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
