1192
J. Phys. Chem. 1983, 87, 1192-1201
Thermodynamic and Kinetic Studies of Hydroxo and Chloro Complexes of Iron( III)in EthanoVWater Mixtures Keith Brldger,+ Ramesh C. Patel," and Egon Matljevie' Department of Chemistry and Instltute of ColloM and Surface Science, Clarkson College of Technoiogy, Potsdam, New York 13676 (Received: July 30, 1982)
Recently it has been shown that uniform cubic hematite particles can be prepared by aging ferric chloride solutions at elevated temperatures in mixed alcohol/water media. In order to explain the precipitation process, we carried out thermodynamic studies of the following reactions in ethanol/water mixtures over a temperature range of 5-80 OC: Fe3+* FeOH2++ H+ ( K H )Fe3+ ; + C1- + FeC12+(Kl); FeC12++ C1- FeC12+(K2). The formation-dissociation reaction of (FeOHIz4+
===
2Fe3+
-2H'
+2H+
k
2FeOH2+& (FeOH)24+ kb
(KD= kf/kb)
was investigated as a function of pH by using the stopped-flow method. Over different pH ranges the overall reverse rate constant, k b , showed a direct, as well as an inverse, [H'] dependence, which allowed the elucidation of the mechanistic pathways in the formation of the dimer. The addition of alcohol enhanced the formation of the studied complexes. The obtained values showed excellent internal consistency and compared well with a limited number of results reported in the literature.
Introduction Recently it has been shown that colloidal dispersions consisting of uniform particles of metal (hydrous) oxides in general and of ferric oxides or oxyhydroxides in particular may be prepared by forced hydrolysis at elevated temperatures of the corresponding metal salts.' The composition and morphology of the precipitated solids are controlled by a number of experimental parameters, among which pH, temperature, and the nature of the anion play the most important roles. In some cases even a minor change in the composition of the aging solution may have a great effect on the properties of the resulting particles. Thus, "monodispersed" basic ferric sulfate sols were prepared from ferric sulfate solutions2 and hematite from ferric nitrate or perchlorate ~ o l u t i o n s . In ~ the presence of chloride ion both rodlike p-FeOOH and hematite particles with a variety of geometries, including spheres, have been ~ b t a i n e d . ~ It is to be expected that the addition of a solvent miscible with water should influence the nature of the products precipitated by aging of metal salt solutions. Indeed, cubic hematite particles of great uniformity have been prepared by hydrolysis of ferric chloride solutions in mixed alcohol/water media.4 In the presence of ethanol @FeOOH appeared first and hematite resulted from a slower phase transformation p r o ~ e s s .The ~ effect of the alcohol was explained in terms of the theory of Burton, Cabrera, and Frank,6 taking into consideration the complex formation of ferric ions in ethanol/water mixtures. For a more complete interpretation of the precipitation phenomena in mixed solvent solutions it is necessary t o have thermodynamic and kinetic data on the metal complexes which form in such media. Values for the equilibrium constants of the hydroxo7r8and chlorogJOcomplexes of iron(II1) in methanol are given in the literature. The corresponding data in the presence of ethanol are scarcer and no complete set of thermodynamic values for either hydroxo or chloro complexes is available. In particular, little experimental evidence can be found on changes that +Presentaddress: Martin Marietta Laboratories, Baltimore, MD 21227. 0022-3654/83/2087-1192$01.50/0
metal ions undergo in solutions at elevated temperatures (>50 OC).lo This information is needed in order to explain the precipitation phenomena which take place on forced aging at temperatures that commonly exceed 80 "C. It is recognized that knowing the composition of the solution is not sufficient to establish the mechanism of a pecipitation process. Careful kinetic studies of solute complex formation under conditions of solid-phase nucleation and growth are necessary. The species distribution data may, however, give an indication of the solutes that are involved in the precipitation reactions when the solvent composition is varied. For example, inclusion of ethanol in the reaction medium lowers the temperature at which the well-defined hematite particles are p r ~ d u c e d . ~ , ~ The purpose of this study is to provide thermodynamic and kinetic data of ferric hydroxo and chloro complexes in ethanol/water mixtures over a temperature range of 5-80 "C. This information should be useful in providing a better understanding of precipitation phenomena in mixed solvents, which are of interest in various applications and particularly in explaining corrosion phenomena of iron in contact with such media. Experimental Section Solutions. Stock solutions of ferric perchlorate were prepared by dissolving the anhydrous salt (G. F. Smith) in doubly distilled water and passing them through Nuclepore filters of 0.2-vm pore size. These solutions are stable over extended periods of time, either in the highly concentrated state (>2 M) or when the ratio of the added (1) MatijeviE, E. Acc. Chem. Res. 1981, 14, 22. (2) MatijeviE, E.; Sapieszko, R. S.; Melville, J. B. J . Colloid Interface Sci. 1975, 50, 567. (3) MatijeviE, E.; Scheiner, P. J . Colloid Interface Sci. 1978, 63, 509. (4) Hamada, S.; MatijeviE, E. J. Colloid Interface Sci. 1981,84, 274. (5) Hamada, S.; MatijeviE, E. J . Chem. SOC.,Faraday Trans. 1 1982, 78, 2147. (6) Burton, W. K.; Cabrera, N.; Frank, F. C. Philos. Trans. R. Soc. London, Ser. A 1951,243, 299. (7) Bowers, E. J.; Weaver, H. D. R o c . Indiana Acad. Sci. 1961, 71, 101. (8) Wada, G.; Kobayashi, Y. Bull. Chem. SOC.Jpn. 1975, 48, 2451. (9) Brykina, G. D.; Filippova, N. L.; Belyavskaya, T. A. Zh. Neorg. .. Khim. 1976,21, 2936. (10) Sapieszko, R. S.; Patel, R. C.; MatijeviE, E. J . Phys. Chem. 1977, 81, 1061.
0 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983
Hydroxo and Chloro Complexes of Iron(1I I)
perchloric acid concentration to [Fe3+Itotis at least 101.lo The total ferric ion contents in the highly concentrated stock solutions were determined gravimetrically as Fez03 after drying to constant weight. The more dilute ferric perchlorate solutions were standardized spectrophotometrically as the iron(II1) thiocyanate complex in acidic media.l' Throughout this work the test solutions were made up as follows. To a weighed-out amount of ethanol were added appropriate volumes of perchloric acid, hydrochloric acid, and sodium perchlorate. The flask was then filled with doubly distilled water, a little free volume being left for the iron(II1) stock solution. After the contents had been thoroughly shaken, the desired quantity of the ferric salt solution was admixed, the solution reshaken, and the flask filled with water up to the mark. The system was allowed to stand for 12 h to assure that no further volume contraction occurred; the solution was then made up to the mark again and weighed. The analysis was carried out approximately 1h after the final addition of water. The test solutions were prepared having ethanol volume fractions C#J~ i= 0.2, 0.4, and 0.6, which corresponded to mole fractions of ethanol, X 2 , of 0.072, 0.165, and 0.3. (In the entire paper the mole fraction of ethanol is given only with reference to water.) All glassware was soaked in concentrated hydrochloric acid for 12 h prior to regular cleaning procedures to remove possible iron deposits from the walls. Methods. Spectrophotometry. Spectral scans and absorbance measurements were made with a Perkin-Elmer Model 559A spectrophotometer; this instrument had a resolution of f0.001 absorbance unit. A thermostated cell holder was temperature controlled to f O . l "C by a Haake Model FK external circulating water bath. A minimum time of 20 min was allowed for the samples to come to thermal equilibrium before taking readings. The matched 1-cm quartz (Markson) cells were tightly stoppered to prevent evaporation losses, particularly at higher temperatures. Stopped Flow. A combined stopped-flow-temperature-jump spectrophotometer, described in detail elsewhere,12 was used to study the kinetics and thermodynamics of the dimerization of FeOH2+. Ferric salt solutions were diluted in the flow apparatus with iron-free solutions having the same ethanol mole fraction and an acid concentration either similar to or somewhat higher than the ferric solution with which they were reacting. Protolytic reactions of FeOH2+and Fe(OH)2+will be very much faster than the formation/decomposition of (FeOH)t+,whereas higher order ferric complexes may be expected to react at a much slower rate than the dimer. Thus, in all kinetic experiments the trace corresponded to the decomposition of the dimer (FeOH)24+.By choosing a suitable time scale (- 10-s total scan), we could exclude the other reactions. Data Treatment and Calculations Spectrophotometric Determinations. FeOP+. The method of Siddall and Vosburgh13was used to determine the equilibrium constant, KH, for the first hydrolysis step of Fe3+ KH
Fe3+
FeOH2+ + H+
where A is the absorbance of a solution having a total iron(II1) concentration [Fe3+], and q e 3 t and EFeOHZt are the extinction coefficients of the solvated ferric ion and of the first hydrolysis product, respectively, in the solvent mixture under consideration. In practice, conditions are chosen such that qe3t[Fe3+Itot 0, so that a plot of [Fe3+],/A vs. [H+] should yield a straight line from which KH and q e O H 2 t can be calculated in the absence of other hydrolysis products. The perchloric acid concentration was kept in large excess (>20:1) over [Fe3+],, in which case [H+] can be equated to the concentration of added perchloric acid, [H+l0. FeC12+. The' equilibrium constant K1 for the reaction Fe3+
(11) Hsu, P.H. Soil Sci. SOC.Am. R o c . 1967, 31, 353. (12) Patel, R.C.J. Chem. Instrum. 1976, 7,83. (13) Siddall,T.H.; Vosbwgh, W.C.J.Am. Chem. SOC.1951,73,4270.
K + C1- 2 FeC12+
(3) and the extinction coefficient fFeC12t for the monochloroiron(II1) complex were calculated from the absorbance of a ferric solution in the absence of chloride ions, A,, and in the presence of chloride ions, A. The reference absorbance is given by
A, = t'~~3t[Fe~+]tot
(4)
where dFe3t is a proportionality factor taking into account contributions from Fe3+,FeOH2+,and any ion pairs which may form in solvent mixtures having a low dielectric constant. When [H'] is sufficiently high to suppress hydrolysis, the law of mass conservation and the principle of mass action yield [C1-lbt/(A - AO)
1/(€FeC12t
l/f(eFeC12t
+
-
- €'~~3+)Ki[Fe~+]tot - Ki(A - A,))
(5)
When [Fe3+], >> [CI-1, data can be described to a good approximation by [Cl-I,t/(A - -40)= 1/(€F&+
- E'Fe3+)
1/((€FeCIzt -
€'~~3+)Ki[Fe~+]tot] (6)
A plot of [Cl-],,/(A - A,) vs. 1/[Fe3+],, should give a straight line from which the required constants can be obtained. Simultaneous Determination of FeC12+and FeC12+. In solutions where [Cl-1, is large compared to [Fe3+Itotthe dichloro ferric complex will form in measurable concentrations. For dilute ferric ion solutions at low pH the entire system is described by
& FeOH2++ H+ K Fe3+ + C1- 5F e C P
Fe3+
FeC12++ C1-
2FeC12+
(1)
(3)
(7)
Combining these equilibria with the respective mass balance requirements yields a cubic equation: (Y[C1-]3 + P[C1-]2 + S[cl-]
(1)
From the equilibrium and mass balance relationships one obtains
1193
where (Y
= KlKz
+y =0
(8)
1194
The Journal of Physical Chemistry, Vol. 87,No. 7, 7983
= -[cl-]tat(1
+ KH/ [H+10)
(84
The equilibrium chloride concentration [C1-] was derived numerically from eq 8 by using the Newton-Raphson method, which allows the species distribution to be calculated. The absorbance is given by
Absorbance data for two separate wavelengths, X1 and X2, were evaluated by using the multiparametric curve-fitting program CFT4A14with six parameters: K1, K,, €FeC12+(X1), q?&12+(X2), CF&~,+(X~),and 9a12+(X2). X1 was chosen such that the E values were of the same order of magnitude whereas absorbances measured at A, were predominantly due to FeC12+(i.e., €FeCl2+(X2) >> €FeC12+(X2)). Stopped Flow. Kinetics of Fission of (FeOWZ4+. Time-voltage data obtained from stopped-flow experiments were analyzed as reported earlier15with the exception that individual voltage values, V, were converted to the corresponding absorbances according to A = log (Vref/ v)
(10)
The reference voltage, Vref,obtained from a photomultiplier receiving light directly from the monochromator via a beam splitter, corresponds to the output voltage when only water is in the cell. The use of the beam splitter and of the reference photomultiplier compensates for lamp intensity variations during the course of a day. The time-absorbance data were considered to follow singleexponential curves AA = AA,[1 - exp(-t/r)]
(11)
in which AA is the absorbance change at time t, AA, is the total absorbance change associated with the reaction, and 7 is the time constant. The formation-dissociation reaction of (FeOH)24+may be represented as KH;-~H+
2Fe3+'
+2H+
k 5 (FeOH)24+
2FeOH2+
(12)
kb
The rapid protolytic reaction is followed by a slow dimerization step. When prehydrolyzed ferric perchlorate solutions are mixed with a sufficiently large excess of perchloric acid, the dimer disappears while [H+] remains nearly constant and equal to [H+],,. If immediately after mixing [H+] >> [FeOH2+]+ [(FeOH),4+],reaction 12 will proceed irreversibly from right to left exhibiting pseudofirst-order kinetics with 7-I = kb. At lower [H+l0,contributions from the forward reaction must be taken into consideration, which alters the kinetics to give the rate expression -d[(FeOH)?+]/dt = kb[(FeoH),4+]- kf[FeOH2+I2 (13) For small perturbations, the following equation results: -d6 [ (FeOH)24+] /dt = kb6[(FeOH)24+] - 2kf[FeOH2+]6[FeOH2+](14) The mass balance for iron(II1) species is given by [Fe3+Itot= [Fe3+]+ [FeOH2+]+ 2[(FeOH)24+]
(15)
(14) Meites, L. 'The General Multi-parametric Curve-Fitting Program CFT4". Hard-copy listings of the basic program and a number of modifications of it that serve a variety of different but related purposes, together with a 220-page manual of instructions, explanation, and documentation may be obtained by remitting $100 to the Computing Laboratory of the Departmentof Chemistry, Clarkson College of Technology, Potsdam, NY 13676. (15) Bridger, K.; Patel, R. C.; MatijeviE, E. Polyhedron 1982, 1, 269.
Bridger et ai.
or 0 = 6[Fe3+]+ 6[FeOH2+]+ 26[(FeOH)24+](15a)
If one assumes that the hydrogen ion concentration is constant during the reaction and that [(FeOH),4+] > 2[(FeOH)?+IR,one can show that AA, = ( K D / ~ ) ( ~ ( F ~ o-H2)€+' ~ + ~ 3 + ) l ( h f [ F e ~ + l E ~(21) )~
where
@ = KH/(KH+ [H'lf)
(22)
Under these conditions plots of AAm vs. (hf[Fe3+]&)2 should be linear. As [H+]t decreases and [Fe3+]ztincreases, the assumptions fail and the plots show curvature which is described by the following rigorous analysis. The electroneutrality condition gives
+
3[Fe3+]+ 2[FeOH2+] 4[(FeOH)24+]+ [H+] = [OH-] + [Clod-]* (23) where [C104-]*is the perchlorate ion concentration originating from the ferric perchlorate and perchloric acid; [OH-] is very small M) and was neglected. Combining eq 23 with the equilibrium and mass balance relations gives ~ K & H ~ ( [ F ~ ~ +KH[Fe3+IR[H+lR ]~)' + [H+]F([H+]R)2 - ([H+]R)3= 0 (24) 2K&H2([Fe3+]R)2+ KH[Fe3+IR[H+lR + [Fe3+]R([H+]R)2 - [Fe3+]Et([H+]R)2 = 0 (25)
The Journal of Physical Chemisfty, Vol. 87,No. 7, 1983
Hydroxo and Chioro Complexes of Iron(II1)
1105
TABLE I : Equilibrium Constants for FeOH" ( K H ) and for Fe2(OH)24+ ( K D )in Ethanol/Water Mixtures at Ionic Strength 0.5 Ma 1 0 3 ~M~ ,
a
x2
5.0 "C
15.0 "C
25.0 "C
35.0 "C
0.072 0.165 0.31
0.7 i 0 . 2 1.4 i: 0.2 3.4
1.5 i 0.3 1.8 4.7
2.5 3.5 i 0 . 5 7.3
4.4 5.6 i: 0.7 10.6
50.0 "C AH", kcal mol-' KD at 25 "C 8.0 10.3 19.1
9.5 f 1 . 2 7.9 i 0.4 7.0 * 0.8
4 5 0 t 80 2 6 0 t 50 70 i: 30
Errors are less than i 10%except where indicated.
0
I
I
0.02
0.04
0.06
CH'I (MI Flgure 1. Plots of [Fe3+]IA against [H'] according to eq 2 at 5, 15, 25, 35, and 50 OC, X 2 = 0.31; 1.1 = 0.5 M; [Fe3+],, = 2 X lo4 M; A = 350 nm.
Equations 24 and 25 were solved simultaneously with a two-dimensional Newton-Raphson procedure and values for KDand (e(F&H)24+ - ~ € ' F ~ S + ) Z were calculated from eq 18 with the aid of the program c ~ ~ 4 . l ~
Results Equilibrium Data. F e O I P . The equilibrium constants for the formation of FeOH2+in ethanol/water mixtures were determined from absorbances, measured over the wavelength range 340-360 nm, of solutions of varying perchloric acid concentration (0.005 5 [H+l0I 0.05 M) and total ferric concentrations (0.5 X 10-4-3 X M). The measurements were made at 5, 15, 25,35, and 50 O C for three different ethanol mole fractions, X 2 , with ionic strength held constant a t 0.5 M. Linear plots of [Fe3+],,/A vs. [H+J0,as expected from eq 2, were obtained for wavelengths 350 nm and longer; below this wavelength corrections had to be made for the small absorbance of the solvated ferric ion. Figure 1 shows the plots obtained for X 2= 0.31 a t 350 nm. The reversibility of the hydrolysis was checked by cooling samples from 50 to 25 O C , the elevated temperature having been maintained for -1 h; the deviations in absorbance values did not exceed 0.001 unit. The solutions stored at room temperature showed no change over a period of l week, although after l month some aging had
0
2
4
CFes+l~,,I'
6
8
xlO'M'
Figure 2. Amplitude data from stopped-flow experiments on dimer fission plotted according to eq 21. X , = 0.31; p = 0.5 M; T = 25 OC; A = 350 nm.
obviously occurred resulting in absorbance changes of approximately 5 1 0 % . Solutions heated 265 OC exhibited irreversible changes. Table I gives values for the hydrolysis constant, K H , obtained at ionic strength 1.1 = 0.5 M for several different temperatures and solvent compositions. The error in KH values is of the order of f10% except where indicated. The enthalpy values were obtained from van't Hoff plots of In K H vs. 1/T. (FeOmZ4+.Values for the dimerization constant, KD, were obtained from the stopped-flow amplitudes on mixing ferric salt solutions (0.1 c K~/[H+]: < 0.725; 0.05 c [Fe3+]Et/[H+]F5 0.20) and 0.5 M perchloric acid solutions having the same ethanol mole fractions. The measurements were made at 340 and 350 nm at a temperature of 25 O C with the ionic strength held constant at 0.5 M. Under these conditions t'FeS+ was negligibly small. Single-exponentialcurves were obtained over time spans of 10 or 20 s. Figure 2 shows the amplitude data for X z = 0.31 plotted according to eq 21. At [H+l0= 0.04 M a linear relationship is obtained as expected if [H+IR= [HI: and [Fe3+]$,>> 2[(FeOH)z4+]R.At lower acid concentrations the deviations from linearity enable measurement of KD. For X z = 0.31 these deviations are small (Le., KD is small); thus, data from solutions having relatively low
1196
Bridger et ai.
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983
TABLE 11: Enthalpies AH" and Equilibrium Constants for the Formation of FeC12+(K,) and for the Reaction FeCI2++ C1 + FeCI,' (K,) K , , M-' /1,M
x,
2.6 2.6 2.6
0.072 0.165 0.31
12.1a 25.5 65.1
14.0 30.6 74.6
18.1 38.5 99.2
23.7 51.3 130
31.3 67.9 177
3.7 3.7 3.8
0.5
0.072 0.165 0.31
7.0 i 0.7 14.1 39
8.9 2 0.9 18.3 i 1.6 47+ 3
12.8 i 1.0 26.0 i 1.8 69
18.5 t 1.5 38.4 i 2.4 1 0 5 r 14
27 f 3 48 t 11 170 i 30
4.9 r 0.4 5.0 r 0.5 5 i 1
0.5 0.5
25.0 "C
50.0 " C
35.0 " C
K,, M, M
x 2
0.5 0.5 0.5
0.072 0.165 0.31
a
25.0 "C 0.7 I 0.2 0.86 1.1
The values are i 5% except where stated.
35.0 " C 0.8 1.0 1.3
i
0.2
65.0 "C
80.0 "C
AH",
kcal mol-' i i i
0.5 0.5 0.6
M-I
50.0 "C
65.0 " C
80.0 "C
1.0 1.3 2.0
1.1 1.6 3.4
1.4 2.1 6 i 2
AH",
kcal mol-'
2.4 r 0.5 3.6 i 0.5 6 +1
The values are f 20% except where stated.
[H+] and relatively high [Fe3+Itotbecome important. Under these conditions there is a chance that some higher order ferric species may be present. Table I gives the values obtained for KD as a function of ethanol content for an ionic strength of 0.5 M at 25 "C. The large error in KD for X 2 = 0.31 is due both to the small value of the constant and to the complications mentioned above. The standard deviations of the best fits ranged from 0.005 to 0.0005 absorbance unit or were approximately equal to 4% when random errors were considered to be proportional to the magnitude of the measurements. FeC12+and Feel2+. Spectrophotometric titration measurements were used to determine the sequential equilibrium constants K1 and K2 for the formation of FeC12+and FeC12+,respectively. The value of K1 alone could be established when the ferric ion concentration was in large excess. Absorbances over the wavelengths 360-420 nm were measured at temperatures 25,35,50,65,and 80 "C M and 0.003 and 2 X for solutions having [Cl-1, = < [Fe3+Ibt< 0.03 M. Data were obtained for the three ethanol mole fractions (0.072,0.165,and 0.31) and for ionic strengths of 0.5 and 2.6 M (perchloric acid). All cases resulted in linear plots as expected from eq 5. Each value for K 1 was calculated from readings at five different wavelengths. The error in these determinations for p = 2.6 M is estimated to be
