Clay Minerals (1968) 7, 261.
STABILITY
OF
ACIDIC
HECTORITE
IN
WEAKLY
SOLUTIONS
II. STUDIES OF Tim CHEMICAL EQUILIBRIUM AND THE
CALCULATION
OF FREE ENERGY
K E V I N G. T I L L E R
Division o~ Soils, C.S.LR.O., Adelaide, South Australia
(Received 14 August 1967)
ABSTRACT:
The chemical equilibrium of a purified sample of hectorite was
studied over a range of pH, silicic acid, and magnesium chloride concentrations.
T h e quasi-equilibrium reached by a b o u t 6 weeks was reversible with respect to
added magnesium ions but only partially so for added silicic acid. The free energy
of formation of hectorite at 25* C was calculated at --2680 k c a l / u n i t call, using
the derived equilibrium constant and the stoichiometry of the reaction as previously established.
INTRODUCTION
In recent years there has been an increasing interest in mineral equilibria from the
point of view of solution chemistry, a trend which has been stimulated by the work
of Garrels (1960). Such studies should provide a better basis for the understanding
of the reactions involving minerals in nature.
In the first paper of this series (Tiller, 1968), the reaction of hectorite suspensions
with dilute acid was examined and the stoichiometry and mechanism of the chemical
dissolution of hectorite discussed. Although the addition of excess amounts of the
products, magnesium and lithium ions and silicic acid, did not affect the extent
of the reaction appreciably, there were some indications that the final concentrations
of the constituents in solution were affected.
In this paper the chemical equilibrium of hectorite suspensions is studied in
more detail, to investigate the degree of reversibility of the dissolution reactions
and to determine whether constants could be found which would adequately describe
the reaction.
EXPERIMENTAL
The procedures and methods used in the work were given in detail in the first paper
of this series. The clay used in these experiments was separated as the < 2 ~ fraction
B
262
Kevin G. Tiller
from A.P.I. No. 34 as supplied by Ward's Natural Science Establishment, Rochester,
N.Y. and then treated with hot NH4C1 solution to remove CaCOs. X-ray diffraction
patterns of the purified sample corresponded to that of pure trioctahedral montmorillonite.
Silicon was measured spectrophotometrically using the reduced form of a
silieo-molybdate complex. Magnesium was measured by atomic absorption. The
pH of the clear supernatant solution after supercentrifugation was determined with
a Radiometer pH meter.
The general procedure was to pipette the clay, usually 50 rag, from a bulk suspension and to wash the sample twice with the appropriate electrolyte solution
before adding variable amounts of dilute acid to achieve a desired range of final
pH values. Reactions were carried out at 20 + 1o C in polypropylene tubes which
were shaken continuously unless stated otherwise, all experiments were carried out
in the presence of calcium chloride and/or magnesium chloride with an initial ionic
strength of 0"15 moles/1. All solutions were prepared from A.R. grade reagents
and extracted with dithizone to' remove traces of heavy metals.
In the previous paper (Tiller, 1968) it was established that the reaction between
acid and hectorite, as far as the quantities of the constituents released were coneerned was virtually completed in 14 days. Preliminary experiments had shown
that the final concentrations of silicic acid, magnesium and hydrogen ions continued
to change for at least 10 weeks following the addition of variable amounts of
acid. After 4 weeks, however, the rate of change of these concentrations decreased
and the relationship between them became relatively constant. All results presented
in this work are from experiments equilibrated for 6 weeks unless stated otherwise.
CHEMICAL
EQUATIONS
In the previous paper, the stoichiometry of the reaction of acid with hectorite,
averaged over several batches, was reported. The analogous relationship for the
sample used in these experiments was,
Heetorite + 2H + = 0-95 Mg + + + 0-1 Li + + 1-00 Si (solution) + 0-35 Si (solid). (1)
The above equation only defines the proportions of the two forms of silicon produeed when the silicon in solution, as monosilicic acid, is undersaturated with respect
to amorphous silica. As before it is assumed that the molar ratio Mg/Li released
into the solution equals 10 and that Li + is released by the same mechanism as
Mg ++. The values for silicon and magnesium have been rounded fo the nearest
0"05. If the reaction reaches equilibrium, the following equation provides a basis
for determining the equilibrium constant.
Kc "-----[Mg++]~ [Li+]~ [Si]
(H+),
On conversion to negative logarithms, the following relations are obtained:
pKc = pSi + 0"95 pMg +0"1 pLi-- 2 pH,
pSi+ 0"95 pMg+0.1 pLi = 2 pH +pKc.
(2)
(3)
(4)
Equilibrium of hectorite dissolution
263
Under conditions of constant [Mg], and neglecting [Li], equation (4) simplifies to
the following,
psi = 2 pH + constant.
(5)
For reactions without the addition of any products magnesium and silicon are
released into solution in virtually equal molar amounts, and if we neglect lithium,
then from equation (2) we obtain,
Kc "" [Mg++]2
_
(H+) ~
[Si]2
=
(H+) z
(6)
and hence,
pMg ~" pSi N pH + 89pKc.
(7)
The results of this paper will be discussed in relation to some of the relations
derived above.
RESULTS AND INTERPRETATION
No reaction products added
The first experiments considered are those in which no magnesium chloride or
silicic acid was added. The relationship between the negative logarithm.~ of the
final molarities of magnesium or silicie acid in solution, referred to as pMg and
pSi, respectively, and the final pH was found to be virtually linear with a slope
of unity. Fig. 1 shows such results for magnesium together with the equation describing the linear relationship between pMg and pH after neglecting samples with
low silicic acid and hydrogen ion concentrations (pH >5"7 and pSi >3"7). Similar
results were found for the release of silicic acid except that the extent of the relationship was limited by the solubility of amorphous silica which was present at lower
pH values. These data are consistent with a quasi-equilibrium between hydrogen
ions and the constituents released from hectorite during dissolution as described
by equation (7) derived in the previous section. The intercept of the relationship
between pMg and pH from Fig. 1 corresponds to pKc = 5"10 + 0-72, where the
standard error was evaluated at pH = 0.
Variable clay~solution ratio
The extent of equilibrium conditions, in the absence of added magnesium, and
silicic acid was also checked by carrying out the dissolution of hectorite using an
eight-fold range of clay/solution ratio. The results of Fig. 2 show that after only
6 weeks there was no divergence of the magnesium data below about pH 5"7; this
agreed with the previous observations (Fig. 1) that the equilibrium conditions did
not extend to high values of pH and psi.
Reaction products added
In the following experiments the reversibility of the reaction with respect to
excess amounts of the products was studied. Preliminary work showed that the
264
Kevin G. Tiller
I
4
0
Reaction time 6 weeks
9
Reaction time 8 weeks
I
1
5
I
6
I
7
pH
FIG. 1. The relation between pMg and pH in hectorite suspensions to which neither
magnesiumchloridenor silicicacid has been added.
addition of excess amounts of lithium chloride or magnesium chloride, compared
with sodium chloride or calciam chloride respectively, depressed the silicon content
of the final solution for the pH range studied. Similarly, additions of silicic acid
also depressed the magnesium concentration. These results, shown in Fig. 3,
demonstrated that the reaction was at least to some extent reversible, with the
changes in final concentrations varying in the direction required by an equilibrium
constant such as that described in equation (2).
The chemical equilibrium was studied further by reacting hectorite with acid
in the presence of M/20 magnesium chloride. The data for the two experiments,
equilibrated for 6 and 8 weeks, respectively, are shown in Fig. 4 together with
the equations of the fitted lines. The results were consistent with equation (5)
and showed that there was a constant relation between the concentrations of
hydrogen ions and silicic acid in the presence of constant amounts of magnesium
in solution for each period of shaking. The slope of the experimental lines confirmed
that approximately 2 moles of hydrogen ions were associated with each mole of
silicic acid in the reaction controlling dissolution. These experiments, and also
\
x
9
25rag cloy per 50 ml suspension
9
50rag clay per 50 ml suspension
o
I00 mcj clay per 50 ml suspension
x
250 mcj clay per 50 ml suspension
\D
%OX
o.
3
I
I
4
[
,
I
5
I
6
7
pH
The relation hetw~n pMg and pH for hectorite suspensions of variable clay/
FIG. 2.
solution ratio.
(a)
~,r
-
-
I (b)
o M NaCI
9 M LiCI
o M/20 CaCI z
21-
o M/20 CaC[ 2 only
(c)
* M/20 MqCI z
L
o
* M/20 CoCtz+ 2 x
10-3M Si
-- e .,~ 21~ m01es/ml
~,~
- ~ - _
3
.3/
b3
\,
~
o,.
",,;
I
I
5
pH
FIG. 3.
pH
pH
(a) Effect o f l i t h i u m ions o n the final concentrations o f silicic acid i n hectorite
suspensions. Reaction time, 4 weeks.
(b) Effect of magnesium ions on the final concentration of silicic acid in
hectorite suspensions. Reaction time, 4 weeks.
(c) Effect of silicic acid on the final concentration of magnesium ions in
hectorite suspensions. Reaction time, 8 weeks.
Kevin G. Tiller
266
those using other levels of magnesium not recorded here showed that, as previously,
the relationship did not hold when both silicic acid and hydrogen ions were at low
concentrations.
The equilibrium was investigated further by varying the initial amounts of
magnesium chloride and silicic acid. The results were assessed by plotting
(pSi+0.95pMg+0.1 pLi) against pH as described by equation (4). All values of
pLi were calculated using the assumptions made above. If all data obeyed the
equilibrium constant (Kc) then a straight line of slope equal to two with an
intercept on the ordinate axis equal to pKc should result. Fig. 5 gives the results
for two sets of data with different reaction times and with 250-fold, 30-fold and
200-fold ranges of magnesium ion, silicic acid and hydrogen ion concentrations,
respectively. Some examples from the data used are shown in Table 1. Samples
with low concentrations of both silicic acid and hydrogen ions as discussed earlier
were not used. The data with variable concentrations of added magnesium chloride
gave fitted lines of slope approximately equal to two with intercepts corresponding
2-5
00
%-~
0
Reaction time 6 weeks 9
~ ~
3.0
-Reactiontime 8 weeks 0
o
~ 3.5
4.0
4-5
I
I
5"0
5"5
6.0
pH
FIG. 4. The relation between equilibrium values of pSi and pH in hectorite suspensions
containing M/20 magnesium chloride.
Equilibrium of hectorite dissolution
267
8.0
(a)
8 week reaction
0 5xlO-ZMCaCIz
7.0
/El
x
0
A
9
CoCI2+2.08x10-3M MgCI~
CeCIl+ 6.25 x [O-3M M9C1~
CaCIz+ 1.25 x IO-ZM MgCIz
5 x IO-ZM MgCI z
/
9
5 x 10-ZM CoCI2+ 2 x 10-3M Si(0H) 4
9
5 x 10-2M MgClz+ bOO x IO-ZM Si (OH}4
,
~
[3
6
+
tO
m.. 6-C
o
-p
Q.
II
5"r
=u
j~.,...~_
^,~..,
//
.q
e/
'
/
4.s
4.5
~=~
I
I
i
5.0
5.5
6"0
'
6-5
pH
Fie. 5. The relation between (pSi+ 0.95 p M g + 0.1 pLi) and pH. An assessment of the
conformity of solutions of variable composition to one equilibrium constant. Ionic
strength of all solutions was approximately 0-15 moles/1.
TABLE 1. Example of data used in Fig. 5
Sample No.
pSi
pMg
pH
pKc*
Comment
H14/26
3.92
1.30
5.40
5.16
Magnesium chloride added
32
2"61
1.26
4-60
5.06
Magnesium chloride added
35
3.61
3.66
6.37
5-19
No reaction products added
40
2.58
2.32
5-04
4-97
No reaction products added
H1315
2.69
3.44
5.45
4.50
Silicic acid added
9
2.55
2.48
4.58
3.93
Silicie add added
* Derived using equation (4).
268
Kevin G. Tiller
to an equilibrium constant of about 10~. From the data of the experiment with the
longer reaction time, values of 5-12 +0-42 for log Kc and 2"01 _+0"08 for the slope
were calculated. The corresponding values for the shorter reaction times were
5"42 +_0-42 and 2"12 _+0"08, respectively. The standard errors given for Kc were
calculated at pH = 0. The data with added silicic acid was not consistent with these
straight lines.
DISCUSSION
The results given in Fig. 3 showed that changes in the concentrations of any of the
chemical species released during dissolution of heetorite can change the final concentration of the other constituents; thus the reaction exhibits a degree of reversibility. Subsequent experiments in which varying amounts of magnesium ions and
silicic acid were also added to the hectorite suspensions before pH adjustment
showed that there was an equilibrium constant which satisfactorily described the
reaction for a range of conditions. Results, such as those in Fig. 5, indicated that
the reaction was readily reversible with respect to magnesium ions but only reversible
to a limited extent with silicic acid. The apparent lack of reversibility with respect
to silicic acid at low pH values may, in fact, be a reflection of the difficulty
of forming the tetrahedral layer of the layer silicates at low temperatures. At
higher pH values, and particularly in the presence of higher amounts of magnesium
ions, there may be a new magnesium silicate phase formed which affects the
equilibrium.
The problem of reversibility with respect to one but not another of the products
can best be explained by considering the overall process as the sum of two separate
reactions. In a previous study (Tiller, 1968) data supported the general view of
earlier workers that the displacement by hydrogen ions of the octahedral cations
exposed at the clay lattice edges was the initial step in the acid attack of clays.
From the present equilibrium studies, it is sugested that, of the two steps for dissolution, the first is a reversible reaction between octahedral cations and hydrogen
ions while the second consists of-1 mole of silicon dissociating as monosilicic
acid from nearby sites in the terahedral layer for each mole of magnesium displaced.
The second reaction is only weakly reversible under the experimental conditions
used. The equilibrium constant describes the chemical equilbrium for all conditions
except where silicic acid is added or where concentrations of hydrogen ions and
silicic acid are low. Extension of the reaction times to far longer periods may
result in somewhat higher values of the equilibrium constant over a wider range
of concentrations.
The evaluation of the stoichiometry of hectorite dissolution and the calculation
of the equilibrium constant allow an estimation of the free energy of formation
of hectorite. There have been several determinations of the free energy of formation
of kaolinite (Garrels, 1957; Barany & Kelly, 1961; Polzer & Hem, 1965; Kittrick,
1966) but not for other layer silicate minerals. An expansion of thermodynamic
data of minerals should provide a better basis for the study of reactions of minerals
in nature.
Equilibrium o f hectorite dissolution
269
The lithium and aluminium content of the purified sample used in this study
were a little lower and higher, respectively, than those of the accepted composition
of hectorite (Grim, 1953). The calculation of the free energy of formation (AGt)
of hectorite is based on the investigations of the author but to enable the result to
have wider application, the accepted composition of hectorite has been used according
to the following equation:
Sis(Mg~.3, LID.66)O20 (OH)4 + 12 H + + (4 + n) HzO =
5-34 Mg ++ + 0"66 Li++ 6 Si(OH)4 solution+ 2 Sit2. nH2Osoltd.
(8)
The solid form of silicon shown above corresponds to the amorphous tetrahedral
residues suggested in the previous paper; the quantity shown was found by difference
after allowing for equimolar release of octahedral cations and monosilicic acid.
After allowing for the activity coefficient of Mg ++ in equation (2) at an ionic
strength of 0"15, the equilibrium constant calculated earlier becomes 104"r when
expressed as activities (K,). The activity coefficient of undissociated silicic acid is
assumed equal to unity. In the calculation AGt (hectorite) it is also assumed that:
(i) the equilibrium constant for the dissolution of hectorite at 25 ~ C is approximately 1-0 x 105.
(ii) the free energy of the reaction (AG O of hydration of the amorphous silica
residues is negligible so that the n moles of water used can be balanced out
in equation (8).
AG t 0aectorite) was calculated as --2680 kcal/unit cell using the relation
E/XGt (reactants)+AG~=EAG/ (products) based on equation (8), and using
AG t values of Mg++aq, Li+aq and HzOt quoted by Latimer (1952), AG t of silicic
acid (--313-0 kcal/mole) calculated from solubility of quartz (van Lier et al., 1960)
and /XGt of quartz (--204:77 kcal/mole) and AGt of amorphous silica (--203"33
kcal/mole) calculated by Wise et al. (1963).
Calculations of the free energies of formation of clays which are based on the
stoichiometry of the dissolution reaction are insensitive to the error in the equilibrium constant if the derived/',G, is very small in relation to the E/XGt (products).
In these studies, the stoichiometry has been established experimentally. Any error
in the relative proportions of the forms of silicon in the products of equation (8)
may be largely self-compensating. If this is so, errors due to stoichiometry as well
as those associated with the thermodynamic data are probably less than + 5 kcal
per unit cell. The suggested value of AG t (hectorite) at 25 ~ C is --2680 kcal/unit
cell.
CONCLUSIONS
It was concluded:
(1) that the reaction of hectorite with dilute acid reached a state of quasiequilibrium after about 6 weeks. The derived equilibrium constant satisfactorily
described the chemical equilibrium for a range of concentrations, excluding low
270
Kevin G. Tiller
values of hydrogen ions and silicic acid, only when variable amounts of magnesium
chloride or no reaction products at all were added. Although silicic acid, when
added initially, did affect the final concentration of the other constituents, the
previously derived equilibrium constant did not apply.
(2) that the dissolution may take place in two consecutive reactions; the displacement of octahedral cations by protons and the dissociation of silicic acid from
the tetrahedral layer. The first reaction was presumed to be readily reversible while
the second was only partly so.
(3) that the equilibrium constant and the stoichiometry of the reaction, as
established previously, provided a basis for the calculation of the free energy of
formation of hectorite.
ACKNOWLEDGMENTS
The author has appreciated helpful discussions with colleagues in the Chemistry Section,
C.S.LR.O., Division of Soils, with Mr K. Cellier, Division of Mathematical Statistics, C.S.I.R.O.,
and the technical assistance of Miss C. Fisher.
REFERENCES
BAl~ANYR. & KELLY K.K. (1961) U.S. Bur. Mines Rept. Invest. No. 5825.
GAm~ELS R.M. (1957) Am. Miner. 42, 780-791.
G~Ls
R.M. (1960) Mineral Equilibria at Low Temperature and Pressure, Harper and
Brothers, New York.
GRIM R.E. (1953) Clay Mineralogy. McGraw-Hill, New York.
Krrrmct J.A. (1966) Am. Miner. 51, 1457-1466.
LATIMER W.M. (1952) The Oxidation States o/ the Elements and their Potentials in Aqueous
Solutions. Prentice-Hall, Englewood Cliffs.
POLZER W.L & HEM J.D. (1965) ./. geophys. Res. 70, 6233-6240.
TILLER K.G. (1968) Clay Miner. 7, 245.
wu,~ LrF.a J.A., DE BRUYNP.L. & OVEPmEEKJ.TH.G. (1960) ./. phys. Chem., Wash. 64, 1675-1682.
WISE S.S., MARGRAVEJ.L., FEDER H.M. & HUBBARDW.N. (1963) J. phys. Chem., Wash. 67,
815-821.