Acid-Base Titrations of Goethite and Rutile Suspensions
rameters inherent in each model.3 Many of these models are also thermodynamically equivalent when interpreted in terms of still another mode1.61~In a predictive sense, the various models are very successful but their underlying physical and chemical descriptions have yet to be verified.8 Hence, our mechanistic understanding of hydrous oxide interfaces is far from complete. In this respect our knowledge of hydrous oxide surface chemistry is deficient compared to the related phenomena of cation exchange and polyelectrolyte chemistry. This results partly because a larger suite of techniques are more routinely employed when these phenomena are investigated. The variety of data which results has led to the observation that none of the popular theories concerning polyelectrolyte behavior is completely a d e q ~ a t e . ~In contrast, the charging behavior of hydrous oxides has been most often investigated by only acid-base titration or electrophoresis and often these techniques are not employed in the same study. It is not too surprising then that in those studies where other types of data have been collected, such as measurements of counterion adsorption densities on anatase'O and the acid-base behavior of magnetite at higher temperatures,l' the popular theories concerning hydrous oxide surface chemistry appear to be inadequate as well. Hopefully, as an even wider variety of techniques are applied to the study of hydrous oxide surfaces, the available models will evolve to take this more diverse data base into account. A useful technique in this regard is titration calorimetry whereby heat changes accompanying adsorption processes can be measured. Polyion investigations have employed this technique for some time. For simple carboxylic acid@ and protonated amines,13differences between successive ionizations in the enthalpies determined by titration calorimetry could, in most cases, be explained by using the electrostatic correction factors from the KirkwoodWestheimer theory. The applicability of this theory can often be extended to larger ions if the bulk dielectric constant of water is replaced by an empirically determined effective dielectric ~ 0 n s t a n t . l However, ~ as polyions become more complex, conformational, counterion, and solvation effects become significant and simple as well as more complex theories15 fail to explain the observed thermodynamic data adequately (the so-called polyelectrolyte effect). An extreme example comes from humic acid titrations where measured enthalpies and calculated entropies are found to be significantly different from simple solution analogues,16although titration calorimetry can differentiate between the phenolic and carboxylic acid functional groups present.17 Titration calorimetry has also been used extensively to investigate cation exchange phenomena. Differences in the free energy, enthalpy, and entropy functions for Cs+, (6) Sposito, G.J. Colloid Interface Sci. 1983, 91, 329-340. (7) Sposito, G. The Surface Chemistry of Soils; Oxford University Press: New York, 1984; Chapter 5. (8) Morel, F. M. M. Principles of Aquatic Chemistry; Wiley-Interscience: New York, 1983; Chapter 8. (9) Lewis, E. A.; Barkley, T. J.; Reams, R. R.; Hansen, L. D.; St. Pierre, T. Macromolecules 1984, 17, 2874-2881. (10) Sprycha, R. J. Colloid Interface Sci. 1984, 102, 173-185. (11) Blesa, M.A.; Figliolia, N. M.; Maroto, A. J. G.; Regazzoni, A. E. J. Colloid Interface Sci. 1984, 101, 410-418. (12) Christensen, J. J.; Izatt, R. M.; Hansen, L. D. J.Am. Chem. SOC. 1967,89, 213-222. (13) Christensen. J. J.: Izatt. R. M.: Wrathall. D. P.: Hansen. L. D. J. Chi& SOC.A, 1969, 1212-1223. (14) Schwarzenbach, G.Pure Appl. Chem. 1970,24,307-334. (15) Manning, G.S. J.Phys. Chem. 1981,85,870-877. (16) Choppin, G. R.; Kullberg, L. J. Inorg. Nucl. Chem. 1978, 40, 651-654. (17) Perdue, E. M. Geochim. Cosmochim. Acta 1978, 42, 351-358.
Langmuir, Vol. 2, No. 5, 1986 583
Na+, and Li+ exchange with H+ on zirconium phosphates have been rationalized in terms of the size and hydration number of these cations.18 The exchange reaction is initially exothermic but becomes progressively more endothermic while the associated entropies begin negative and become more positive. Initially, the cations exchange with their hydration sheaths largely intact, with Li+ being least exothermic because it loses the most water. As the reaction proceeds, the cations give up more of their hydration sheaths resulting in net endothermic heat changes and more positive entropies. Titration calorimetry has also been used to characterize the heterogeneous site distribution which exists on cation-exchanging A l - s i l i ~ a t e s . ~ ~ ~ ~ ~ The purpose of this study is to discuss results from calorimetric acid-base titrations of goethite and rutile. This combination of techniques is especially attractive because free energy and enthalpy data can be obtained from the same sample and the required instrumentation is readily combined and computer-interfaced.21 This is part of a larger study that was also concerned with anion adsorption onto goethite and these results are discussed elsewhere.22 It will be demonstrated that combined calorimetric and acid-base titrations extend interpretations beyond those possible from isothermal acid-base titration data alone.
Experimental Section Goethite was synthesized according to a procedure of Atkinson et al.,23using ACS reagent grade chemicals and Milli-Q HzO. Ferric nitrate (8.2 L, 0.83 M) was partially neutralized with 5 M NaOH to an OH/Fe ratio of 2.0 in a polypropylene container and the resulting solution was aged for 2 days at room temperature. Then, over a 3-h period, additional 5 M NaOH was added until the pH reached 12.5 and this slurry was aged at 60 "C for 6 days. The solid was washed by settling and decantation until no further decrease in supernatant conductivity was observed (-5 wS/cm). The solid was then freeze-dried, ground slightly with an agate mortar and pestle, and stored in a desiccator. A yield of -450 g ensured that the same batch could be used for all experiments. The Nz, BET surface area was 81 m2/g and electron microscopy revealed acicular, rodlike particles with approximate dimensions of 60 X 20 nm. X-ray diffraction confirmed the solid as goethite. Rutile was obtained from Tioxide International Ltd. (Cleveland, England) in dry form. It was washed by using centrifugationdecantation until a stable conductivity (- 5 pS/cm) was attained. The Nz, BET surface area for this sample was 28 m2/g. A n o n a c Model 450 isoperibol calorimeter (Tronac, Inc., Orem, UT), modified to include pH electrodes and interfaced through a two-channel, 16-bit A/D converter to an Apple IIe computer, was used to obtain the calorimetric data. Details of the interface design and calibration are given elsewhere.22 Suspension preparation was as uniform as possible to keep aging effects (whether biological, chemical, or physical) relatively constant. Briefly, dry solid was added to Milli-Q water in 500-mL polycarbonate centrifuge bottles to attain a suspension concentration of 10 g/L. Standardized, 0.2 M HN03 (ultrex grade) was then added to decrease the pH to 4.5. Solid NaN03 (ultrapure) was added if a particular ionic strength was desired. Suspensions were ultrasonically dispersed for a total time of -24 h. During this period, pH increased slightly but was adjusted with standard acid. The pH after fiial dispersion was 4.2-4.5. One to two weeks were allowed before a particular suspension was used for titration ~~
~~~
(18) Clearfield, A.; Tuhtar, D. A. J-Phys. Chem. 1976,80,1302-1305. (19) Gouldiw, - K. W. T.: Talibudeen. 0.J. Colloid Interface Sci. 1980. 78, 15-24. (20) Talibudeen, 0.; Goulding, K. W. T. Clays Clay Miner. 1983,31, 37-42. (21) Machesky, M. L.;Bischoff, B. L.; Anderson, M. A. unpublished results. (22) Machesky, M. L.Ph.D. Dissertation, University of WisconsinMadison, 1985. (23) Atkinson, R. J.; Posner, A. M.; Quirk, J. P. J. Inorg. Nucl. Chem. 1968,30, 2371-2381.
584 Langmuir, Vol. 2, No. 5. 1986
Machesky and Anderson
and any particular preparation was exhausted in less than a month. Aliquots filtered from these suspensions contained f5%) occurring at extreme pH (9.5) values. This agreement is considered to be satisfactory given the uncertanties inherent in the measured pH values, titrant delivery volumes and levels of impurities in the blank solutions. Formulas used to correct the measured heat changes for nonchemical effects are similar to those given elsewhere32 as are corrections for extraneous chemical reactions%which take the form i=l
(4)
Where Aai = change in the fraction of species i between the measured initial and final pH values for a particular interval, AHi = heat of formation for the ith species, CTA = total concentration of component A, and V = volume. The largest chemical correction term (particularly at pH 9) was due to water formation. Corrections (in r terms of acid or base consumed and heat changes) associated with shifts in dissolved carbonate and Fe equilibria were insignificant at the and lo-* M total concentration levels which were assumed to be present, respectively. These concentrations were estimates of those present in our aged goethite slurries before acid-base titration. Simulations (arbitrary manipulation of CTHZCo3 and CTFe KWO in eq 2) revealed that total concentrations 10-20 times greater are required to produce significant effects (>5%). (aH+)'(y - 1) + 1 (2) Dissolved Ti was assumed to be absent. Subtraction of Where X = volume of base theoretically required to attain chemical and nonchemical heat correction terms from an observed pH value; CAo = [ ( u H + ) / ( ~+ I)]- [K,O/(UH+)(T solution blank determinations left residual heats of f 1 6 - l)]= initial concentration of strong acid present; CTHzC03 mJ, which are in the range of instrument noise.21 The end = total carbonate concentration assumed to be present results of the theoretical blanking procedure are moles of during the titration; aHCo3-,a C O Z- = proportion of total H+ adsorbed or desorbed by the solid and the correat a particular pH carbonate present as HC03- or &032sponding heat change. Evidence from our laboratory34 confirms a previous which suggested that the most significant exper(24) Bates, R. G. Determination of p H . Theory and Practice, 2nd ed.
-"I
Wiley-Interscience: New York, 1973; Chapter 4. (25) Berube, Y. G.; De Bruyn, P. L. J . Colloid Interface Sci. 1968,2%, 92-105. (26) Breeuwsma, A,; Lyklema, J. Discuss Faraday SOC.1971, 52, 324-333. (27) Yates, D. E.; Healy, T. W. J . Chem. Soc., Faraday Discuss. 1 1980, 76, 9-18. (28) Huang, C. P. In Adsorption of Inorganics at Solid-Liquid Interfaces; Anderson, M. A,, Rubin, A. J., Eds.: Ann Arbor Science: Ann Arbor. MI. 1981: Chanter 5. (29j Brewer, S. Soiving Problems In Analytical Chemistry; Wiley: New York, 1980; pp 179-187.
(30) Butler, J. N. Ionic Equilibrium-A Mathematical Approach; Addison-Wesley: Reading, MA, 1964; Chapter 7. (31) Smith, R. M.; Martell, A. E. Critical Stability Constants; Plenum Press: New York, 1977;Vols. 3 and 4. (32) Hansen, L. D.; Lewis, E. A.; Eatough, D. J. In Analytical Solution Calorimetry; Grime, J. K., Ed.: Wiley-Interscience: New York, 1985; Chapter 3. (33) Holmes, F.; Williams, D. R. J. Chem. SOC.A 1967, 729-731. (34) Zeltner, W. A., University of Wisconsin, personal communication, 1985.
Langmuir, Vol. 2, No. 5, 1986 585
Acid-Base Titrations of Goethite and Rutile Suspensions 45
I
;40 A
E
\
6 35
c,
t 4
5
6
7
8
9
1
0
PI’
Figure 1. Proton adsorption (+), desorption (a),and combined ( X , fl SD) enthalpies as a function of pH for goethite (10 g/L in 0.014.1 M NaN03). Adsorption enthalpies are exothermic (-1
and desorption enthalpies endothermic (+). Combined enthalpies are absolute value weighted averages for adsorption and desorption.
imental variable affecting the zero point of charge (zpc) observed for goethite is the length of purging with C02-free gas. Most previous studies have used pretitration purge times of a few days at best whereas purge times of more than a week can increase the zpc from 8 to 9.5 for as yet an unexplained reason.% At present our calorimeter is not equipped for purging but titrations performed at different ionic strengths (0.01-0.1 M) gave an apparent zpc of 8.0 f 0.2, which agrees with independent determinations for which short (e1 week) purge times were employed to eliminate COPu For rutile, the apparent zpc obtained was 6.0 f 0.2 which is near values obtained by other investig a t o r ~ . *Purging ~ is probably not as critical in this case, however, since rutile is negatively charged at pH values where HCO, and CO2- are the dominant carbonate species and hence adsorption of these anions is likely to be less favorable than for goethite suspensions at similar pH values. Because suspensions were aged near pH 4 and titrations performed rapidly (10 and assigning the midpoint pH (e.g., 4.5) to the calculated average. Each enthalpy value represents an average of at least 20 determinations for goethite and 4 for rutile. Some of the averaged data are attempts to measure an ionic strength dependence (0.01-0.1 M) with NaNO, as the ionic strength buffer. However, no consistent differences between these ionic strengths were obtained given the variability between experiments. Not included in the goethite averages are a number of experiments with NaC104 (0.01-0.1 M) as the ionic strength buffer. These additional data do not change the averages (35) Evans, T.D.; Leal, 3. R.; Arnold, P.W. 1979, 105, 161-167.
J. Electroanal. Chem.
Figure 2. Proton adsorption (+), desorption (a),and combined (x, fl SD) enthalpies as a function of pH for rutile (10 g/L in 0.01-0.1 M NaNOs). Adsorption enthalpies are exothermic (-) and desorption enthalpies endothermic (+). Combined enthalpies are absolute value weighted averages for adsorption and de-
sorption.
l1
+ -25
-40
I
-.io
kJ/mol
I X
5 7
20
+
i
~
50
65
X
+
X
+ + +
5
35, X .
X
X X
.
’+:.
+ +
+
x x
x
Figure 3. pH as a function of proton desorption enthalpy (m), free energy (X), and entropy (+, TAS) for goethite. The axes intersect at the zpc and 0 kJ/mol.
significantly. Averaging many determinations has been recommended as the best way to interpret humic and fulvic acid titration^.^^ Also, averaging acid and base titration data together should tend to “cancel out” extraneous reactions not included in the theoretical blank. For both solids, enthalpies are largely reversible (i.e., absolute values are similar) when partitioned according to the following scheme: Proton Adsorption
+ H+F! SOH2+(exothermic) SO- + H+ 2 SOH (exothermic)
SOH
(5) (6)
Proton Desorption SOH2++ OH-
+ H 2 0 (exothermic) SOH + OHSO- + H 2 0 (exothermic) H,O OH- + H+ (endothermic) SOH2+2 SOH + H+(endothermic) SOH + SO- + H+ (endothermic) ~t
SOH
(7) (8) (9)
(10) (11)
To obtain reversibility, proton desorption enthalpies required correction for the heat of water dissociation. Desorption enthalpies for both solids were endothermic (+) and adsorption enthalpies exothermic (-) over the entire pH range examined. Both enthalpy curves exhibit a (36)Gambel, D. S. Can. J. Chem. 1972,50, 2680-2690.
Machesky and Anderson
586 Langmuir, Vol. 2, No. 5 , 1986
change of slope near the apparent zpc's and adsorptiondesorption irreversibility is most apparent in this region. From pH 4 to 9 goethite enthalpies are larger than those for rutile in accordance with the apparent zpc's and the stronger acidic character attributable to rutile.2 Data are scarce above the apparent zpc for goethite and below that for rutile because of the difficulty in obtaining accurate pH data below pH 4 above pH 10. Proton desorption heats become more endothermic as the apparent zpc's are approached from low pH values. Above the apparent zpc's however, the enthalpy curves exhibit different trends. Proton desorption enthalpies become less endothermic for goethite and more endothermic for rutile. Below the apparent zpc's, enthalpy trends are consistent with electrostatics. As the surface becomes more positive, proton desorption should become more favorable (less endothermic). Following the admittedly nonthermodynamic assumptions required to calculate the electrostatic component of the free energy,37the electrostatic contribution to the enthalpy is m,1,,= FAZT(d\k,/dT), + FAZ\k, (12)
++ +
Y X
8
+
9
+
X
8
P"
+
X
X
7 8
-25
-40
-10
k J/mo 1
5
2Q
35
50
65
5
+
++
mX X X
3
Table I. Constants and Equations Used for the Constant Capacitance Model Calculations constants surface area, m2/g
goethite 81
rutile 28
Where F = Faraday unit of charge; AZ = change in charge sites/nm2 16.8 12.24 of the surface due to the adsorption reaction; T = temdensity, g/cm3 4.28 4.26 perature (K); (d\k,/dT), = temperature coefficient of the suspension concn, g/L 10 10 suspension vol, L 0.05 0.05 surface potential (ao) at constant pressure; and FAZ\ko = 8.0 ( i 0 . 2 ) 6.0 ( i 0 . 2 ) apparent zpc electrostatic contribution to the Gibbs free energy (AGelw). ionic strength, M 0.05 0.05 Equation 12 is a form of the Gibbs-Helmholtz relationtemp, " C 25.0 25.0 ship.37 The electrostatic enthalpy contribution can be equations larger or smaller than the electrostatic free energy, depH >zpc pH ACe1,. dissociation constants (Q) q(H+)/(XT + q ) (X, - q)(H+)/q However, titration data obtained for magnetite at different free energy -1.364 log Q temperatures (30,50,80 "C) suggest that the surface potential temperature coefficient is small and negative." Figures 3 and 4 summarize the thermodynamic paramThis implies that AHelecC AGel, although much more data eters for proton dissociation from goethite and rutile, refor various solids is needed to confirm this generalization. spectively. Enthalpy data are the weighted average values Acid-base titrations at different temperatures can also from Figures 1 and 2. Free energy values were calculated be used to estimate surface protolysis enthalpy values. by using the constant capacitance m0deP9~and the conChanges in zpc with temperature for hydrous oxides have stants and equations from Table I along with representbeen investigated in several s t ~ d i e s . " , ~ The ~ ~rela~ ~ ~ ~ ~ative acid-base titration data. Entropy functions ( T A S ) tionship were obtained by difference from linear regression fits to the AG and AH data on either side of the zpc. The (0.5pKW")- pH,,, = (4.606RT)-'AH' - (4.606R)-lAS' magnitude of the free energy values is a function of the (13) surface site density which is a fitting parameter. However, has been used to calculate thermodynamic parameters under the assumption that the slope of the total free energy (AH'and AS') that describe the following reaction: function is independent of the surface site density, interpretations can be made concerning trends in the therSO- + H 2 0 + H+ t+ SOH,+ + OH(14) modynamic parameters. Free energy data are similar to those published (usually as pK values) previously.40 Below For rutile, the difference between the neutral point for the zpc, enthalpy data for both solids can be qualitatively water (0.5pKW0)and the zpc was found to decrease with interpreted as being due to electrostatics as mentioned temperat~re?~ while for magnetite the opposite trend was above. Rutile proton dissociation enthalpies continue to found.11y3' Subtracting the heat of water formation from increase above the zpc (though with lesser slope) again in eq 14 makes it possible to compare the resulting enthalpy accordance with electrostatics as evidenced by the correvalues with those obtained in this study. For rutile the sponding total free energy values. For goethite, however, enthalpy of -42 kJ/mol from eq 14 is approximately twice enthalpies decrease above the zpc while free energy inthe value obtained near the zpc in this study (-22 kJ/mol). creases. Differences in the enthalpy values between the Literature comparisons are not available for our goethite two oxides are probably due, at least in part, to differences data but surface protolysis enthalpies for magnetite (also in water structuring and counterion interaction. an iron oxide) corresponding to eq 5 and 11 are -28.7 and Below the zpc, NO3- is associated with proton desorption +32.8 kJ/mol, respectively. as SOH2+N03-+ OH- e SOH + H30+ + NO3- (15) (37) Guggenheim, E. A. Thermodynamics, 5th ed.; North-Holland: Amsterdam, 1967; Chapter 8. Above the zpc cations participate as (38) Tewari, P. H.; McLean, A. W. J . Colloid Interface Sci. 1972, 40, 267-272. (39) Tewari, P. H.; Campbell, A. B. J . Colloid Interface Sei. 1976,55. 531-539.
(40) sigg,
L.;Stumm, W. Colloids Surf. 1981, 2, 101-117.
Acid-Base Titrations of Goethite and Rutile Suspensions SOH
+ OH- + Na+
$
SO-Na+ + H30+ (16)
Langmuir, Vol. 2, No. 5, 1986 587 differences, especially since the contrast between the enthalpy curves for goethite and rutile is most apparent on the negative side of the zpc. However, the absence of a measurable ionic strength dependence does not contradict arguments that the water structuring ability of rutile is greater than that of goethite at similar pH and ionic strength values. Analogies to these qualitative interpretations exist in the polyion literature. In comparing C1- and Clod- as counterions during the acid-base titration of poly(viny1amine) salts, it was observed that enthalpies were greater with C1due to its greater screening power (closeness of approach) for the polyion ~ h a r g e .Similarly, ~ for negatively charged maleic acid copolymers, Li+ was observed to disrupt water structure to a greater extent than the tetramethylammonium i m because of its ability to bind to the COOgroups.46 Similar analogies exist in the cation-exchange literature18 and were briefly summarized in the introduction.
The importance of counterions in the charging behavior of hydrous oxides is well d o ~ u m e n t e d . ' Enthalpy ~ ~ ~ ~ ~ ~data ~ seem to reflect this interaction in a more obvious manner than acid-base titration curves. Apparently, the enthalpy associated with Na+ adsorption onto goethite is sufficiently exothermic to exceed the electrostatic attraction that the desorbing proton experiences. For rutile, Na+ adsorption is less exothermic. Below the zpc, NO< desorption occurs which supplements the endothermic proton desorption reaction. This endothermic supplement appears greater for goethite because the enthalpy values increase at a slower rate as the zpc is approached. Trends in the entropy function reflect the increasing order or disorder of the interfacial region which, in related cation exchange18and polyion s t ~ d i e swas , ~ shown to be due, in part, to changes in water structure. Above the zpc for both oxides, the interface is becoming more ordered as the pH increases because of the combined sturcturepromoting effects of the increasing negative surface charge Conclusions and associated counterbalancing cation a d ~ o r p t i o n . ~ ~ Combined calorimetric and acid-base titrations allow Below the zpc for goethite, the entropy function becomes the extent of proton adsorption and the accompanying heat more positive (increasing disorder) away from the zpc due changes to be obtained from the same sample. These two to the structure-disrupting influence of NO
