19F NMR study of the equilibria and dynamics of the Al3+/F- system

Article abstract of DOI:10.1021/ic991248w

A careful reinvestigation by high-field ¹⁹F NMR (470 MHz) spectroscopy has been made of the Al³⁺/F^- system in aqueous solution under carefully controlled conditions of pH, concentration, ionic strength (I), and temperature. The ¹⁹F NMR spectra show five distinct signals at 278 K and I = 0.6 M (TMACl) which have been attributed to the complexes AlF(i)((3-i)+)(aq) with i ≤ 5. There was no need to invoke AlF(i)(OH)(j)((3-i-j)+) mixed complexes in the model under our experimental conditions (pH ≤ 6.5), nor was any evidence obtained for the formation of AlF₆^3-(aq) at very high ratios of F^-/Al³⁺. The stepwise equilibrium constants obtained for the complexes by integration of the ¹⁹F signals are in good agreement with literature data given the differences in medium and temperature. In I = 0.6 M TMACl at 278 K and in I = 3 M KCl at 298 K the log K(i) values are 6.42, 5.41, 3.99, 2.50, and 0.84 (for species i = 1 - 5) and 6.35, 5.25, and 4.11 (for species i = 1 - 3), respectively. Disappearance of the ¹⁹F NMR signals under certain conditions was shown to be due to precipitation. Certain ¹⁹F NMR signals exhibit temperature- and concentration-dependent exchange broadening. Detailed line shape analysis of the spectra and magnetization transfer measurements indicate that the kinetics are dominated by F^- exchange rather than complex formation. The detected reactions and their rate constants are AlF₂²⁺ + *F^- ? AlF*F²⁺ + F^- (k₀₂ = (1.8 ± 0.3) x 10⁶ M^-1 s^-1), AlF₃⁰ + *F^- ? AlF₂*F⁰ + F^- (k₀₃ = (3.9 ± 0.9) x 10⁶ M^-1 s^-1), and AlF₃⁰ + H*F ? AlF₂*F⁰ + HF (k(H)₀₃ = (6.6 ± 0.5) x 10⁴ M^-1 s^-1). The rates of these exchange reactions increase markedly with increasing F^- substitution. Thus, the reactions of AlF²⁺(aq) were too inert to be detected even on the T₁ NMR time scale, while some of the reactions of AlF₃⁰(aq) were fast, causing large line broadening. The ligand exchange appears to follow an associative interchange mechanism. The cis-trans isomerization of AlF₂⁺(aq), consistent with octahedral geometry for that complex, is slowed sufficiently to be observed at temperatures around 270 K. Difference between the Al³⁺/F^- system and the much studied Al³⁺/OH^- system are briefly commented on.

Full text of DOI:10.1021/ic991248w

2530
Inorg. Chem. 2000, 39, 2530-2537
19F NMR Study of the Equilibria and Dynamics of the Al3+/F- System
A. Bodor,† I. To´th,*,† I. Ba´nyai,‡ Z. Szabo´,§ and G. T. Hefter|
Department of Inorganic and Analytical Chemistry, Lajos Kossuth University (KLTE), H-4010
Debrecen, Pf. 21, Hungary, Department of Physical Chemistry, Lajos Kossuth University (KLTE),
H-4010 Debrecen, Pf. 7, Hungary, Inorganic Chemistry, Department of Chemistry, The Royal Institute
of Technology (KTH), 100 44 Stockholm, Sweden, and Chemistry Department, Murdoch University,
Murdoch WA 6150, Australia
ReceiVed October 25, 1999
A careful reinvestigation by high-field 19F NMR (470 MHz) spectroscopy has been made of the Al3+/F- system
in aqueous solution under carefully controlled conditions of pH, concentration, ionic strength (I), and temperature.
The 19F NMR spectra show five distinct signals at 278 K and I ) 0.6 M (TMACl) which have been attributed to
the complexes AlFi(3-i)+(aq) with i e 5. There was no need to invoke AlFi(OH)j(3-i-j)+ mixed complexes in the
model under our experimental conditions (pH e 6.5), nor was any evidence obtained for the formation of AlF63-(aq)
at very high ratios of F-/Al3+. The stepwise equilibrium constants obtained for the complexes by integration of
the 19F signals are in good agreement with literature data given the differences in medium and temperature. In I
) 0.6 M TMACl at 278 K and in I ) 3 M KCl at 298 K the log Ki values are 6.42, 5.41, 3.99, 2.50, and 0.84
(for species i ) 1-5) and 6.35, 5.25, and 4.11 (for species i ) 1-3), respectively. Disappearance of the 19F
NMR signals under certain conditions was shown to be due to precipitation. Certain 19F NMR signals exhibit
temperature- and concentration-dependent exchange broadening. Detailed line shape analysis of the spectra and
magnetization transfer measurements indicate that the kinetics are dominated by F- exchange rather than complex
formation. The detected reactions and their rate constants are AlF22+ + *F- h AlF*F2+ + F- (k02 ) (1.8 ( 0.3)
× 106 M-1 s-1), AlF30 + *F- h AlF2*F0 + F- (k03 ) (3.9 ( 0.9) × 106 M-1 s-1), and AlF30 + H*F h AlF2*F0
+ HF (kH03 ) (6.6 ( 0.5) × 104 M-1 s-1). The rates of these exchange reactions increase markedly with increasing
F- substitution. Thus, the reactions of AlF2+(aq) were too inert to be detected even on the T1 NMR time scale,
0
while some of the reactions of AlF3 (aq) were fast, causing large line broadening. The ligand exchange appears
to follow an associative interchange mechanism. The cis-trans isomerization of AlF2+(aq), consistent with
octahedral geometry for that complex, is slowed sufficiently to be observed at temperatures around 270 K. Difference
between the Al3+/F- system and the much studied Al3+/OH- system are briefly commented on.
1. Introduction
The fluoride complexes of Al3+ have been intensively studied.
The system is deceptively simple; it is well represented by the
formation of a series of complexes, AlFi(3-i)+(aq). The values
of the stepwise equilibrium constants have been critically
reviewed5 and are in excellent agreement for the lower order
complexes (i e 3). However, estimates of K4 vary by an order
of magnitude. Despite the existence of higher order fluoroalu-
minate species in the solid state, there is little evidence6 for the
existence of complexes with i g 5 in aqueous solution.
The Al3+/F- system has been investigated by NMR spec-
troscopy on a number of occasions.7 For example, a variety of
AlFi(3-i)+ complexes with i ) 1-3 were reported in water and
organic solvents.8-11 Unfortunately, owing to technological
limitations of the times and the inadequate control of important
solution parameters, the early NMR work is only of qualitative
Aluminum is the most abundant metal in the earth’s crust.
However, aluminum is not an essential element in biological
processes. Indeed, soluble Al3+ is a well-known toxin to both
plants and animals, and it may also be involved in human
diseases.1 As a hard metal ion Al3+(aq) interacts most strongly
with hard donors, and therefore its complexes with O- and
F-donor ligands are very stable. Such species have been shown
to be important in the transport of aluminum in both natural
waters and biological fluids2,3 and are believed to act as “seed”
poisons in the Bayer process.4 Complexation of Al3+ by F- also
plays an important role in the Watts-Utley titration; the reaction
is normally represented as Al(OH)4- + 6F- f AlF63- + 4OH-.
* Corresponding author. E-mail: imretoth@delfin.klte.hu.
† Department of Inorganic and Analytical Chemistry, Lajos Kossuth
University (KLTE).
(5) Bond, A. M.; Hefter, G. T. Critical SurVey of Stability Constants and
Related Thermodynamic Data of Fluoride Complexes in Aqueous
Solution; IUPAC Chemical Date Series No. 27; Pergamon: Oxford,
1980.
‡ Department of Physical Chemistry, Lajos Kossuth University (KLTE).
§ The Royal Institute of Technology (KTH).
| Murdoch University.
(1) Corain, B.; Bombi, G. G.; Tapparo, A.; Perazzolo, M.; Zatta, P.Coord.
Chem. ReV. 1996, 149, 11.
(6) Brosset, C.; Orring, J. SVensk. Kem. Tidskr. 1943, 5, 101.
(7) Akitt, J. W. Prog. NMR Spectrosc. 1989, 21, 41.
(2) Smith, R. W. Coord. Chem. ReV. 1996, 149, 81.
(3) (a) Martin, R. B. In Encyclopedia of Inorganic Chemistry; King, R.
B., Ed.; John Wiley & Sons: Chichester, 1994; Vol. 4, p 2193. (b)
Martin, B. R. Biochem. Biophys. Res. Commun. 1988, 155, 1194.
(4) Ullman’s Encylcopedia of Industrial Chemistry, 5th completely revd
ed.; VCH Verlag: Weinheim 1985; pp 566-568.
(8) Yamazaki, M.; Takeuchi, T. Kogyo Kagaku Zasshi 1967, 70, 656.
(9) (a) Buslaev, Y. A.; Petrosyants, S. P. Koord. Khim. 1979, 5, 163. (b)
Petrosyants, S. P.; Buslaev, Y. A. Koord. Khim. 1981, 7, 907.
(10) Hass, D.; Petrosyants, S. P.; Buslaev, Y. A.; Hartley, I. Dokl. Akad.
Nauk. SSSR 1983, 269, 380.
(11) Petrosyants, S. P.; Buslaev, Y. A. Koord. Khim. 1986, 12, 907.
10.1021/ic991248w CCC: $19.00 © 2000 American Chemical Society
Published on Web 05/19/2000

Equilibria and Dynamics of the Al3+/F- System
Inorganic Chemistry, Vol. 39, No. 12, 2000 2531
use. Evidence for the existence of AlF63- in 90% H2O2 solution
has been provided.12 More recently,13 the existence of
AlFi(3-i)+(aq) with i ) 1 and 2 was confirmed, but significantly,
difficulties were noted in obtaining signals for higher species.
These authors attributed other signals to the formation (at pH
g 2) of mixed Al(OH)Fi(2-i)+ complexes.
Kinetic measurements were performed on samples with I ) 3 M
(KCl) at 298 K with 0.05 e cH e 0.4 M.
pH Measurements. Free hydrogen ion concentrations in solutions
of moderate acidity were measured by a HF-resistant combined glass
electrode (Ingold, HF-405-60-57) connected to a pH meter and
calibrated by the method of Irving et al.19 to give pH ) -log [H+].
Equilibrium concentrations of the different species were obtained by
integration of the appropriate NMR peaks. Therefore, all stability
constants reported in this paper are stoichiometric constants (cf. eq 3).
In more acidic samples, because of dissolution of glass from the
Ingold electrode, acid concentrations were taken to be those of the added
acid. Occasionally, however, the pH had to be measured in acid samples
with little or no buffer capacity. In such cases pH was measured in
situ by monitoring the observed time-averaged 19F NMR shift (δobs) of
the HF/F- signal. Providing the proton exchange is rapid, it is readily
shown that
The structural chemistry of Al3+ is dominated by the
formation of octahedral species. Other geometries, such as the
-
-
tetrahedral Al(OH)4 in aqueous solution and AlF4 in non-
aqueous solvents, are also known.14,15
The kinetics of the formation of AlF2+(aq) was studied.16,17
On the basis of conventional kinetic measurements18 (followed
by 19F NMR) a reactivity order was proposed toward F- of Al-
3+
(H2O)6 , Al(H2O)5F2+ , Al(H2O)4F2+. No dynamic NMR
studies of the AlFi(3-i)+(aq) complexes appear to have been
made. The temperature dependence of 19F line widths8 suggested
the presence of exchange reactions. Similar effects were
observed recently;13 the temperature-dependent line broadening
was explained by proton exchange reactions (i.e., between
ligated OH- and H2O).
pH ) pKHF - log [δF - δobs]/[δobs - δHF
]
(1)
where δF is the chemical shift of F- in extreme basic solution and δHF
is the chemical shift of HF in the extreme acidic solution. The values
of pKHF ) 3.32 (I ) 3 M (KCl), 298 K) and pKHF ) 3.10 (I ) 0.6 M
(TMACl), 298 K) were determined with δHF ) -43.08 ppm and δF )
0.40 ppm. This method is sensitive to pH change in the pH range
corresponding to pKHF ( 1.9.
A number of questions remain unanswered about the Al3+
/
F- system. Is there unambiguous evidence for the existence of
AlFi(3-i)+(aq) with i > 4? What are the structures and reaction
dynamics of the AlFi(3-i)+(aq) species? Accordingly, this paper
presents a reinvestigation of the system by 19F NMR spectros-
copy under carefully controlled conditions of pH, temperature,
and ionic strength.
NMR Measurements. 19F NMR spectra were recorded at 470.5 MHz
with Bruker DMX500 and DRX500 spectrometers using a 5 mm inverse
probehead in locked mode. The samples were introduced into PTFE
NMR tubes, which were inserted into conventional 5 mm glass tubes.
The temperature of the probehead was checked by the “methanol-
thermometer method”.20 Typical NMR parameters were flip angle ∼30°
(6-8 µs), pulse repetition time 0.8-1.5 s, spectral window 4250-
11800 Hz, and number of scans 64-160. These parameters allowed
quantitative integrations to be obtained from the spectra. The chemical
shifts are reported in parts per million toward lower frequencies with
respect to an aqueous alkaline solution of 0.01 M NaF (δ ) 0.00 ppm)
as an external standard. Recalculation to the usual CFCl3 standard can
2. Experimental Section
Chemicals. Sodium fluoride (Merck p.a.) was crystallized from
distilled water, dried at 120 °C, and kept in a desiccator. Stock solutions
of 0.200 and 0.0500 M were prepared by weight. Tetramethylammo-
nium fluoride (TMAF) stock solution was prepared (1.00 M) from
carbonate-free tetramethylammonium hydroxide (TMAOH) solution by
adding HF solution to pH 6.0. The TMAOH solution was standardized
by pH-metric titration. Aluminum chloride was prepared from 99.9999%
purity Al wire (Ajka, Hungary). A weighed quantity of wire was reacted
with a stoichiometric quantity of HCl in a Pt boat kept in a glass vessel.
As well as acting as a container the Pt served as a catalyst to speed the
reaction time to 1 day. The vessel was cooled and protected against
the introduction of impurities by allowing the H2 formed to evolve Via
a gas-washing bottle containing dilute HCl. A stock aluminum solution
of 0.400 M, containing a minimum of free acid, was prepared and its
concentration checked by EDTA titration. Potassium chloride (Merck
p.a.) and tetramethylammonium chloride (TMACl; Aldrich p.a.) were
used without further purification. Hydrochloric acid solutions were made
by diluting a standard (Merck, Titrisol) or 37% HCl (Merck p.a.)
standardized against potassium hydrogen phthalate.
All measurements were made on solutions at ionic strength I ) 3
M (KCl) or 0.6 M (TMACl), where I ) 0.5∑zi2ci, and zi and ci are,
respectively, the charge and the molar concentration of the ith ion.
Samples for NMR spectroscopy were prepared in polypropylene vessels.
Solid KCl (by weight) or TMACl solution (by volume) was added first,
followed by solutions of acid, AlCl3, D2O (10% v/v), double-distilled
water, and fluoride. The samples were prepared 1 day before the
measurement.
be done, if δCFCl ) 0 ppm and δNaF ) -121.1 ppm. Magnetization
3
transfer experiments were performed by shaped pulse sequences. Line
widths were determined by fitting Lorentzian curves to the signals.
All spectral analyses were done using the Bruker WIN-NMR software.
3. Results and Discussion
Assignment of Species. Stepwise formation of AlFi(3-i)+
species can easily be followed by 19F NMR; however, it is vital
that such measurements be performed under carefully controlled
conditions of pH, temperature, and ionic strength. Changing cF/
cAl at constant pH or changing pH at constant cF/cAl enables
the assignment of chemical shifts to specific complexes. More
importantly, the sensitivity of high-field 19F NMR makes
possible measurements at concentrations comparable to those
used in classical thermodynamic studies.
The lower complexes are easily detected in solutions of high
acidity. Figure 1 shows a typical series of spectra at cAl ) 5
mM and cF/cAl ) 3 in 3 M KCl solutions at 298 K measured as
a function of HCl concentration. Four signals, corresponding
to AlF2+, AlF2+, AlF3 , and HF, are seen. As expected, the
0
(12) Kon’shin, V. V.; Chernyshov, B. N.; Ippolitov, E. G. Dokl. Akad.
Nauk. SSSR 1984, 278, 370 (English translation). 27Al and 19F NMR
spectra, measured in 90% (not 80%7) H2O2 at ca. -40 °C, showed
coupling consistent with a central Al3+ coordinated to six equivalent
higher the acid concentration, the lower the intensity of the
signals of the higher order species. The chemical shift of the
“free” fluoride, HF/F-, changes slightly at lower acidities due
to exchange with the small amounts of unprotonated F-, but
those of the AlFi(3-i)+ species do not vary significantly. On the
other hand, there is a substantial change in the line widths,
1
fluoride ligands, with JAl-F ) 19 Hz.
(13) Martinez, E. J.; Girardet, J.-L.; Morat, C. Inorg. Chem. 1996, 35, 706.
(14) Herron, N.; Harlow, R. L.; Thorn, D. L. Inorg. Chem. 1993, 32, 2985.
(15) Herron, N.; Thorn, D. L.; Harlow, R. L.; Davidson, F. J. Am. Chem.
Soc. 1993, 115, 3028.
0
especially for the AlF3 and HF/F- signals.
(16) Shurukin, V. V.; Kozlov, Yu. A.; Blochin, V. V.; Mironov, V. E.
Russ. J. Phys. Chem. 1976, 50, 145.
(17) Plankey, B. J.; Patterson, H. H. Inorg. Chem. 1989, 28, 4331.
(18) Zbinden, P. Ph.D. Thesis, University of Lausanne, Lausanne, Swit-
zerland, 1994.
(19) Irving, H. M.; Miles, M. G.; Pettit, L. P. Anal. Chim. Acta 1967, 38,
475.
(20) Anthony, L. van Geet Anal. Chem. 1970, 42, 679.

2532 Inorganic Chemistry, Vol. 39, No. 12, 2000
Bodor et al.
Figure 1. 19F NMR spectra of a solution with cAl ) 5 mM, cF ) 15
mM, and 3 M KCl at 298 K, at different total acid concentrations, cH:
(a) 0.1 M, (b) 0.3 M, (c) 0.4 M, (d) 0.6 M. Numbers 1, 2, and 3 refer
Figure 2. 19F NMR spectra of a solution with cAl ) 5 mM, HAc/Ac-
buffer (0.05 M), pH ≈ 6.1 and 0.6 M TMACl at 278 K, at different cF
values: (a) 5 mM, (b) 10 mM, (c) 15 mM, (d) 20 mM, (e) 25 mM, (f)
to species AlF2+, AlF2+, and AlF3 .
0
30 mM, (g) 40 mM. Numbers 1, 2, 3, 4, and 5 refer to species AlF2+
,
0
AlF2+, AlF3 , AlF4-, and AlF52-. The narrow signal of free fluoride at
An obvious way for detecting higher AlFi(3-i)+ species is to
prepare samples with higher cF/cAl ratios and/or at higher pH.
Accordingly, cF was varied at constant cAl and with the pH held
constant at 4.5 with 0.05 M HAc/Ac- buffer in 3 M KCl. At
cF/cAl e 3 no new signals were detected. Further, at higher ratios,
cF/cAl g 8, the signals of the AlFi(3-i)+ complexes disappeared!
This phenomenon was also reported by Martinez et al.,13 who
attributed it to exchange processes. However, as the chemical
shift differences for the various AlFi(3-i)+ species are relatively
small, a few parts per million, a complete loss of intensity by
broadening seems to be very unlikely. Close inspection of the
(semitranslucent plastic) NMR tubes indicated the presence of
a fine, colorless precipitate at such concentrations. Analysis by
ICP AES of filtered solutions indicated virtually no Al(III) in
solution. Dissolution of the solid in 1 M HNO3 followed by
ICP AES accounted for all the “missing” Al(III). The nature of
the solid was not investigated further, but AlF3, Na3AlF6 (and
therefore perhaps K3AlF6), and a range of Al3+/OH-/F- solids
are all sparingly soluble in near-neutral aqueous solutions.21
δ ≈ 0 ppm is not shown.22a
The most obvious explanation for signals 4 and 5 is to
attribute them to the species AlF4-(aq) and AlF52-(aq), respec-
tively. However, at the pH employed (∼6.0), the formation of
ternary AlFi(OH)j(3-i-j)+(aq) species must also be considered.
Formation of such complexes is favored at higher pH and
modest cF. Accordingly, a series of solutions were prepared in
0.6 M TMACl at cF/cAl ) 40/5 and 20/5 and 3.7 e pH e 6.5
at 278 K. Typical spectra are shown in Figure S1 of the
Supporting Information. The line widths and relative intensities
of the signals obtained changed, but the chemical shifts were
independent of pH. Thus, ternary complexes do not account
for signals 4 and 5, and it is concluded that they can be ascribed
to AlF4-(aq) and AlF52-(aq).
The assignments of signals 1-5 and their chemical shifts are
summarized in Table 1. The chemical shifts for the lower order
complexes (i e 3) are similar to those of previous studies;
quantitative agreement would not be expected given the widely
varying concentrations, temperatures, pH, counterions, and
chemical shift standards, and the absence of a constant ionic
medium in the earlier studies.
Equilibrium Constants. Although NMR spectroscopy does
not usually have the precision of potentiometric measurements,
it can provide an important independent check on their accuracy.
Providing the signal assignments in Table 1 are correct,
measurement of the integrated intensities as a function of pH
and/or cF/cAl enables the stability constants of all detected
AlFi(3-i)+(aq) species to be determined (see the Supporting
Information). The formation of the complexes (i g 1) can be
written as
Following Brosset and Orring6 and others9 who reported
greater solubilities in R4N+ media, a series of solutions were
prepared in 0.6 M TMACl (0.05 M HAc/Ac- buffer) at pH ≈
6.0. No precipitation at cAl ) 5 mM occurred, even up to cF )
600 mM. More importantly, at 278 K, in addition to the three
signals observed for AlFi(3-i)+ with i e 3 in 3 M KCl media at
298 K (Figure 1), two further signals were detected (Figure 2).
At low cF (e5 mM), signals 1 (AlF2+) and 2 (AlF2+) were
0
dominant with minor amounts of signal 3 (AlF3 ). As cF was
increased to 15 mM, signals 1 and 2 progressively decreased,
while signal 3 increased along with that of a new signal, 4. At
cF ) 25 mM (cF/cAl ) 5) signal 4 became dominant, with signal
3 decreasing and a further resonance, 5, beginning to grow.
Signal 5 continued to grow up to cF ) 40 mM, but remained
quite broad. No evidence for a sixth signal was found even up
to cF ) 600 mM (cF/cAl ) 120). In the absence of excessive
line broadening or precipitation, no missing 19F NMR intensity
could be detected within the limits of precision of the integration
((5%).22b
AlFi-1(4-i)+ + F- h AlFi(3-i)+
and the equation of the stepwise stability constants as
Ki ) [AlFi(3-i)+]/[AlFi-1(4-i)+][F-]
(2)
(3)
(21) Parthasaraty, N.; Buffle, J.; Haerdi, W. Can. J. Chem. 1986, 64, 24.
(22) (a) The “slow exchange regime” for AlFi(3-i)+ and F- at 278 K turns
to “fast exchange” at 298 K, where only one, time-averaged, broad
signal of the complexes is detected. Interestingly, the signal of free
fluoride remains narrow. Thus, the kinetics of AlFi(3-i)+ (i g 3) at
higher pH, where these complexes are dominant, could be different
from the kinetics discussed below for AlFi(3-i)+ and HF/F-. Detailed
studies are needed. (b) Hefter, G. T.; To´th, I.; Bodor, A. Submitted
for publication.
The values of Ki obtained in this way at 278 K and I ) 0.6 M
(TMACl) and at 298 K and I ) 3 M (KCl) are summarized in
Table 1. Although a detailed comparison with previous data is
beyond the scope of the present work, given the differences in
the media and the relatively low precision of NMR integrations
of broad signals, the agreement with reliable literature values
for the lower order complexes (i e 4) is excellent. Note that

Equilibria and Dynamics of the Al3+/F- System
Inorganic Chemistry, Vol. 39, No. 12, 2000 2533
Table 1. Equilibrium Constants and Chemical Shift Values of AlFi(3-i)+ Complexes
0.6 M TMACl, 278 K
3 M KCl, 298 K
signal
assignment
AlF2+
log Ki (lit.)a
δ (ppm)
log Ki ( est err
δ (ppm)
log Ki ( est err
1
2
3
4
5
6
6.11
4.96
3.85
2.35
1.33
(0.47)
-35.76
6.42 ( 0.03 (3 points)
5.41 ( 0.09 (7 points)
3.99 ( 0.09 (6 points)
2.50 ( 0.05 (8 points)
0.84 ( 0.20 (9 points)
-37.27
6.35 ( 0.08 (8 points)
5.25 ( 0.07 (30 points)
4.11 ( 0.12 (7 points)
+
AlF2
AlF3
AlF4
AlF5
-35.36
-36.93
0
-34.29
-36.18
-
-33.32
b
b
b
2-
-31.66
3-
AlF6
not detected
a I ) 0.5 M (KNO3), 298 K;6 see also refs 5 and 3b. b Precipitation occurred.
Scheme 1
temperature effects are small (<ca. 0.1 in log Ki for a
temperature difference of 20 K) on the basis of the known values
of ∆Hi.5
It is interesting and almost certainly significant that the present
value of K5 (Table 1) is about a factor of 3 lower than the only
previous report of this constant. As noted earlier and discussed
in detail elsewhere22b no evidence has been obtained for the
existence of AlF63-(aq) at T g 255 K and cF/cAl e 120 by 19
F
HF; the subscript ij means the magnetization transfer from site
i to site j):
NMR. A typical distribution diagram is shown in Figure S2.
(3x-y)+
Note that Alx(OH)y
species3b are also included in the
model calculation, but they show no contribution to the
speciation under our experimental conditions.
k02
*F- + AlF2+ y
\
z AlF*F+ + F-
(6)
(7)
(8)
(9)
k20
kH
Dynamics. As seen from Figure 1 the line widths of the
signals except that of AlF2+ vary with acidity. With increasing
acid concentration the HF signal narrows, whereas those of
02
H*F + AlF2+ y z AlF*F+ + HF
kH
20
+
0
AlF2 and AlF3 broaden. This is a certain indication of the
presence of exchange processes. As the number of peaks is equal
to the number of species reported by equilibrium studies, the
“slow exchange” situation is valid. In this case the line width
of the signal for the species i (LWi) is
k03
*F- + AlF30 y
\
z AlF2*F0 + F-
k30
kH
03
H*F + AlF30 y z AlF2*F0 + HF
kH
30
1 1
1
1
LWi )
+
+
(4)
(ii) Complex formation (superscript c or cH):
(
)
π T2,i τinh τex,i
kc03,kc
23
F- + AlF2+ y
z AlF3
(10)
(11)
0
where T2,i is the transverse relaxation time of species i, τinh the
relaxation time due to inhomogeneity of the magnetic field, and
τex,i the contribution of chemical exchange to the transverse
relaxation.
kc30,kc
32
kcH03,kcH
23
HF + AlF2+ y
z AlF30 + H+
kcH30,kcH
32
The line broadening of species i (LBi) resulting from chemical
exchange is defined as the difference between the observed line
width and the nonexchange line width:
(iii) Ligand exchange between complexes, “self-exchange” 23
with no net chemical change:
n
1 1
1
1
1
k23
\
LBi ) LWi -
+
)
k
obs ) kiobs (5)
AlF2+ + AlF2*F0 y
z AlF*F+ + AlF3
(12)
0
∑
ij
k32
(
)
π T2,i τinh
πi)0,i*j
π
Considering reactions 6-12, we deduced the reaction rates
for the various species, using the usual kinetic analysis (see the
Supporting Information). The regression analysis of LBi vs
equilibrium concentration data showed that the following rate
equations describe the dynamic system (Figure 3):
where n is the number of species, kijobs is the pseudo-first-order
rate constant of each reaction from site i to site j, and kiobs is
the pseudo-first-order rate constant of all parallel reactions from
site i. The nonexchange line width is considered to be 12 Hz,
which is the line width of AlF12+, which is proven not to be
involved in any exchange processes (Vide infra). Thus, LBi
values can be used for kinetic analysis of the system.
w0 ) 2k02[AlF2 ][F-] + 2k03[AlF3][F-] +
+
Knowledge of the speciation in the Al3+/F- system (Vide
supra) and the analysis of the exchange-broadened spectra show
that three sites take part in the exchange process in I ) 3 M
KCl at 298 K. The species AlF2+ is excluded, because its line
width does not vary with concentration. Therefore, Scheme 1
is an appropriate starting point for the kinetic analysis.
2kH03[AlF3][HF] (13)
w2 ) 2k20[AlF2 ][F-]
(14)
(15)
+
w3 ) 2k30[AlF3][F-] + 2kH30[AlF3][HF]
The next step is to find the chemical exchange reactions which
can transfer magnetization between the different sites. Three
types of such processes are possible. (i) Ligand exchange
between the complexes and free ligand (HF and/or F-) with no
net chemical change (the superscript H indicates exchange with
These rate expressions indicate that the observed LBi are
consistent with the occurrence of only three parallel reactions,
6, 8, and 9, with rate constants k′02 ) k′20 ) (8.8 ( 1.4) × 105
(23) Ba´nyai, I.; Glaser, J. J. Am. Chem. Soc. 1989, 111, 3186.

2534 Inorganic Chemistry, Vol. 39, No. 12, 2000
Bodor et al.
the data. Using eqs 5 and 13-15 and the k′ij values determined
from the line broadenings, the pseudo-first-order rate constants
were calculated to be k30obs ) 230 s-1 and k20obs ) 35 s-1. The
agreement between the rate constants obtained from the line
broadenings and the magnetization transfer data is excellent for
obs
k30 but is less satisfactory for k20obs. However, it should be
remembered that even though the T1 time scale is more suitable
for measuring such slow processes, the magnetization transfer
experiments were performed on a single sample, while the line
broadening analysis was based on a series of samples.
In summary, the dynamics of the Al3+/F- system, at least
0
for AlF2+(aq) and AlF3 (aq) are dominated by fluoride exchange
(eqs 6-9) between the complexes and free fluoride (HF/F-).
Complex formation (water substitution) reactions (eqs 10 and
11) and fluoride exchange between complexes (eq 12) are much
slower. Each of these processes will now be considered in detail
along with the additional possibility of isomerization.
Fluoride Complexation Processes. In general the ligand
substitution reactions of Al3+ in aqueous solution are known to
follow the Id mechanism. That is, the rate-determining step (rds)
of complex formation is the leaving of a coordinated water
molecule from the outer-sphere complex formed in a fast
preequilibrium. Thus, for fluoride complexation the mechanism
would be expected to be
Figure 3. Dependence of line broadening on cH. The points represent
the measured values, while the lines show the calculated values using
eqs 13-15 and S19-S21 in the Supporting Information. Symbols 9,
2, and [ refer to species HF/F-, AlF3 , and AlF2+, respectively.
0
fast
AlFi(H2O)6-i(3-i)+ + F- y z AlFi(H2O)6-i(3-i)+, F-
(16)
AlFi(H2O)6-i(3-i)+, F- 9rds8 AlFi+1(H2O)5-i(2-i)+ + H2O (17)
Figure 4. Intensities (arbitrary units) vs delay time (s) for a sample
with cAl ) 5 mM, cF ) 15 mM, cH ) 0.1 M, and 3 M KCl at 298 K.
0
Numbers 2 and 3 refer to species AlF2+ and AlF3 . Symbols represent
If the mechanism of complex formation is indeed dissociative
in character, the first-order rate constant of the rds, krds, is
expected to be very close to the water exchange rate constant
of AlFi(H2O)6-i(3-i)+. From eqs 16 and 17 krds ) k/Kos, where
the equilibrium constant for eq 16, Kos, is usually estimated from
one of the Fuoss-type equations.25 Since the water exchange
rates are known26 (Table 2), the expected rate constants of the
measured values.
H
M-1 s-1, k′03 ) k′30 ) (1.3 ( 0.3) × 106 M-1 s-1, k′03H ) k′30
) (2.2 ( 0.16) × 104 M-1 s-1. The k′ values are the rate
constants of a specific24 F- ligand exchange according to the
definition k′i0 ) ki0/i. It is notable that all these reactions are
symmetrical; i.e., the processes responsible for line broadening
are ligand exchange rather than complex formation reactions.
0
+
reactions for the formation of AlF3 from AlF2 (eqs 10 and
11) can be calculated. For eq 10 this value is kc03 ) kc23 ) 2.4
× 104 M-1 s-1; the value for 11 is even smaller (HF reacts
more slowly than F-). As these values are considerably smaller
than the experimental rate constant (8.8 × 105 M-1 s-1), this
accounts for why complex formation makes no significant
contribution to the observed dynamics.
In an attempt to determine the influence of any slower
processes, inversion transfer experiments were carried out by
selective excitation of each peak, since the longitudinal relax-
ation time (T1) is usually longer than the transverse relaxation
time (T2). A typical experiment is shown in Figure 4, where
inversion was performed on the HF/F- site. The magnetization
transfer to AlF30 started before the initial observation time, and
equilibration between it and HF/F- was complete in 4-5 ms,
consistent with the line broadening results. A decrease in the
intensity of the AlF2+ signal in the range of 10-100 ms shows
Another way of expressing the relative slowness of the
complex formation reactions is to calculate the line broadenings
caused by complex formation, assuming they follow the Id
mechanism (eqs 16 and 17). These values, Table 2 (column 5),
calculated from the water exchange rate data (also in Table 2)
indicate that none of the complex formation reactions contribute
significantly to the observed line broadening.
0
that this complex reacts slower than AlF3 . Consistent with the
absence of line broadening of the AlF2+ signal, no magnetization
transfer was observed to the AlF2+ site, thus fixing an upper
rate limit for its exchange processes. The total negative
longitudinal magnetization “leaked out” from the system in 2-3
s, illustrating the longer time scale.
It is interesting to note that an associatiVe (Ia) mechanism
has been suggested by Plankey and Pattersson17 for the
formation of the first complex, AlF(H2O)52+, on the basis of
3+
the fact that the rate of substitution of H2O on Al(H2O)6 by
F- was greater than that of H2O exchange, after the application
of some statistical corrections. However, this difference was
very small.
The change in longitudinal magnetization with time is
described by the matrix equation M∞ - Mt ) exp(-Rt)‚
(M∞ - M0). The matrix of pseudo-first-order rate constants (R)
was determined by nonlinear least-squares analysis. Within
Fluoride Exchange Processes. A logical starting point to
discuss fluoride exchange processes is to assume that they follow
obs
experimental errors only two rate constants with values k30
) 240 ( 14 s-1 and k20obs ) 12 ( 0.2 s-1 were required to fit
(25) Fuoss, R. M. J. Am. Chem. Soc. 1958, 80, 5059.
(24) Lincoln, S. F.; Merbach, A. E. In Substitution Reaction of SolVated
Metal Ions; Sykes, A. G., Ed.; Advances in Inorganic Chemistry Vol.
42; Academic Press: London, 1995; pp 2-78.
(26) (a) Phillips, B. L.; Casey, W. H.; Crawford, N. S. Geochim.
Cosmochim. Acta 1997, 61, 3041. (b) Phillips, B. L.; Tossell J. A.;
Casey W. H. EnViron. Sci. Technol. 1998, 32, 2865.

Equilibria and Dynamics of the Al3+/F- System
Inorganic Chemistry, Vol. 39, No. 12, 2000 2535
Table 2. Rates of Water Exchange kex (H2O) and Calculated Values of Kos, Rate Constants kc0i, and HF/F- Line Broadenings for Formation
(3-i)+
Reactions of Various AlFi(H2O)6-i
Species
26
reaction
kex (H2O) (s-1
)
Kos (M-1
)
kc0i (M-1 s-1
)
LB (Hz)a
Al(H2O)63+ + F- h Al(H2O)5F2+
AlF(H2O)52+ + F- h AlF2(H2O)4
AlF2(H2O)4+ + F- h AlF3(H2O)3
2
20
5
1.2
4 × 101
5 × 102
2.4 × 104
<10-4,b
∼10-3
∼0.1
1 × 102
+
2 × 104
0
a Under the conditions of the inversion transfer experiments. b The concentration of the Al(H2O)63+ complex was estimated from the equilibrium
constant.
Table 3. Rate Constants of Ligand Exchange Reactions between
a mechanism formally similar to that of complex formation:
the Complexes and HF/F-
k0i, kH
krds ) k0i/Kos
(s-1
e2 × 103
1.5 × 106
1.3 × 107
2.2 × 105
fast
0i
AlFi(H2O)6-i(3-i)+ + *F- y z
b
reaction
(M-1 s-1
)
)
AlFi(H2O)6-i(3-i)+, *F- (18)
AlF2+ + *F- h Al*F2+ + F- a
AlF2+ + *F- h Al*FF+ + F- a
AlF30 + *F- h AlF2*F0 + F-
AlF30 + H*F h AlF2*F0 + HF
e1 × 104 c
1.8 × 106
3.9 × 106
6.6 × 104
AlFi(H2O)6-i(3-i)+, *F- 9rds8
Al*FFi-1(H2O)6-i(3-i)+ + F- (19)
+
a Exchanges of AlF2+ with HF/F- and of AlF2 with HF are too
slow to be measured. b Exchange constant for partial (unspecified)
exchange. c Considering the magnetization transfer experiment com-
mented on above, it is observable that in ∼3 s the initial situation is
reestablished. Therefore, the half-time (t1/2) for this experiment is ∼0.6
s and kobs ) (ln 2)/t1/2 ≈ 1 s-1. The accuracy of this type of measurement
shows that processes which have a first-order rate constant of less than
∼0.1kobs cannot be detected on the T1 time scale. As the reaction referred
to is not detectable, we can calculate an upper limit for k01. The rate
equation is w ) 2k01[AlF2+][F-] and kobs ) w/TF ) 2k01([AlF2+]/1 +
Note, however, this formalism does not indicate whether the
rds is dissociative, associative, or concerted.
Comparison of the rate constants for the following three
processes
AlF3(H2O)30 + *F- h Al*FF2(H2O)30 + F-
k′30 ) 1.3 × 106 M-1 s-1
AlF3(H2O)30 + H*F h Al*FF2(H2O)30 + HF
k′H30 ) 2.2 × 104 M-1 s-1
AlF3(H2O)30 + AlF*F+ h Al*FF2(H2O)30 + AlF2
k
HF[H+]). Calculating the corresponding concentration values from the
spectra, we obtain k01 e 104 M-1 s-1
.
As the overall reaction embodied in eqs 18 and 19 is
unaffected by the nature of the activation in the rds, the rate
constants of the rds (eq 19) can be calculated in a manner similar
to those for the complexation reactions. The values so obtained
are given in Table 3 for those exchange reactions for which the
appropriate data are available. Comparison of the rate constants
for AlF2+, the only complex for which numerical data are
available, for F- exchange (Table 3) with those for water
exchange (Table 2) indicate that coordinated fluoride is more
labile in these reactions than coordinated water by a factor of
about 40, after allowing for the relevant statistical factor.
Interestingly, Phillips et al. claimed faster water exchange than
fluoride exchange, but only reactions 10-12 seemed to be
considered. However, similar trends are apparent for both types
of bond breaking; i.e., the higher order the complex (the less
positive the net charge on the complex), the more labile are
both the coordinated F- and water molecules.
+
k′32 ≈ 0
indicates that the rates of fluoride exchange reactions depend
dramatically on the nature of the entering group, typical for
associative interchange. (Note that as AlF3 is neutral there is
no significant correction to be made for the variation in the
charge of the incoming group.) A similar but more limited effect
0
+
is observed for AlF2
AlF2(H2O)4+ + *F- h Al*FF(H2O)4+ + F-
k′20 ) 8.8 × 105 M-1 s-1
AlF2(H2O)4+ + H*F h Al*FF(H2O)4+ + HF
k′H20 ≈ 0
It is notable that the present results show that F- exchanges
more quickly on AlFi3-i(aq) than does HF. This is opposite those
found for exchange on UO2Fi(2-i)+(aq), the only other system
for which F- exchange rates have been measured.28 However,
the latter is likely to involve some unusual H-bonding effects.
The present order is consistent with the reported rates of
although here allowance must be made for the difference in
charge. Nevertheless, on the basis of these two groups of results,
it may be concluded that fluoride exchange reactions are
associatively activated.
The occurrence of an Ia mechanism for fluoride exchange is
unusual given, as already noted,17 that most, but possibly not
all, Al3+ substitution processes follow Id behavior. According
to Lo and Swaddle,27 all substitution processes for octahedral
M3+ species are Ia unless r(M3+) < 0.6 Å. However, such
substitution processes usually refer to the replacement of
coordinated H2O. Since F- is smaller than H2O and as Al3+ is
only slightly smaller than 0.6 Å, it is possible that there is
sufficient space in the coordination sphere of the Al3+ to
accommodate an extra (incoming) F-. The role of H-bonding
is likely to be significant because all of the species under
consideration, including HF0, are very strongly solvated.
substitution reactions of F- and HF with both Be2+ and Fe3+ 29,30
.
Fluoride Exchange between Complexes. Once it is recog-
nized that fluoride exchange processes occur Via an associative
mechanism, then it is readily understood why the exchange of
F- between complexes is unimportant on the 19F NMR time
+
scale. The much greater bulkiness, cf. AlF2 and F- or HF, of
an incoming complex inevitably means that in comparison such
reactions will be extremely slow.
Isomerization Processes. The temperature dependence of the
19F NMR spectra suggests another dynamic process in the Al3+
/
(28) Szabo´, Z.; Glaser, J.; Grenthe, I. Inorg. Chem. 1996, 35, 2036.
(29) Baldwin, W. G.; Stranks, D. R. Aust. J. Chem. 1968, 21, 2161.
(30) Pouli, D.; Smith, W. M. Can. J. Chem. 1960, 38, 567.
(27) Lo, S. T.; Swaddle, T. W. Inorg. Chem. 1975, 14, 1878.

2536 Inorganic Chemistry, Vol. 39, No. 12, 2000
Bodor et al.
Scheme 2
than those of AlF2+, signals for the mer- and fac-AlF30 isomers
cannot be separated under our experimental conditions.
Given that the present NMR measurements indicate that the
free ligand (HF/F-) is not involved in the isomerization reaction
+
0
of AlF2 (and very likely also not for AlF3 either) at lower
temperatures, the probable isomerization mechanism is an
intramolecular process rather than an intermolecular ligand
exchange reaction. The NMR measurements indicate that the
temperature dependence for the intra- and intermolecular
fluoride exchange processes are different; indeed this difference
allows their separation.
In summary, the different exchange processes proposed for
the AlFi(3-i)+(aq) complexes are illustrated in Scheme 2 for AlF2-
(H2O)4+. The water exchange process (1) cannot of course be
detected by 19F NMR. (However, 17O NMR data are available.26)
Further, the complex formation reactions (2) and the exchange
reactions of AlF2+ are too slow to study by NMR. The rates of
Figure 5. (a, top) 19F NMR spectra of a solution with cAl ) 5 mM, cF
) 15 mM, cH ) 0.1 M, and 3 M KCl at different temperatures, T: (a)
255 K, (b) 259 K, (c) 262 K, (d) 273 K, (e) 287 K, (f) 306 K. Numbers
ligand exchange (3) between free fluoride (HF/F-) and AlF2
+
or AlF30 are faster and fall within the 19F NMR time scale. The
isomerization (4) is an intramolecular process.
0
1, 2, and 3 refer to species AlF2+, AlF2+, and AlF3 , respectively. (b,
bottom) Band shape analysis for spectra at 255 K from (a). Numbers
Geometry of the Complexes. The existence of cis and trans
isomers of AlF2+(aq) is a straightforward proof of its octahedral
geometry and thus by implication that of AlF2+(aq) too. It has
often been assumed by extension that this must also be true for
the higher order complexes (i g 3). On the other hand, as noted
earlier, complexes with geometries other than octahedral
certainly exist in the solid state, in melts, and in some
nonaqueous solutions. Our measurements, like those of previous
NMR investigations, do not provide direct information on this
matter. Thus, although the observed broadening of signal 3
1, 2, and 3 refer to species AlF2+, AlF2 (cis and trans isomers), and
+
0
AlF3 .
F- system. Selected spectra are shown in Figure 5a. At near
ambient temperatures, broadened signals of HF and its exchange
0
+
partners AlF3 and AlF2 indicate ligand exchange processes
between the free and coordinated ligands (see above). Lowering
the temperature causes the HF signal to narrow, until at ∼262
K its half-width becomes constant. The explanation for this
temperature dependence is the lowered rate of exchange between
0
HF and AlF3 /AlF2+; i.e., the intermolecular exchange becomes
0
implies their existence, the mer an fac isomers of AlF3 (aq)
frozen on the T2 time scale. (The chemical shift also shows some
could not be positively identified under our experimental
conditions. Similarly, while the existence of AlF52-(aq) implies
octahedral geometry, failure to detect AlF63- suggests that hasty
conclusions on this subject may not be wise. Nevertheless, the
constant chemical shift and intensity of 27Al NMR signals, found
previously13,26b and measured in this study at different cF/cAl
ratios (see Figure 2 caption), also support an unchanged
geometry for the higher complexes.
Comparison of the Al3+/F- and Al3+/OH- Systems. It is
interesting to contrast the behavior of the Al3+/F- system with
that of the industrially important Al3+/OH- system. Although
unambiguous proof is not as readily available as commonly
supposed, a variety of measurements indicate that Al(OH)4-(aq)
is tetrahedral.31a Given that OH- and F- are isoelectronic and
isochoric and show many parallelisms in their chemistry, in both
the solution and solid states, it is somewhat surprising that their
interaction with Al3+(aq) should be so dissimilar. As noted by
temperature dependence toward lower fields.) A similar decrease
0
is expected for the line widths of the other sites, AlF3 and
AlF2+, involved in the exchange. In fact, these peaks do start
to narrow as the temperature is lowered from 306 to 298 K
(not shown), but they broaden again at T < 287 K.
Although it is not obvious from the raw 19F spectra (Figure
5a), band shape analysis (Figure 5b) indicates that signal 2
(AlF2+) splits in two at T < 265 K. Signal 1 almost disappeared
under the envelope of signal 2 but is revealed by the numerical
analysis, with its correct intensity. The signals become slightly
narrower with decreasing temperature to the freezing point of
the solutions, ∼253 K. The most plausible explanation of the
splitting of signal 2 is that the exchange between the cis- and
+
trans-AlF2 complexes enters into the slow exchange regime
on the NMR time scale with decreasing temperature. If it is
assumed that the trans isomer is favored because of its more
symmetrical charge distribution, then the cis/trans ratio of the
+
AlF2 isomers at 255 K, estimated from the deconvolution
(31) (a) Watling, H. R.; Sipos, P.; Byrne, L.; Hefter, G. T.; May, P. M.
Appl. Spectrosc. 1999, 53, 415. (b) Watling, H. R.; Fleming, S. D.;
von Bronswijk, W.; Rohl, A. L. J. Chem. Soc., Dalton Trans. 1998,
3911.
shown in Figure 5b, is approximately 2:1. The line width of
signal 3 shows a dependence on temperature broadly similar to
0
that of signal 2. However, as the reactions of AlF3 are faster

Equilibria and Dynamics of the Al3+/F- System
Inorganic Chemistry, Vol. 39, No. 12, 2000 2537
Tuck32 this is a reflection of the very fine balance among the
strengths of interaction of Al3+ with the three hard donor ligands
H2O, OH-, and F-.
continues for the higher order complexes. Thus, Al(OH)63-(aq)
exists but only at very high concentrations (>10 M) of
OH-.31b,34 No reliable evidence for Al(OH)52-(aq) exists. In
contrast, as shown in this paper, AlF52-(aq) forms readily, yet
AlF63-(aq) remains unproven.
The values of log Ki(AlFi(3-i)+) show the normal regular
decrease with increasing i (Table 1), which is circumstantial
evidence for the preservation of octahedral geometry in this
Acknowledgment. We thank Dr. Miha´ly Braun for ICP
measurements and the Hungarian National Science Research
Foundation (OTKA), Project T 026115, for financial support.
series of complexes. In contrast, the values of log Ki(Al(OH)i(3-i)+
)
are 9.0, 8.7, 8.2, and 6.4 for i ) 1-4, respectively.33 This lack
of variation has been noted by many authors and has been used
as evidence of a change in geometry from the octahedral Al-
(H2O)63+(aq) to tetrahedral Al(OH)4-(aq). Where this change
occurs is unknown because of experimental difficulties associ-
ated with solubility and polymer formation. This dissimilarity
Supporting Information Available: Text describing the determi-
nation of the stability constants from 19F integral values and analysis
of kinetic data and figures showing 19F NMR spectra, typical distribution
diagrams for the Al- and F-fractions, and 19F NMR serial plot of a
magnetization transfer experiment. This material is available free of
charge via the Internet at http://pubs.acs.org.
(32) Tuck, D. G. In Chemistry of Aluminium, Gallium, Indium and Thallium;
Downs, A. J., Ed.; Blackie Academic & Professional: London, 1993;
p 430.
IC991248W
(33) Baes, C. F.; Mesmer, R. E. The Hydrolysis of Cations; Wiley: New
York, 1976; p 112.
(34) Sipos P.; May, P. M.; Hefter, G. T. To be published.