity

the

free

of

validity

saturation

standard

calculated only

was

energy

and

conclude the of

observed that

the

original

established. of

equilibrium

provisional

formation

If of

the

activity assumption independent solid

26.

PLUMMER

solutions

Approach

can

be

introduced

of

calculated

if

stoichiometric

Equation between that

and

observed

Stoessell

the

calculated in

at

By the

examining solid

the

Gibbs-Duhem the

For

phase

the

valid

comparison

constants

established,

containing

required

close

distribution by

determines

as

found

(9)

experiments

compositional the

by

agreement

coefficient

and

assuming

trace

amounts

dependence

provisional

can

equation

be

of

to

be

the

Br

derived

binary

the

the properties

Activity

measured

in

system

of

thermodynamic

determined.

may

constant

KCl-KBr-R^O

source,

565

saturation.

components

equilibrium

the

was

Carpenter

halite

solutions

solid

another

equilibrium

constant,

for of

of

System

2

from

growth

stoichiometric

equilibrium of

and

slow

recrystallization

in the KCl-KBr-H 0

equilibrium

saturation

6.

measured

occurs

to Equilibrium

from

an

coefficients

application

compositional

solid

following

of

dependence

solutions

(10).

relationships

are

(10):

a log

a

KCl(s)

38

-x

(log

K( ))

+

x

log

K( )

-

x

log

K

K

C

(7)

1

3x and 3 log

aKB ( ) r

-

s

(1-x)

(log

K

(

x

)

)

+

log

K(

x

-

)

log

(8)

3x where is

χ

denotes

defined

by

equilibrium component

the

mole

Equation

constants

activity

a

fraction

6, for

of

and

KBr

and

Equations

coefficients,

in

Κ^Β

3 and are

γ

the

solid,

are

the

4.

The

defined

K( ) x

end-member

individual by

KCl(s)

*KC1 =

() 9

1-x

and a

λ KBr

By e x a m i n i n g constant, can or

be

(10)

the

the

stoichiometric

equilibrium solubility The used

to

and or

compositional

thermodynamic

determined

activities

KBr(s)

=

if

activity

is

That

the

is,

will

saturation

the

the

equilibrium

solid

either

solution

at

equilibrium

provisional

be is

valid

if

attained

either in

the

data.

provisional calculate solution. ratio

distribution

activities

the

equilibrium

equilibrium

of

of

solution

coefficients

stoichiometric

are The

final

saturation.

aqueous the

the

dependence

properties

expected

Two of

and

compositional

distibution the

is

coefficients

composition

properties

coefficient,

activities

coefficient

activity

equilibrium

of

defined

Br"

to

to

D q, e

be and

C l " in

of

are the

tested the solution.

G E O C H E M I C A L P R O C E S S E S AT M I N E R A L S U R F A C E S

566

1-x D =

where

m

KCl

e

molality

in is

-

q

KC1

where γ

equilibrium

expected

in

Equations

KCl(s)

ΎΒΓ"

x

KBr(s)

y

the

equilibrium

a

equilibrium,

)

the

(12)

ion

activity

aqueous

solutions

is

Br~

to

coefficient

in

Cl~ activity

obtained

by

ratio

combining

2,

KBr

K

The

At

1 1

CI"

individual

solution.

1 and

° *BΒrΓ " \\

/

is

solution.

x

.

KBr

K

12)

(

coefficient

K

D

(11,

KBr

m denotes

distribution

the

m

KBr(s)

a

( 1 3 )

\ a

-/

c l

K

eq

KC1

a

KCl(s)

Equilibrium

Constants

Equilibrium

constants

saturated

solutions

thermodynamic dynamics well

of

known

model

single and

of

Pitzer

of

KC1 and

be

reliably

here

from

the

are

elsewhere

given

parameters Table

As

a means

of

the

model

within

that

realistic. uncertainty the

of

aqueous

mixtures

(16-17)

solid The

KCl-KBr-I^O

very

approach and

The

phase

saturated

19).

thermo­

are

equations.

the of

The

KBr

of the

virial

studied

Pitzer

18,

the

was

model

equilibrium

Pitzer

solutions

may

Pitzer

aqueous

parameters

calculated

data

is

from

solutions

model

are

summarized

the

of

Table

isopiestic

(17)

for

of

Table

I I

the

within

0.15%

or

better

Agreement or

zero

with

better

(Table

thermodynamic of

in

original

less

if

the

I I ,

the

vapor

KCl-KBr-R^O

system

ΨΟΙ,ΒΓ,Κ

I I ) .

We may of

of

equilibrium analytical

for

in

(8).

from

ψςχ

may

I I )

Br,Κ

Κ(χ)· thus

solutions

(Table

(Table

in

log

all

results

0*0003

conclude

constants data

=

Pitzer

0.0003

t h a n 0.4%

calculated

experimental

model

An u n c e r t a i n t y

uncertainties to

to

parameters

0.02%

of

the

the

of

I I I ) .

coefficient

instead

the

(13-15,

measurement

investigated. is

KC1 o r

using

calculate

verifying

(Table

osmotic

solution.

of

well

composition accuracy

I I .

pressure Using

been

compositions

coefficient

25°C

the the

thermodynamics

using to

aqueous

modeled

also

applicable

in

at

The

modeled

used

the

on

solutions

been

KBr have

constants

osmotic

for

(13-15).

from

dependent

salt

have

equations

calculated

are

T

n

be

e

this is 3-

(17) I I I ) comparison

very

e a d s

t

o

largest attributed

26.

Approach

PLUMMER

Table

II.

Summary

to Equilibrium

of

Pitzer

parameters

for

KCl-KBr-H 0 Parameter

KCÏ .04835 .2122

.2212

-.00084

-.00180

9

CI

Br

III.

9

.0569

0.000

s

*Cl|Br,K -

Table

(U 15).

KBr

3° C

system

25°C

3

1

°-

0

0

0

Comparison observed

of

calculated

osmotic

KCl-KBr-H 0

at

Osmotic

1

KBr

0

2

KCl

m

.935

Pitzer ψ=0.0

(17)

in

25°C

Coefficient

From m

and

coefficients

solutions

2

No.

System

2

model

the

at

2

in the KCl-KBr-H 0

model ψ=0.0003

4.816

.9893

.9893

.9893

3.546

.9843

.9833

.9843 .9921

3

2.128

2.425

.9919

.9905

4

2.489

2.153

.9960

.9945

.9961

5

3.048

1.753

1.0026

1.0012

1.0028

6

3.681

1.285

1.0094

1.0082

1.0096

7

4.543

.690

1.0193

1.0185

1.0194

8

5.737

1.0354

1.0354

1.0354

Table the

0

IV

solids

summarizes

and

aqueous

the

final

solutions

constants.

Values

of

log

composition

differ

by

no more

Because

there

constants either that

solid

follow

average for

for

Values and

are

of

used

5 are

on

the

KBr

(Table

shown

as

of

compositions

calculated

companion for

log

runs

A or

at

the

contained calculations

solid

compositions

A and

Β runs

The

function

for

and

each

equilibrium of

constant

equilibrium

solution B),

of

equilibria

Κ units.

selecting

initial

IV). a

with

0.003

(runs

average

constants

reported

total

constants

KBr mole

fraction

1. Equilibrium 3log to

K( )/3x

Values

were

x

calculate

coefficients 7-10.

based

than

reason

i n which solid

from

x

obvious

KC1 o r

Equation Figure

Test

no

runs

equilibrium

composition in

is

from

K( )

reported

(8)

of of

the

KC1 and log

KBr

K( ), x

interpolated

provisional in Slog

the

solids

K( )/3x, x

from

Figure

activities using

and

1 activity

Equations

provisional

568

GEOCHEMICAL PROCESSES AT MINERAL SURFACES

Table

No.

IV.

Summary o f c a l c u l a t e d p r o v i s i o n a l constants Molality i n Solution KC1 KBr

Mole Fraction KBr

.000 .935 .963 2.128 2.118 2.489 2.475 3.048 3.017 3.681 3.688 4.543 4.567 5.737

.000 .051 .044 .188 .188 .276 .271 .485 .483 .729 .728 .891 .891 1.000

1. 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B 7A 7B 8

Table V.

Average : V a l u e s log Κ KBr

Log Κ

x

.9037 .7071 .7039 .5779 .5802 .5685 .5699 .6047 .6047 .7147 .7142 .8780 .8789 1.1288

4.816 3.546 3.499 2.425 2.440 2.153 2.169 1.753 1.779 1.285 1.278 .690 .669 .000

equilibrium

.000

0.904

.048

0.706

.188

0.579

.274

0.569

.484

0.605

.729

0.714

.891 1.000

0.878 1.129

Summary o f p r o v i s i o n a l a c t i v i t i e s and a c t i v i t y coefficients for K B r C l ( i - ) at 25°C x

31og K No.

log K

X

(

x

ax 2 3 4 5 6 7

.706 .579 .569 .605 .714 .878

.048 .188 .274 .484 .729 .891

(

x

)

x

)

-1.56 -.28 -.05 .29 .74 1.54

x

KBr

.257 .888 .925 .863 .837 .927

X

KC1 K B r ( s )

.791 .658 .657 .708 .688 .367

a

.012 .167 .253 .421 .610 .826

a

KCl(s)

.753 .534 .477 .363 .186 .040

a c t i v i t i e s and p r o v i s i o n a l a c t i v i t y c o e f f i c i e n t s a r e g i v e n i n Table V. T a b l e V I summarizes v a l u e s o f t h e a c t i v i t y c o e f f i c i e n t r a t i o YBr""/YCl~ i s a t u r a t e d s o l u t i o n f o r each average s o l i d c o m p o s i t i o n (as c a l c u l a t e d from t h e model o f T a b l e I I ) , t h e calculated provisional equilibrium distribution coefficient ( E q u a t i o n 12) and t h e p r o v i s i o n a l e q u i l i b r i u m aqueous s o l u t i o n a c t i v i t y r a t i o o f B r ~ t o CI"" ( E q u a t i o n 13) based on t h e d a t a of Table V . F i g u r e 2 compares the e x p e r i m e n t a l d a t a ( 8 ) w i t h t h e p r o v i s i o n a l e q u i l i b r i u m c o m p o s i t i o n s on a c o n v e n t i o n a l Roozeboom d i a g r a m . I t appears t h a t e q u i l i b r i u m i s most c l o s e l y approached i n t h e m i d - r a n g e c o m p o s i t i o n s , but c o m p o s i t i o n s c l o s e r t o t h e end-members KC1 and KBr d e v i a t e n

t

n

e

PLUMMER

Approach

to Equilibrium

in the KCl-KBr-H 0 2

System

1.2

0.5

'

c

' ' 0.2

0.0

'

1

0.4

1

' 0.6

1

' 0.8

1

1.0

MOLE FRACTION KBr

Figure

1.

Provisional

KBr Cl(i^) x

at

equilibrium

constants

of

solids

25°C.

0.0

0.2

0.4

0.6

0.8

1.0

MOLE FRACTION KBr (SOLID) Figure

2.

provisional system

at

Roozeboom

diagram

equilibrium 25°C.

comparing

compositions

experimental and

i n the KCl-KBr-R^O

570

G E O C H E M I C A L P R O C E S S E S AT M I N E R A L S U R F A C E S

Table

VI.

Comparison

of experimental

equilibrium

solid/aqueous

and p r o v i s i o n a l solution

properties Equilibrium

Experimental No.

χ

a

B

- / a

r

c

-

l

eq

D

a

2

.048

1.068

.183

.288

1.96

3

.188

1.069

.265

.933

.47

Br"/ Cl" a

.028 .53

4

.274

1.069

.329

1.228

.45

.89

5

.484

1.071

.554

1.746

.52

1.95

6

.729

1.072

.938

3.082

.53

5.50

7

.891

1.074

1.207

7.200

.25

34.67

more

significantly

range factor from

of

two o f

the experimental

VI).

are found

Figure

These

activities

solubility

data

It

of

3log are 3log

K( )/3x x

solid

this

been

they

requires

pointed

a r e known

are based. (Table

from

Figure

known w i t h i n translate

1.

Slopes

20%.

estimated

e

points

r

of

ratio

from

Figure

e

of

ratio

of

40%.

the f i n a l

the approach i n solution

agreement

slope of

of

i f

t o maximum This

solid

does n o t

solution-aqueous

to calculate

at equilibrium.

the a c t i v i t i e s

from of

equilibrium.

to equilibrium,

i n calculated

i s defined

1

coefficients.

correspond

x

l o g Κ vs x,

by c l o s e

The e q u i l i b r i u m solution

test

aB -/aci~

on p l o t s

i n t h e aqueous

estimating

o f 20%

K( )/3x

many

the and

i n the KCl-KBr-B^O system are out of

a further

indicated

that

values

to uncertainties

r

the conclusion

calculated

20% i n

i n D q and ( a B - / a c ^ - ) q

slope

thermodynamic

of

and a c t i v i t y

20% i n 3 l o g

in

Uncertainties

of

observed

the

the a n a l y t i c a l

to uncertainties

uncertainties

directly

activities

the

than

equilibrium

uncertainties

As

that

saturation,

So we may n o t a t t r i b u t e

VI)

a r e , however,

phase

solution

o f KC1

fraction.

c a n be shown

out that

Uncertainties alter

range

activities

independent

better

i n provisional

values

There

K(x)/3x

compositional

are at stoichiometric

above,

difference

probably

i t

a

deviations

x

constants

experimental model.

Larger

o f KBr mole

i f

distribution

are within

K( ).

on which

observed

this

as a f u n c t i o n

(8)

has a l r e a d y

equilibrium

ratio

the provisional

c a n be v e r i f i e d of

as mentioned

definition

data

In the compositional equilibrium

values.

outside

3 shows

KBr i n the s o l i d s

but

equilibrium.

and B r " t o C I " a c t i v i t y

equilibrium

(Table and

from

. 1 8 8 _< χ _< . 7 3 0 t h e p r o v i s i o n a l

coefficient

in

D

Y C I -

we u s e t h e

the

expected

Equilibrium is

and observed

the equilibrium

slopes.

aqueous

B r " t o C I " (14)

(14)

Using the

the experimental

calculated

YBr"/ïci~

aqueous

(Table

VI),

solution

compositions

solution

activity

Figure

4 shows

(Table

IV) and

coefficient

the slopes

of

ratio

log Κ

26.

PLUMMER

Approach

to Equilibrium

\

KCI

in the KCl-KBr-H 0

System

2

\

/

KBr

>




1

0.8

1.0

MOLE FRACTION KBr Figure if

4.

Comparison

the experimental

line

segments

compositional •ci,Br K

i

f

as

a

s

function

established. as

300% f r o m

through 0

1

>

χ which

those

t h e ψς^ B r Κ P

curve

of

The s e n s i t i v i t y

and 0 . 0 2 . ' is

and s l o p e s

a r

Figure

close

log K( )

required

x

to equilibrium point)

with

calculated

x

equilibrium

estimated

4).

there

K( )/3x)

experimental

are required

The i m p l i e d

(Figure

.02,

each

(3log

correspond

(8)

(short

the

assuming

0 . 0 0 , 0.01 and 0 . 0 2 .

varying -0.01

slopes

dependence

-°·

of

of

data

from of

ameter

log K( ) x

of

4 shows from

equilibrium

slopes was

the P i t z e r

that

i f

the observed

as

log Κ

much

curve

investigated model

Ψ^ι B r Κ

i n slopes

is

deviate

t h e smoothed

correspondence

calculated

i f

o\

i

s

between n

e

a

r

the l o g Κ

Br"*/Cl"~

by

572

G E O C H E M I C A L PROCESSES AT M I N E R A L

activity be

near

ratio

using

0.02

for

the

equilibrium.

It

was

that

(17)

ΨΟΙ,ΒΓ,Κ

i

Equation

osmotic

11%

from

observed

the

coefficient reliably during

is

previously

shown

n

computed

e

closely

values to

in

the

example,

the

substitution than

the

of

two

for

the

Considerable conclusion

caution

that

temperatures

in

Finally, properties

coefficients equilibrium applies

to

for

the

(10)

testing

However,

from

it

shown

can

substitution close on

as

KCl-KBr

be

that

system

at

occurs

this

solid

has

solid One

reaching

the

relatively

low

distribution that

exception

for

of

the

predominant behavior

Thorstenson

dependence

study,

is

of

and

the

well

suited

compositions.

been

found,

the

remain

provisional

dependence

of

the

thermodynamic

equilibrium

means

of

verification

recrystallization

in

the

stoichiometric

systems.

thermodynamic

solution

not

factor equilibrium.

solutions

compositional

verified.

demonstration

in

all

a

at

solution

of

Sr

larger

distribution

equilibrium

The method

used

for

was for

assumptions

compositional

equilibrium

observed can

(9).

the

before

activity of

carbonate

it

not

at

25°C.

times

possible

the

as

more

in

the

derive

One

unit

at

independently

approximation

constant,

the

to

where

and

components based

of

be

12

experimental

established.

saturation

because

the

constant

appropriate

solutions

equilibrium

properties until

solution-aqueous

been

allow

equilibrium to

other

trace

trace

Plummer

established

unless

stoichiometric component

exercised

not

>

the

(4),

clearly

is

is

2

be

was

within

be

solid

has

but

0

much

can

it

of

are

should solid

it

than

is

equilibrium

it

of

value,

data

as

coefficient

Most

system

t

osmotic

of

system

value.

KCl-KBr-R^O

equilibrium

system

aragonite

s

to

° ·

E

system

analysis

solution

R

u

established

established,

distribution

equilibrium the

(17), not

E

by

the

KCl-KBr-R^O

into

W

deviate

10,000

not

m

isopiestic

Because

similar

solid

seawater

expected

of

a

experimental

from

coefficients

the

K

using

would

in

Br

correspond

Ψαΐ,ΒΓ,Κ

KCl-KBr-R^O

in

strontianite-aragonite that

in

Yrji

to

e q u i l i b r i u m was

e q u i l i b r i u m was

For

is,

(8)

If

(17).

1 part

that

approached

systems.

0.0003.

r

recrystallization

Although

found

a

coefficients

known

concluded

That

data

s

the

14.

solubility

SURFACES

is

the

KCl-KBr-R^O

saturation.

Conclusion Most

thermodynamic

relatively have

depended

experimentally pointed they

are

through

out

to

test

at

if

the

of

dependence No

other

solutions

that

Thorstenson

the of

if

solution

properties

of

the

solid

(10)

equilibrium

Therefore, to

constant,

the it

e q u i l i b r i u m has

property

equilibria

equilibrium

at

studies

was

equation

equilibrium

compositional

from

Plummer

are

saturation.

independently

If

and

data

Gibbs-Duhem

the

derived

(equilibration) equilibrium

experimental

stoichiometric

equilibrium.

thermodynamic

solid

solubility

established.

solution-aqueous for

for

assumption

determine

established. solid

the

application

compositional possible

on

that

also an

data

low-temperature

is

of

experimental

provides

an

demonstrated,

solution

are

is

been

also

independent the

26.

P L U M M ER

Approach

to Equilibrium

in the KCl-KBr-H

2

Ο System

573

determined. However, i f e q u i l i b r i u m i s n o t a t t a i n e d , t h e thermodynamic p r o p e r t i e s o f t h e s o l i d c a n be d e t e r m i n e d from the s o l u b i l i t y d a t a o n l y i f t h e system c a n be demonstrated t o be a t s t o i c h i o m e t r i c s a t u r a t i o n . In a p p l i c a t i o n o f t h i s method t o s o l u b i l i t y d a t a ( 8 ) i n t h e K C l - K B r - H ^ O system a t 25°C, i t i s found t h a t e q u i l i b r i u m i s i n g e n e r a l n o t a t t a i n e d , though some m i d - r a n g e c o m p o s i t i o n s may be near e q u i l i b r i u m . As t h e h i g h l y s o l u b l e s a l t s a r e e x p e c t e d t o r e a c h e q u i l i b r i u m most e a s i l y , considerable c a u t i o n s h o u l d be e x e r c i s e d b e f o r e r e a c h i n g t h e c o n c l u s i o n that e q u i l i b r i u m i s e s t a b l i s h e d i n other low-temperature s o l i d solution-aqueous s o l u t i o n systems. I t i s not appropriate t o d e r i v e thermodynamic p r o p e r t i e s o f s o l i d s o l u t i o n s from e x p e r i m e n t a l d i s t r i b u t i o n c o e f f i c i e n t s u n l e s s i t c a n be demonstrated t h a t e q u i l i b r i u m has been a t t a i n e d . Acknowledgments Review comments o f E . Busenberg gratefully acknowledged.

and B . F . Jones a r e

Literature Cited 1. Schmeling, P. Svensk Kern. Tidskr. 1953, 65, 123-34. 2. Crocket, J. H.; Winchester, J. W. Geochim. Cosmochim. Acta 1966, 30, 1093-1109. 3. Kirgintsev, A. N.; Trushnikova, L. N. Russian J. Inorg. Chem. 1966, 11, 1250-5. 4. Plummer, L. N.; Busenberg, E., unpublished data. 5. Denis, J . ; Michard, G. Bull. Mineral. 1983, 106, 309-19, 6. Amadori, M.; Pampanini, G. Atti acscad. Lineei II 1911, 20, 473. 7. Flatt, R.; Burkhardt, G. Helv. Chem. Acta 1944, 27, 1605-10. 8. Durham, G. S.; Rock, E. J.; Frayn, J. S. J. Am. Chem. Soc. 1953, 75, 5792-4. 9. Stoessell, R. K.; Carpenter, A. B. Geochim. Cosmochim. Acta 1986, 50, in press. 10. Thorstenson, D. C.; Plummer, L. N. Am. J. Sci. 1977, 277, 1203-23. 11. Vaslow, F.; Boyd, G. E. J. Am. Chem. Soc. 1952, 74, 4691-95. 12. McIntire, W. L. Geochim. Cosmochim. Acta 1963, 27, 1209-64. 13. Pitzer, K. S. J. Phys. Chem. 1973, 77, 268-77. 14. Pitzer, K. S.; Mayorga, G. J. Phys. Chem. 1973, 77, 2300-8. 15. Pitzer, K. S.; Kim, J. J. J. Am. Chem. Soc. 1974, 96-5701-7. 16. McCoy, W. H.; Wallace, W. E. J. Am. Chem. Soc. 1956, 78, 1830-3. 17. Covington, A. K.; Lilley, T. H.; Robinson, R. A. J. Phys. Chem. 1968, 72, 2759-63. 18. Harvie, C. E.; Weare, J. H. Geochim. Cosmochim. Acta 1980, 44, 981-97. 19. Harvie, C. E.; Moller, N.; Weare, J. H. Geochim. Cosmochim. Acta 1984, 48, 723-51. RECEIVED

June 25, 1986