AN ABSTRACT OF THE THESIS OF
RICHARD FREDRICK GATES for the
(Name)
in
OCEANOGRAPHY
(Major)
MASTER OF SCIENCE
(Degree)
presented on V)?ni7fAi 4' 17(a
(Date)
Title: MAGNESIUM SULFATE ION ASSOCIATION IN SEAWATER
Abstract approved:
Redacted for Privacy
Ricardo M. Py(kowicz
The extent of MgSO4° association in an artificial seawater
solu-
tion corresponding to 34. 8% salinity was determined at 5°C, 15°C,
and 25°C at one atmosphere pressure. The effect of pressure on the
extent of MgSO4° association was studied at 25°C. The data also
yielded the stoichiometric association constant of MgSO4° at 25°C
and one atmosphere pressure. It also permitted the calculation of
the thermodynamic solubility product of brucite as a function of tern-
perature.
Magnesium Sulfate Ion Association in Seawater
by
Richard Fredrick Gates
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
June 1969
APPROVED:
Redacted for Privacy
As
in charge of major
Redacted for Privacy
Chair an of Department of Oceanography
Redacted for Privacy
Dean of Graduate School
Date thesis is
Typed by Clover Redfern for
V/
7
Richard Fredrick Gates
ACKNOWLEDGEMENTS
I would like to express my sincerest thanks to Dr. Ricardo M.
Pytkowicz for suggesting this project and for his helpful criticisms
throughout all phases of this work. His theoretical derivations provided the foundation for this work.
I would also like to express my appreciation to Mr. Charles H.
Culberson for his assistance in preparing the pressure system used
in this work and to Mr. Dana R. Kester for helpful discussions. This
work was supported by the National Science Foundation Grant GA-l252
and the Office of Naval Research Contract Nonr 1Z86(lO).
TABLE OF CONTENTS
Page
Chapter
I.
INTRODUCTION
I
II.
THEORETICAL
5
Definition of Thermodynamic Equilibrium Constants
and Activities
Determination of the Free Magnesium at One
Atmosphere
Determination of the Free Magnesium at High Pressure
Determination of the Stoichiometric Association
Constant of MgSO4
III.
IV.
EXPERIMENTAL
Free Magnesium at One Atmosphere Pressure
Free Magnesium at High Pressure
Electronics
Preparation of the Brucite
Solution Preparation
RESULTS
Data at One Atmosphere
High Pressure Data
V. DISCUSSION
Comparison of Results with Previous Estimates
Discussion of Errors
Pressure Experiments
5
6
9
12
15
15
16
21
23
24
25
25
27
31
31
31
32
BIBLIOGRAPHY
34
APPENDIX
Appendix I.
37
LIST OF FIGURES
Page
Figure
1.
Apparatus used for experiments at one atmosphere.
16
2.
Apparatus used for experiments at high pressure.
18
3.
High pressure system.
20
4.
Electronics.
22
5.
Linear relation of
6.
Curve for calculation of enthalpy.
and temperature.
28
39
LIST OF TABLES
Page
Table
1.
Composition of the experimental solutions.
2.
Results at one atmosphere.
3.
Molal concentrations.
4.
Solubility product of brucite as a function of temperature. 30
5.
High pressure results at 25°C.
30
6.
Supplementary pressure results.
33
7
26
LIST OF SYMBOLS
aA
Activity of A.
(A)
Molal concentration of A.
E
Potential of pH cell.
Easym Asymmetry potential of high pressure cell.
F
Free, unassociated, quantities.
i
Subscript designating the solution inside the glass electrode of
the high pressure cell.
K
Thermodynamic Equilibrium constant.
K
Thermodynamic solubility product.
K
Ion product of water.
KA
Stoichiometric constant of A.
w
Apparent constant of A.
o
Subscript designating the solution outside the glass electrode
of the high pressure cell.
p
Subscript designating the measurement at pressure.
loga
pH
pH
eq
Equilibrium pH.
S
Slope of the glass electrode response.
T
Total, free plus associated, quantities.
eff
Effective ionic strength.
Activity coefficient of A.
1
Subscript designating measurement at one atmosphere.
*
Superscript designating pressure at p.
MAGNESIUM SULFATE ION
ASSOCIATION IN SEAWATER
I.
INTRODUCTION
A knowledge of the extent of ion pair formation between mag
nesium and sulfate ions in seawater, as a function of temperature and
pressure, will enhance our understanding of the structure of seawater,
the effect of ion pairs on colligative and transport properties, and the
mechanism of acoustical energy absorption.
From a structural point of view, the determination of the chemical model of seawater will need to be supported by the results of sev-
eral experimental techniques, each with its own assumptions, in order
to substantiate the final results. Published results on the ext;ent of
MgSO4° formation in seawater at 25°C and one atmosphere pressure
exhibit some scatter.
Carrels and Thompson (1962) estimated that 87 percent cf the
total magnesium in seawater exist as the free ion and that 11 percent
exist as MgSO40.
This result was obtained by making use of a mathe
matical model which incorporated the dissociation constants and the
individual activity coefficients of the major species in seawater.
Platford (1965) concluded that 3 percent of the total magnesium in sea-
water exist as MgSO40. He utilized an optical detection technique to
determine the point of Mg (OH)2 precipitation, upon addition of NaOH
2
to carbonate free seawater. This method required a knowledge of the
thermodynamic solubility product of brucite. Pytkowicz, Duedali and
Connors (1966) estimated that 47 percent of the total magnesium in
seawater exist as the free ion and that between 39 percent and 53 per-.
cent are present as MgSO40. Their technique made use of a saturometer (Weyl, 1961) with which they measured the solubility of brucite
in natural seawater containing carbonates. Their calculations also
require a knowledge of the thermodynamic solubility product of brucite. Thompson (1966, personal communication) showed that 88 per-.
cent of the total magnesium in seawater exist as the free ion. Thomp-.
son used a cation sensitive electrode which was calibrated in solutions
of known concentrations. Fisher (1967), based on the attenuation of
sound, calculated that 9. 2 percent of the total magnesium in seawater
exist as MgSO40.
Pytkowicz and Gates (1968), using further solubil-.
ity measurements described in this thesis, revised the earlier data
of Pytkowicz, Duedall and Connors and found that 90 percent of the
total magnesium in seawater are present as the free ion. Recently,
Kester and Pytkowicz (personal communication) found that 89. 0 per-.
cent of the total magnesium in seawater exist as the free ion while
I 0. 3 percent exist as MgSO40. Their method made use of cation elec-
trodes, sensitive to sodium, magnesium and calcium, in order to de-.
termine the stoichiometric association constants for the major sulfate
species (CaSO40, MgSO40, NaSO4). These constants were then used,
together with Garrels and Thompso&s (1962) estimates of the carbon-
ate and bi-carbonate speciations, in order to calculate the percent
ages of free and of associated sulfate species in seawater.
Fisher (1962) also studied the pressure dependence of the
MgSO4° concentration. This work was done in magnesium sulfate so-
lutions rather than in seawater. He made use of the four state model
of Eigen and Tamm (1962) to explain conductivity data in these single
salt solutions, and observed that the dissociation constant of MgSO4°
increased with pressure while the degree of association decreased
with pressure.
A quantitative knowledge of MgSO4° ion pair formation in sea-
water will help us to better understand the absorption of acoustical
energy in seawater. Theories for this effect state that, as sound
energy is transmitted through a fluid medium, it is ultimately converted to heat. The proposed mechanisms of sound absorption have
been broken up into two categories by Lindsey (1960):
1.
Viscous and heat conduction relaxations in which shearing
effects between portions of the medium, during the corn-
press ion and rarefaction cycles of the sound wave, form
local thermal gradients which dissipate energy by heat con
ducti on.
2.
Thermal, structural and chemical relaxations in which energy is removed from the acoustical pressure wave and
4
used internally for a time sufficiently long to result in a
permanent loss of energy from the wave.
Liberman (1948) was the first to observe the absorption anomaly
between fresh water and seawater, which occurs at frequencies below
1000 kc/sec. This anomaly was later attributed to the presence of
MgSO4° species in seawater by Leonard, Combs and Skidmore (1949).
The methods and results of this work will also contribute to our
understanding of the structural, transport and colligative properties
of concentrated, mixed electrolyte solutions. Support is given to an
ion association model, in which charged ions are capable of forming
a new species of sufficient stability to last several molecular collisions. In the interpretation of the results it appears possible to sepa_
rate the nonspecific effects of ionic strength from the specific effects
of ion association.
The primary purpose of this work was to determine the behavior
of MgSO4° ion pairs as a function of temperature and pressure and to
check the earlier data reported by Pytkowicz, Duedall and Connors
(1966).
In addition, the present method permitted the determination
of the stoichiometric association constant for MgSO4° and a calculation of the thermodynamic solubility product of brucite as a function
of temperature.
5
IL THEORETICAL
Definition of Thermodynamic Equilibrium Constants
and Activities
The thermodynamic equilibrium constant,
K,
for the reac-
tion
Axy
B
is defined by:
xA+yB
(1)
x
y
(aA) (aB)
(2)
(aAB)
xy
where
a
is the activity of the species defined by the subscript. This
constant is only a function of temperature and pressure and is independent of the interactions occurring in the solution.
When AxBy is a solid, the thermodynamic solubility product
is defined by:
K
=
(aA)c(aB)Y
In the solubility product the solid phase activity,
(3)
xy
aA B
which is
a function of the mineral composition and particle size, is incorpo_
rated into the equilibrium constant. The solid phase activity is usually taken as unity in solutions with an ionic strength of less than 0. 2
(KortUm, 1965).
For a given solution, the following equation, discussed by
Pytkowicz, Duedall and Connors (1966), is valid:
a=VF(F)YT(T)
where
a
is the activity,
theses represent molalities,
y
(4)
is the activity coefficient, the paren_
F
indicates free quantities and
T
indicates total (free plus associated) quantities.
Determination of the Free Magnesium
at One Atmosphere
The determination of the extent of ion pair formation is based
on the equilibrium pH of brucite, Mg(OH)2, in two solutions, A and
B.
Solution A contains only chlorides while solution B simulates sea-
water. The difference in the solubilities of brucite in the two solu-
tions is related to MgSO4° formation in solution B.
The following cell was used for the studies at atmospheric pres_
sure:
Ag_AgC1/HC1 reference / /GLASS/ / Brucite:Soln A
or B:Satr'd KC1/KC1/Hg_HgCl
The thermodynamic solubility product for brucite in the two
solutions is given by Equation (6):
(5)
7
(K
)
Mg(OH)2
Mg)OH) 2
(aMg)(aOH)
2
(6)
in which one assumes identical solid phase activities in each solution.
This assumption will be discussed later. From Equations (4) and (6)
one obtains:
(aMg)
(aMg)
(aOH)
Mg)(MBF
2
(7)
Mg)(M)AF
aOH)
The compositions of solutions A and B are shown in Table 1 and
are compared qualitatively below.
Table 1. Composition of the experimental solutions.
Total molal concentration
Solution B
Ion
Solution A
Na+
0.473
Mg
Ca++
K+
.
.
0548
0106
.0102
Sr++
Cl
0.482
.
.
.
.
.
614
SO4
Br
F
.
.
.
.
Omitted in pressure runs.
0548
0106
0102
00009
564
0291
00086*
00005
roi
= (Mg)
(Ca)AT = (Ca)BT
(8)
(K)AT = (K)BT
(Na)AT
(Cl)AT
1=
(Na)BT
(Cl)BT
These two solutions were constructed so that:
effA
eff
effB
(9)
is the effective ionic strength, that is, the ionic strength taking
ion association into consideration. The effective ionic strength of
solution B was calculated from Garrels and Thompsons
(1962)
chemi-
cal model of seawater, and that of solution A was calculated by assuming complete dissociation of the chlorides (Davies,
1962).
The
effective ionic strengths of solutions A and B were equalized by the
addition of sodium chloride to solution A.
The relationships that evolve from the above restrictions,
Equations (8) and
(9),
are shown below:
(10)
(Mg)
= (Mg)
= (Mg)
(11)
Substitution of Equations (10) and (11) into Equation (7) yields:
(aOH)
(Mg)
(Mg)
(aOH)
2
(12)
2
One arrives at the following expression for the percentage of free
magnesium in seawater by introducing
K
into Equation
= aHaOH
(12):
2
Percent free magnesium
(M g )
BT
x 100
(aH)B
2
X 100
(13)
(aH)A
Therefore, in order to calculate the amount of free magnesium in
seawater, one just needs to know the equilibrium pH of brucite in the
two solutions.
pH measurements in seawater do not yield the thermodynamic
hydrogen ion activity. However, Pytkowicz, Kester and Burgener
(1966) showed that it is the reproducibility rather than the accuracy
of pH measurements which matters in oceanographic practice.
Determination of the Free Magnesium
at High Pressure
The determination of the percentage of free magnesium in seawater at high pressure was attempted with the following cell:
inner compartment
outer compartment
AgAgC1/Soln A:Brucite//GLASS// Brucite:Soln B/Ag-AgC1
(14)
10
The observed EMF of the cell at any pressure is given by:
log (aHaCi) + E a s ym
log (aHaCi) - S
E=S
where
and
i
(15)
0
1
refer to the inside and outside of the hydrogen ion
o
sensitive membranes. S is the electrode slope which is independent
of pressure (Disteche and Disteche, 1967; Culberson, 1968). The
value of
S
was assumed to be the theoretical value, as given by
Bates (1964).
By subtracting the potential at pressure from that at one atmos-
phere, one arrives at:
E-E
p
log
=S
(aHaCl) (aHaCl)
1
(aHaCl) (aHaCl)
0
The subscript
p
E
as ym
*
E
+
(16)
a sym
i
and the superscript
measurements, and
0
*
refer to high pressure
is given by:
- E asym
asym = E asym
(17)
pH = - log [aHI
(18)
Introducing;
into Equation (16) yields:
E-E
S
(y1mi) (yim1
*
(pH-pH.) +
*
pH
+ log
)
o
(Y1m1) (y1m1)
0
LEasym
S
(19)
11
In order to simplify this expression the following assumptions
were made:
1.
The molal concentration of chloride ion does not change
with pressure.
(m1)
0
*
(mci)
(mCl)
(20)
(mrn)
i
2.
The ratio of the activity coefficients inside the glass shell
should be approximately equal to the ratio outside the glass
shell.
''Cl
(21)
The validity of this assumption will be discussed later.
Then, the logarithmic term in Equation (19) becomes zero, and one
obtains:
pH.
pH
E-E -E asym
PS
- (pH-pH.)
(22)
at
asym , (E-Ep) and (pHo -pH.)
one atmosphere, it is possible to calculate pH. - pH and to arrive
From a knowledge of
E
1
at an expression, similar to Equation (13), for the percentage of free
magnesium in seawater at high pressure:
12
Percent of free magnesium =
at pressure
(aH)
*2
x 100 = 10
- 2(pH-pH)
1
(aH)
(23)
One must bring into consideration the affect of pressure on an
individual ionic activity c oefficient.
8 in y.
V1-V.
T, m
(24)
RT
to discuss the validity of Equation (21). V.
is the partial molar vol-
ume of the ion in the test solution, and
is the partial molar
volume of the ion in its standard state. Equation (21) is valid if
in solution A is nearly the same as in solution B. Owen and Brinkley
was only a function of ionic strength. Gui-
(1941) assumed that
berson (1968) showed that
'NaCl
values in seawater and in single
salt solutions were nearly identical, provided that the ionic strengths
of the solutions were the same. In view of these observations and the
fact that the ionic strengths of solutions A and B were made equal, it
seems reasonable to assume that Equation (21) is valid.
Determination of the Stoichiometric
Association Constant of MgSO4
Three association constants can be defined for the reaction:
Mg
+ SO
MgSO4°
(25)
13
1.
Thermodynamic Constant
(aMgsoo)
K=
2.
Stoichiometric Constant
K
3.
(26)
(aMg)(aso)
(MgSO40)
(Mg)(SO4)
Mg)SO4)
=K
MgSO4°
(27)
Apparent Constant
(MgSO40)
K
(Mg)(SO4)
=K
'MgSO4°
(28)
The need to estimate single ion activity coefficients can be
avoided by the use of concentration constants, which are preferred
over activity constants by Rossotti and Rossotti (1961). Kester and
Pyticowicz (1969) showed that concentration constants are independent
of composition and are indeed constant at a given effective ionic
strength.
The stoichiometric association constant of MgSO4° was calculated from the following cubic equation, which is derived in Appendix
I:
A(Kg50O)3 + B(Kgsoo)2 + C(Kgsoo + D = 0
The constants are given by:
(29)
14
A = { (MgSO4°)T(SO4)J(Mg)3
B = (MgSO4°)(Mg){1+K
(30)
5Q[ (MgSO40)+T(Ca)- T(SO4)J
+ KNSO [(MgSO40)+T(Na)-T(SO4)] }
(31)
+ K50
(32)
C
D
NaSO4 (MgSO40)+T(Ca)+T(Na)-T(SO4)I }
=KQ.KQ(MgSO4°)3
(33)
15
IlL EXPERIMENTAL
Free Magnesium at One Atmosphere Pressure
The cell described by Equation (5), and shown in Figure 1, was
prepared by the following procedure:
1.
The brucite crystals were washed in the experimental solution under consideration and immersed into a thermostated
beaker containing the experimental solution.
Z.
A stopper holding the electrode pair was inserted in the
thermostated beaker so that the glass membrane lay just
above the crystal layer.
3.
The beaker was tilted back to move the crystals onto the
side of the cell, and the glass electrode was pushed down
so that the crystals would cover the glass membrane when
the cell was uprighted. A small vent in the stopper, which
was sealed during the measurements, allowed for a volume
displacement of water.
Care was taken to avoid exchange of CO2 during these steps. The
reasons for this precaution are discussed later.
The possibility of a contact potential between the glass mem-
brane and the crystal surface was examined. pH measurements were
taken until equilibrium was reached with the glass membrane in the
crystals and also with the membrane in the bulk solution.
In both
16
[ass
Rubber
stopper
Styrofoam
plug
Vent
'test
S
olutioi
Brucite
Beaker
Glass
membrane
Water from
constant
Tiperature bath
Figure 1. Apparatus used for experiments at one atmosphere.
17
cases the equilibrium pHs were identical, regardless of the place_
ment of the glass membrane. The contact technique was used in most
measurements because of a more rapid equilibration in the interstitial
waters.
The pH of the above cell, described by Equation (5), was calcu
lated from the equation (Bates, 1964):
PHeq
where
S1
and
pH5 f (EeqEs)
S2
pH5
pH5
E2-E1
1
(34)
refer to the buffer solutions. The electrodes
were checked before and after each run with two or three Beckman
buffers. The pHs of the buffers at 25°C were 7.413, 4. 00 and 7. 00.
Free Magnesium at High Pressure
The preparation of the Ag_AgCl electrodes and the cell design
for the high pressure measurements were based on the work
of
Culberson and Pytkowicz (1968). The asymmetry of the pressure
cell, described by Equation (14) and illustrated in Figure 2, is caused
by differences between the outer and inner surfaces of the glass mem..
brane and by differences in the Ag..AgCl electrodes. This potential
was used as a criterion to distinguish between good and faulty electrodes. The electrodes were considered good if the absolute value of
the symmetry at one atmosphere was less than one millivolt, and the
Rubber
stopper
Silicon
stopcoc
grease
tors
Dber stopper
it
Test tul
Solution I
Beckman G. P.
gass electrode
shell
con rubber
nale contact
con stopcock
grease
.AgC1
ution A
Glass
membrane
icite
Figure 2. Apparatus used for experiments at high pressure.
19
change in the asymmetry per 500 atmospheres was less than 0, 8 millivolts.
The asymmetry potential was measured with the following cell:
Ag-AgCl/O. 7lm NaC1 + 0. Olrn HC1//GLASS//0. 71m NaCl
+ 0. Olm HC1/Ag-AgCl
(35)
Once this cell was assembled, it was placed in a pressure bomb contaming high resistance and low viscosity transformer oiL The pressure bomb was then placed in an AMINCO Temperature Bath (±0.05° C)
and connected to the pressure system. This system consisted of an
Enerpac Hydraulic Pump and a Crosby Pressure Gauge, and is shown
in Figure 3.
For the actual experimental measurements with brucite, the
pressure cell was prepared according to the following scheme:
1.
Brucite crystals were washed in solution B and then dropped
into the glass electrode shell (containing solution B) in or-
der to just cover the membrane portion of the electrode.
2.
The internal Ag_AgC1 electrode was then inserted with care
so that no air bubbles remained. Silicon stopcock grease
was used around all the stopperglass interfaces to ensure
good seals and to act as a lubricant during compression
cycles.
3.
The remaining brucite crystals were washed in solution A
20
Crosby pressure gauge
0-20, 000 psi
1. Mecca
ele ctrical
terminals
AMINCO non-rotati
stem valve
Enerpac hydraulic pump
P- 228
Stainless steel
pressure bomb
Plexiglass
plates
Aluminum
rod
AMINCO constant
temperature bath
Figure 3. High pressure system.
21
and dropped into the outer compartment containing solution
4.
A rubber stopper holding the glass and external electrodes
was inserted, so that the glass membrane was positioned
just above the crystal level.
5.
The cell was then tilted, and the stopper pushed in so that
the crystals would cover the outer membrane surface when
the cell was uprighted. A small vent, which was sealed
during the experiment, allowed for displacement of excess
solution. Silicon grease was applied as mentioned above,
and the completed cell was then placed in the pressure
bomb.
Electronics
The leads from the electrodes were connected directly to an
Orion Digital pH Meter, Model 801, with a precision of ±0. 1 my or
±0. 002 pH units. For the runs at one atmosphere the millivolt read-
ings were taken directly off the Orion meter; however, for the high
pressure experiments a recording system was placed in the circuit.
This consisted of a Heathkit Recorder, modified to yield one millivolt
full scale, and a Leeds and Northrup volt potentiometer, which was
used as a source of bucking potential.
2z
Leads from
electrodes
Orion digital pH
meter model
Leeds & Northr
volt
potentiometer
Figure 4. Electronics.
Heathkit
servorecorder
23
Preparation of the Brucite
The brucite was obtained from Ward's Natural Science Establishment. The crystals were ground to size with a porcelain mortar
and pestle (the hardness of porcelain is given as 6 1/2 and that of
brucite as 2 1/2, Hurlbut, 1961). Large quantities of brucite were
ground and then sieved between 40 and 60 mesh copper screens (the
pore sizes were 0. 42 mm and 0. 25 mm respectively). The crystals
were then quickly washed in distilled water in order to remove any
adhering powder and dried at room temperature. It was assumed that
this procedure would minimize any differences in the solid phase ac-
tivity of the crystals used in separate experiments.
The formation of a cloudy white precipitate was noticed during
the preliminary runs with natural seawater and Nevada Massive Bluff
Brucite. Replacement of the natural seawater by carbonate-free arti-
ficial seawater did not eliminate the formation of the precipitate; how-
ever, it greatly reduced its amount. X-ray diffraction analysis was
performed on the precipitate, after it had been decanted off and concentrated by centrifuging. The analysis showed that the precipitate
was predominately aragonite. In addition, x_ray analyses were con-
ducted on the various types of brucite that were available. Nevada
Massive Bluff Brucite was found to contain a substantial amount of
dolomite, MgCa (CO3)2. Quebec Platy Brucite showed no evidence
for either dolomite or magnesium calcite impurities. For these
24
reasons Quebec Platy Brucite and carbonate-free artificial seawater
were used in the actual runs. Precautions were taken in handling the
crystals to avoid formation of any carbonate impurities on their surface. Once the crystals had been moistened, the high equilibrium pH
of brucite in water would enable CO2 to dissolve, and the resulting
carbonic acid could easily react with the brucite to form a magnesium
carbonate species on the surface of the crystal. The quick washings
just prior to use removed any such species.
Solution Preparation
A chloride solution, A, and an artificial seawater solution, B,
were used as the two experimental solutions. Both were made from
Baker Analyzed Reagents, and their compositions are shown in Table
1.
Solution B, the artificial seawater, was prepared by the method
of Kester etal. (1967), with the following exceptions:
1.
NaHCO was replaced by a molar equivalent of NaCl.
2.
Boric acid was omitted.
3.
KBr was replaced by KC1 in the pressure runs due to the
affect of Br on Ag_AgC1 electrodes.
This solution was made equivalent to a seawater of 34. 8 parts per
mule salinity. Its effective ionic strength was calculated to be 0.680,
by the use of the Garrels and Thompson's (1962) model.
25
IV.
RESULTS
Data at One Atmosphere
The results for the percentage of free magneisum in seawater
at one atmosphere are presented as a function of temperature in Table
2.
Values were obtained at 5°C, 15°C and 25°C in an artificial sea-
water solution corresponding to seawater of 34. 8 parts per mule
salinity.
The molal concentrations of free magnesium, total sulfate and
magnesium sulfate ion pairs as a function of temperature are given
in Table 3.
The concentration of MgSO4° was calculated from the
equation:
(Mg++)
(MgSO40)
(Mg)
(36)
The stoichiometric association constant for MgSO4° was calcu-
lated from Equation (29), using a method of successive approximations on a Monroe Programmable Calculator, Epic 3000. The values
of KCSO0 and KNSO
*
4
were taken to be 10. 8 and 2. 02 respec-
tively (Kester, personal communication).
The resultant Kg50o
was found to be 9. 5 ± 1 at 25°C and one atmosphere pressure.
The calculation of the thermodynamic solubility product of bru-
cite as a function of temperature, Table 4, was made by the expres_
sion:
Table 2. Results at one atmosphere.
Experiment Electronics
I
II
III
IV
V
VI
VII
Heathkit
Keithley
Orion
Orion
Orion
Orion
Orion
Temperature
(
C)
23
±1
25. 00±0. 05
25.00±0.05
25. 00±0.05
15. 00±0. 05
15. 00±0. 05
pH
eq (ASW)
9. 41 ±0. 01
9. 337± . 002
9.316± .002
9.330±
9. 631±
9. 633±
pH eq (Cl
9. 37 ±0. 01
9. 314± . 002
.002
9.289± .002.
9.309± .002
. 002
. 002
.
002
9. 606±
9. 610*
002
9.993± .002 9.965± .002
Average percent
Temperature free magnesium
5.00±0.05
25. 00±0. 05
15. 00±0. 05
5. 00±0. 05
.
pH
)
eq
0. 04
0. 023±. 004
0.027±. 004
004
025±. 004
0. 023±. 004
0.021±.
0.
0.028±. 004
Percent free
magnesium
83±8
90±8
88±2
91±2
89±2
90±2
88±2
90±2
90*2
88±2
Table 3. Molal concentrations.
Temperature
(°C)
25. 00*0. 05
15. 00±0.
05
5. 00±0. 05
Total
Total
0. 0548
0. 0548
0. 0548
0. 0291
0. 0291
0. 0291
Mg
SO4"
Free
Mg++
0. 049±0. 001
0. 049±0. 001
0. 048±0. 001
MgSO4
o
0. 005±0, 001
0. 005±0. 001
0. 006±0. 001
N.)
C.'
27
[KspIIMg(OH)
=
Mg)(MFoH] 2
(37)
The activity coefficient for the free magnesium was obtained by the
mean salt method (Garrels and Thompson, 1962) using the data of
Latimer (1938), Landolt (1936) and Harned and Cook (1937). Figure 5
shows that the solubility product of brucite varies linearly with ternperature,
The enthalpy of this solubility reaction was calculated from:
dlnK
dT
A plot of
slope
ln K
-AH/R.
against
l/T,
RT2
(38)
Figure 6, yields a straight line of
The resulting enthalpy is 2. 33 Kcals/rnole.
High Pressure Data
The results at pressure are shown in Table 5. These results
suggest an increase in the degree of association of MgSO4° with pressure at 25°C.
11. 30
11. 20
11. 10
5
10
15
20
Temperature (°C)
Figure 5. Linear relation of
and temperature.
25
l/T x
fl
4fl
0.350
0.360
.Z5. 60
-25. 7C
in K
sp
- 25. 8(
_2_ 9i
Figure 6. Curve for calculation of enthalpy.
Table 4. Solubility product of brucite as a function of temperature.
Temperature
25. 00 ± 0. 05
15. 00 ± 0. 05
5. 00
±
0. 05
Activity
coefficient
Free Mg
Average
of Mg ++
Solution
(molal
conc.
0.36
0.36
Chloride
0. 0548
9. 304
14. 005
tificial
seawater
1. 99 x l0
7. 8 x 10
0. 049
9.328
14. 005
2, 104 x 10
7.9 x
0.38
0.38
Chloride
0.0548
0.049
9.608
9.632
14. 355
1.799 x l0
14. 355
1. 901 x
1O
6.7 x i0
6.7 x 1O'
0.39
0.39
Chloride
0. 0548
Artificial
seawater
14. 739
1. 683 x
1O
0. 048
9.965
9.993
14.739
1.795 x
1O
Artificial
seawater
pH
pK
eq
w
a
K
OH-
sp
10
6. Ox iO
6. Ox 10
Table 5. High pressure results at 25° C.
Experiment
I
II
III
Pressure
(atm)
500
1000
1000
1000
Percent free
Mg
64
53
51
56
0
31
V.
DISCUSSION
Comparison of Results with Previous Estimates
There is good agreement between the results of this work and
those of Garrels and Thomspon (1962), Thompson (1966), Fisher
(1967) and Kester and Pytkowicz (1968) for the percentage of free
magnesium at 25° C and one atmosphere pressure. No explanation
was found for the discrepancy between the present results and those
of Pytkowicz, Duedall and Connors (1966).
Temperature was found to have a negligible effect on the extent
of MgSO4° formation, within the limits of experimental error. These
results cannot be interpreted without a detailed knowledge of the hy-
drated structures of the ion pair and of the magnesium and sulfate
ions.
The stoichiometric association constant for MgSO40, 9. 5 ± 1,
agrees well with that found by Kester and Pytkowicz (1968), 10. 2±0.5.
The solubility product of brucite at 25°C, 10
agreement with the value obtained by Hostetler (1963),
11,
is in good
15
Discussion of Errors
Garrels and Thompson (1962) estimated that only 1 percent of
the total magnesium in seawater is bound in carbonate and bicarbon-
ate ion pairs. Therefore, the absence of carbonates in this work
32
should not greatly affect the extent of MgSO4° formation.
The possible affect of MgOH+ ion pair formation was investigated with the use of the dissociation constant of MgOH+ (Davies in
Hamer, 1959). It was calculated that only 0. 4 percent of the total
magnesium would be tied up as MgOH+. This effect can be neglected.
Pressure Experiments
The pressure results are anomalous in terms of the generally
accepted enhanced ionization of weak electrolytes with pressure (Lown
etal.
,
1968).
They also differ greatly from those of Fisher (1962)
which show a decrease in the degree of association in solutions of
MgSO4° with increasing pressure.
An assumption that is incorporated into the calculation of the
percentage of free magnesium at high pressure is that the free activity coefficient of magnesium is equal in the two solutions.
This im-
plies that the activity coefficient at high pressure is only a function of
the effective ionic strength. While Kester and Pytkowicz (1969) have
shown a similar assumption to be true at one atmosphere, it is not
necessarily applicable at high pressure.
An additional implication of this assumption is that the effect
of enhanced association or dissociation of ion pairs at high pressure
on the effective ionic strength is negligible. The apparent increase
in MgSO4° association would cause an eight percent decrease in
33
the effective ionic strength. Additionaldata regarding the effect of
pressure on the other ion pairs present in seawater is required before
the change in effective ionic strength can be rigorously calculated.
An additional determination of the percentage of free magnesium
at pressure was made with the following cell, to observe the effect of
pressure on the solubility of:brucite:
Ag-AgCl/ 07 im NaC1 0. Olm HC1//GLASS// Brucite:Expt. Soin. /AgAgCl
(39)
The physical arrangement of this cell was similar to that of the earlier one. The equilibrium pH of brucite at pressure was given by:
pH
where subscript
1
= pH1 +
[E1-E -1E asym ]
(40)
p
refers to equilibrium at one atmosphere.
The results are shown in Table 6. They show that the solubility
of brucite decreases slightly with pressure in the chloride solution,
and that it increases slightly with pressure in the artificial seawater.
The data further supports the increased association of MgSO4° with
pressure.
Table 6. Supplementary pressure results.
Equilib. pH
Solution @l000atm
Chloride
A.S.W.
Equilib. pH pH=pH -pH1
@ 1 atm
9. Z67
9. 304
-0. 037
9.340
9.3Z8
0.012
Percent
free Mg++
70
34
BIBLIOGRAPHY
Bates, Roger G, 1964. Determination of pH: Theory and practice.
New york, Wiley. 435 p.
Culberson, C., D.R. KesterandR.M. Pytkowicz. 1967. Highpressure dissociation of carbonic and boric acids in seawater. Science 157:59-61.
Culberson, C. 1968. Pressure dependence of the apparent dissociation constants of carbonic and boric acids in seawater. Master's
thesis. Corvallis, Oregon State University. 85 numb. leaves.
Culberson, C. and R. M. Pytkowicz. 1968. Effect of pressure on
carbonic acid, boric acid, and the pH in seawater. Limnology
and Oceanography 13:403-41 7.
Davies, C. W. 1959. Incomplete dissociation in aqueous salt solutions. In: The structure of electrolytic solutions, ed. by W. J.
Hamer. New York, Wiley.
p. 19-34.
Davies, C. W. 1962. Ion association. Washington, D.C., Butterworth. 190 p.
Disteche, A. and S. Disteche. 1967. The effect of pressure on the
dissociation of carbonic acid from measurements with buffered
glass electrode cells. Journal of the Electrochemical Society
114:330-340.
Eigen, M. and K. Tamm. 1962. Schallabsorption in Electrolytlosungen als folge chemischen Relaxation. Zeitschrift far
Elektrochemie 66:93-106, 107-121.
Fisher, F. H.
1962. The effect of pressure on the equilibrium of
magnesium sulfate. Journal of Physical Chemistry 66:1607.
Fisher, F. H. 1967. Ion pairing of magnesium sulfate in seawater:
Determined by ultrasonic absorption. Science 157:823.
Garrels, R.M. and M. E. Thompson. 1962. A chemical model for
seawater at 25°C and one atmosphere total pressure. American
Journal of Science 260:57- 66.
35
Hamann, S. D. 1963. The ionization of water at high pressures.
Journal of Physical Chemistry 67:2233-2235.
Harned, H.S. andM.A. Cook. 1937. The thermodynamics of aqueous potassium chloride solutions from electromotive force measurements. Journal of American Chemical Society 59:1290-1292.
Harvey, H. W. 1963. The chemistry and fertility of seawaters.
Cambridge, Cambridge University. 240 p.
Hostetler, Paul B. 1963. The stability and surface energy of brucite
in water at 25°C. American Journal of Science 261:238-258.
Hurlbut, Cornelius 5. 1961. Dana's manual of mineralogy.
New York, Wiley. 350 p.
Kester, D. R. etal.
1967.
17th ed.
Preparation of artificial seawater.
nology and Oceanography 12:176-179.
Lim-
Kester, D. R. and R. M. Pytkowicz. 1968. Magnesium sulfate as sociation at 25°C in aqueous NaCl-MgCl2-Na2SO4 at 0. 670 ionic
strength. Limnology and Oceanography 13:670- 674.
Kester, D. R. and R. M. Pytkowicz. 1969. Harnedts rule behavior
of NaCl-Na2SO4 solutions explained by an ion association model.
American Journal of Science 267:217- 229.
Korti1m, Gustay.
1965.
Elsevier. 637 p.
Treatise on electrochemistry. Amsterdam,
Landolt, Hans H. 1936. Landolt- Bornstein Physikalis ch-Chemis che
Tabellen. Vol. III. Berlin, Springer. 2150 p.
Latimer, W. M.
Hall.
324 p.
1938.
Oxidation potentials. New York, Prentice
Leonard, R.W., P.C. Combs andL.R. Skidmore.
1949. The attenuation of sound in synthetic seawater. Journal of the Acoustical
Society of America 21:63.
Liberman, L. N. 1948. The origin of sound absorption in water and
in seawater. Journal of the Acoustical Society of America
20:868-873.
Lindsey, R. B. 1960. Mechanical radiation. New York, McGraw
Hill.
415 p.
36
Lown, D. A., H. R. Thirsk and Lord Wynne-Jones. 1968. Effect of
pressure on ionization equilibrium in water at 25°C. Transactions of the Faraday Society 64:2073-2080.
Millero, Frank J. 1969. The partial molar volumes of ions in sea-.
water. Limnology and Oceanography. (In press)
Owen, Benton B. and Stuart R. Brinkley, Jr. 1941. Calculations of
the effect of pressure upon the ionic equilibria in pure water and
in salt solutions. Chemical Reviews 29:461-474.
Platford, R. F. 1965. Activity coefficient of the magnesium ion in
seawater. Journal of the Fisheries Research Board of Canada
22:113-116.
Pytkowicz, R.M., I.W. DuedallandD.N. Connors.
1966.
sium ions: Activity in seawater. Science 152:640-642.
Magne-
Pytkowicz, R. M., D. R. Kester and B.C. Burgener. 1966. Reproducibility of pH measurements in seawater. Limnology and
Oceanography 11:41 7-419.
Pytkowicz, R. M. and R. F. Gates. 1968. Magnesium sulfate interactions in seawater from solubility measurements. Science
161:690-691.
Rossotti, Francis J. C. and Hazel Rossotti. 1961. The determination of stability constants. New York, McGraw Hill. 425 p.
Thompson, Mary E.
867.
1966.
Magnesium in seawater. Science 153:
Weyl, P. K. 1961. The carbonate saturometer.
69:32-44.
Journal of Geology
APPENDIX
37
APPENDIX I
Derivation of Equation (29)
This approach is similar to that of Kester and Pytkowicz (1968)
except that it accounts for the presence of calcium in solution B.
The following definitions are found applicable to this work:
T(Mg) = Mg++) + MgSO4°
(41)
T(Na) = (Na+) + NaSO4
(42)
T(Ca)
(Ca++) + CaSO4°
T(SO4) = (SO4) + CaSO4° + MgSO4° + NaSO4
(NaSO4)
(Na+)(SO4)
Kcsoo
*
Kgsoo
(CaSO40)
(Ca)(SO4)
(MgSO40)
(Mg++)(so4=)
(43)
(44)
(45)
(46)
(47)
The bracketed quantities represent the free concentration of that spe
cies, and a
T
preceding the bracket indicated the total concentra.
tion of that species in solution.
By substituting Equation (45) into Equation (42), one obtains:
(Na+) = T(Na) -
K;SO(Na+)(SO)
(48)
which simplifies to:
(Na+)
T(Na)
(49)
l+KNsQ(SO4 _)
Further substitution of Equation (45) into Equation (49) yields:
Kso T(Na)(SO4)
(NaSO4)
l+K180(SO4' )
(50)
A similar argument, using Equations (43) and (46), can be used
for calcium in order to obtain:
K80T(Ca)(SO
(CaSO40)
=
l+K30(SO _)
_)
(51)
Rearranging Equation (47), so that,
(SO4
(MgSO40)
)=
(Mg)Ko
(52)
and substituting Equations (50, 51 and 52) into Equation (44), one obtains:
39
T(SO4) =
(MgSO40)
(M g±+)Ko
K'CaSO4 T(Ca)
1-
(MgSO°)
(MgSO40)
(Mg)K0o
.
II
l+KaSO
(MgSO40)
(Mg++)K0
4
f...
(53)
°
By performing the appropriate algebraic manipulations, Equation (53)
can be reduced to a cubic equation in terms
of Kgg0o
Equation
(29):
A(Kgsoo)3 + B(Kgsoo)2 +
C(Kgso
o) + D
0