Langmuir 1993,9, 3457-3460
3457
Enthalpies of Reactions at the Metal Oxide/Aqueous Interfacet N.Kallay; S. &lac, and G. Stefan% Laboratory of Physical Chemistry, Faculty of Science, University of Zagreb, P.O. Box 163, 41001 Zagreb, Croatia Received July 28, 199P A detailed thermodynamicanalysisof simultaneoussurfacereactionsis presented, with a special emphasis on the definition of standard enthalpies. An experimental study of the surface reactions at the anatasel water interface is also reported. Generally, the reaction enthalpy is defied as the ratio of the reaction heat and its extent. The latter cannotbe calculated unlessthe stoichiometricequationsand corresponding extents of all processestaking place are known. According to the surface complexation model, the surface charge is a result of protonation and deprotonation of amphoteric surface sites. In the case of surface reactions, an additional problem is the electrostatic effect on the enthalpies. In order to solve the above problems, a new design of the calorimetric experiment is proposed the electrostatic contributions to the enthalpy will cancel if the difference between initial pH of the suspension and point of zero charge (PAC.) equals the difference between final pH and p.2.c. In such a case, one obtains the difference in standard enthalpies AbHO-AJI” which, for anatase, was found to be 14.7kJ mol-’. This value agrees well with those obtained from potentiometricmeasurements of the temperaturedependence of p.z.c. (14.6kJ mol-’). The point of zero charge is determined by the so-called “mass titration method”,originally proposed by Noh and Schwarz. Thismethod yieldsmore accurateP.Z.C. valueswithrespecttoother methodsand consequently results in a more accurate value of enthalpy.
Introduction The characterizationof surface reactions at metal oxide/ water interfacesinvolvesspecificationof surfacereactions. The surface complexation model assumes formation of charged surface groups by protonation and deprotonation of amphoteric surface sites and also the association of charged surface groups with counterions.lb As to the enthalpy, two approaches are common in the literature, i.e. direct calorimetricexperiments&l0and measurements of the temperature dependency of the point of zero charge.11-16 In addition to the relatively low accuracy of the calorimetric experiments with the suspension, one meets the problem of computing the reaction enthalpy from the overall heat, which is the sum of heats of all reactions taking place in the calorimeter. When, for example, a base is added to an acidic suspension, several reactions (neutralization, creation of negative sites, disappearance of positive sites, and, frequently, the counterion association/dissociation)are taking place. Accord+ Sponeored by US-Croatian Grant DOE JF 969. Abstract published in Advance ACS Abstracts, November 1, 1993. (1) Stumm, W.; Huang, C.P.; Jenkins, S.R. Croat. Chem. Acta 1970, 42, 223. (2) Bmumma, A.; Lyklema,J. J. Colloid Interface Sci. 1973,43,437. (3) Hohl,H.; Stumm, W. J. Colloid Interface Sei. 1976,55,281. (4) Stumm, W.; Kummert, R.; Sigg, L. Croat. Chem. Acta 1980,53, 291. (5) Dzombak, D. A.; Morel, F. M. M. Surface Complexation Modeling; A Wile~IntereciencePub~cation;John Wiley and Sons: New York, 1990. (6) MacheaLy, M. L.; Andereon, M. A. Langmuir 1986,2, 682. (7) Wierer, K. A.; Dobid, B. J. Colloid Interface Sci. 1988,122,171. (8)De Keizer, A.; Fokkink, L. G. J.; Lyklema, J. Colloid Surf. 1990, 49, 149. (9) Macheeky, M. L.; Jacobs, P. F. Colloid Surf. 1991,53, 297. (10) Macheaky, M. L.; Jacobs, P. F. Colloid Surf. 1991,53, 315. (11) Berube,Y. G.; de Bmyn, P. L. J. Colloid Interface Sci. 1968,27,
ingly, the task of evaluating the enthalpy change of a particular reaction is all but simple. The commonpractice, to divide heat with the amount (“moles”) of the surface charges created in the experiments, does not lead to a reaction enthalpy of a specified reaction, as would be the case with all other (bulk) reactions.l6 Another problem is related to the electrostatic contribution to the enthalpy. The shortcoming of the second approach, temperature dependency of the point of zero charge, is the low accuracy of data and, sometimes, an ambiguous assignment of the reaction enthalpy. The aim of this study was to design properly the calorimetric experiment, Le. to control extents of surface reactions so that the true reaction enthalpies are obtained. The problem of electrostatic contribution to the enthalpy will also be taken into account. The accuracy of the point of zero charge determination is improved by applying the so-called “mass titration method”.”
Theoretical Section Calorimetry. According to the surface complexation model, the following reactions will be considered
- + + -
MOH + H+ MOH
MOH;;
MO-
H+ OH-
H+;Kbo;A P ; Ata
0743-7463193/2409-3457$04.0010
(1) (2)
H,O; Kno;A,,HO; At,,
(3) where M denotes metal at the solid surface and Kr0 the equilibrium constant, A,.?€O the standard reaction enthalpy, and A& the change of the extent of reaction r. The equilibrium constants are given by
305.
(12) Tewari,P. H.; Campbell,A. J. Colloidlnterface Sei. 1976,66,531. (19) Fokkink, L. G. J.; de Keizer, A.; Lyklema, J. J. Colloid Interface Sci. 1989,127, 116. (14) Bleaa,M.;Maroto, A.; Regazzoni,A.J. Colloidlnterface Sci. 1990, 140, 287. (15) Koemulaki, M.; Matysiak, J.; Szczypa, J. To be submitted for publication.
Kao;AJP; Ata
(4) (16).Milla, I.; CvitaB, T.; Homann., K.; Kallay, N.; Kuchitsu, K. Quuntites, Unites andSym&& inPhysical C h e m k t r y ; I U P A ~ B l a c h d Scientific Publications: Oxford, 1988. (17) Noh, J. S.; Schwarz, J. A. J. Colloid Interface Sci. 1989,130,167.
0 1993 American Chemical Society
Kallay et al.
3458 Langmuir, Vol. 9, No. 12, 1993 Kbo = e
rMO
- 'H+
(5)
~MOH
Kn0 = l/Kwo = (aH+aOH-)-l (6) where r is the surface concentration (r = ns/A, amount divided by surface area) of active sites, $ is the electrostatic potential at the O-plane in which charged surface groups are located, and F, R and T have their usual meaning, while Kwois so-called "ionic product of water". Since the experiments will be performed in the vicinity of the point of zero charge (P.z.c.), i.e. at the low surface potentials, the counterion association will be neglected. Such an approximation is supported by the concept of "intrinsic surface equilibrium constants" and also by considering the statistical distribution of counterions around the charged surface g r o ~ p s . ' ~ J ~ The (hypothetical) relative activities of ions, ai, in the solution are defined as (7)
(where ci is their concentration and co = 1 mol dm-9 and can be estimated by means of the Debye-Hiickel limiting formula for the activity coefficient,yi, provided the ionic strength is low enough (forinstance,the activity coefficient for I , = 10-4 mol dm3 is 0.967). The interpretation of experimental data requires knowledge of the relationship between measured values and relevant thermodynamic functions. Generally, the reaction enthalpy is definedlBas
aH = QJAS (8) where Qp is the heat of reaction measured at the constant pressure and A t is the change of the extent of reaction. For a system in which the change of the amount of component i, Ani, is due to only one process, the extent of that reaction, At, is given by16 At = Ani/vi (9) By definition, the stoichiometriccoefficient,Y, is negative for reactants and positive for products. Accordingly, the extents of surface reactions 1 and 2 are defined as Ala =
A A~MoH*+
(10)
*MOH?+
."
(11) VM@
where A is the surface area of a solid oxide. The total , changes of the amounts of H+ and OH- ions ( A ~ H +AnoH-) are due to the addition of acid or base; they depend on the extents of all three reactions in the calorimeter so that AnH+
- Ata + Atb - Ahs, = Y1
(13) where V denotes the volume of the system, AnH+(add)and AnOH-(add) are the amounts of added acid and base, respectively. The initial and final states are denoted by (18) Kallay, N.; Tomib, M. Langmuir 1988,4, 559. (19) Tomib, M.; Kallay, N. Langmuir 1988,4, 565.
subscripts 1 and 2, respectively. Equations 12 and 13 are general, it is obvious that if one adds base to the suspension in a calorimeter that AnH+(add)= 0. By combinationof eqs 4, 5, and 10-13, the following relationship is obtained
The ratio Kao/Kbois related to the point of zero charge by
Surface potential in the vicinity of P.Z.C. can be approximated by using the Nernstian approachm *o=
- pH) a
RTFIn lo(pH,,
The Nernstian approach is based on the linear relationship between the surface potential and pH, independent of the ionic strength. However,the values of surface potentials, calculated by using the surface complexation model, are always lower than RT In 10/Fand decrease with the ionic strength.m*21This effect is considered by the coefficient a in eq 16. Relationships 14-16 yield =-~O(~-~)(~PH~PHS-PHI)
(17)
b['
Equation 17 gives the ratio of Ata and &. These extents are equal in magnitude but opposite in sign
(18) in two cases. The first one is the ideal Nernstian behavior i.e. when a = 1. However, such a condition cannot be achieved, by only approached to a certain degree. The second case will be met if the experimental conditions are properly chosen. If the additions of base (or acid) are chosen so that the mean of the initial and final pH values equals P.Z.C. AEb
the second factor in the exponential term of eq 17 will become zero. In any case, the error due to the accuracy of pH measurements and P.Z.C. determination is reduced as the surface exhibit the behavior closer to the Nernstian concept. This condition can be experimentally achieved by performing the experiments at lower ionic strengths. The measured heat Q is a s u m of products of the particular reactionsenthalpies and correspondingchanges in extents of reactions
It is obvious that the values of A& and A& cannot be simply evaluated from the measured overall heat. One possibility is to design the experiment so that initial and final pH values are "symmetrical" with respect to P.z.c., as described by eq 19. In such a case, according to eqs 18-20, one can obtain the enthalpy difference A& - AaH =
Q-
A l p At,
(21)
b['
The extent of neutralization (eq 3) can be obtainedfrom the initial and final pH values via eq 13. Once the value (20) Blesa, M. A.; Kallay, N. Adv. Colloid Interface Sei. 1988,28,11. (21) Kallay, N.; BabiC, D. Colloid Surf. 1986, 19, 375.
Langmuir, Vol. 9, No. 12, 1993 3459
Reactions at Metal Oxidelwater Interfaces of A&, is known,one calculates A&, via eqs 12 and 18 so that the enthalpy difference A f l - A& can be evaluated by using the literature data for A& The above procedure does not enable the evaluation of the single reaction enthalpies, only their difference can be obtained, just as in the case of temperature dependency of the P.Z.C. which will be discussed later. The next problem is the electrostatic effect on the enthalpies of the surface reactions. The enthalpy of particular surface reaction can be separated into an electrostatic, Afi(e1) and a "chemical" term (Le. the standard AH") contributions AJ-i = AJP
+ AP(e1)
(22) The electrostatic contribution to the enthalpy is related to the electrostatic contribution to the Gibbs energy
4G(el) = zF$ (23) through its derivative with respect to temperature. In the case of a "symmetrical" experiment, when the difference between initial pH and P.Z.C. is equal to the difference between final pH and P.z.c., one can assume, for any temperature, that initial and final potentials ($1 and $2) are equal in magnitude but opposite in sign =-42 (24) If so, the derivatives of 9, with respect to temperature, should also be equal in magnitude but opposite in sign. According to the above analysis, the electrostatic contributions to the enthalpy cancel if the calorimetric experiment is performed in the "symmetrical" manner, i.e. if initial and final pH values are given by eq 19. In such a case, by using eq 21, one obtains the "chemical" contribuiton, i.e. the difference in standard enthalpies A a 0 - AJl". TemperatureDependence of Point of Zero Charge. The results obtained from calorimetricmeasurements can be compared with corresponding enthalpies derived from the shift of pH,, with temperature. The dependence of pH,, upon temperature can be related to the nature of the chemical and physical interactions between the interfaces and the potential-determining ions. The relations between standard Gibbs energy and corresponding equilibriumconstants of surfacereactions 1and 2 are given by - RT In Kao = AaGo = AaHo- TAaSo (25) - RT In Kbo = AbG" = A f l - TAbso (26) $1
At the point of zero charge one can take rMc+ = ~ M O H , +and $ = 0 so that eqs 4, 5, 15, 25, and 26 yield
Thus, the difference between standard enthalpies of the protonation and deprotonation of surface groups can be determined from the slope in presentation pH,, us UT.
Experimental Section and Results Chemicals. All chemicals (HN03, NaOH, NaNO3, CsH5K04, KHzP04, Na2HP04) used in this study were of the analytical purity grade. Anatase powder (Laboratory reagent, The British Drug Houses Ltd.) had a specific surface area of s = 7.5 m2 g-1. Potentiometry (P.z.c. Determination). Point of zero charge of rutile was determined by the so-called umass
% 6.0
5.9
5.8
'
3.1
I
I
3.3
3.5
3.7
1000 ( ~ 1 ~ 1 - 1 Figure 1. Dependence of pH, of Ti02 Suspension on temperature. The mass concentration of the Ti02 suspension is 250 g dm". titration method". It was demon~tratedl7t~~ that pH of purified and concentrated oxide suspension corresponds to the P.Z.C. This method is simple and accurate and consequentlysuitable for determinationof the temperature effect. The mass concentration (250 g dm-3) used in these experimentswas high enough to produce pH equal to PAC. within the experimental error. The ionic strength was controlled by N d 0 3 (I,= 10-4 mol dms) and was chosen to be low in order to reduce the counterion association with charged surface groups. The system was under an argon atmosphere and thermostated (*0.05 OC). The electrodes were calibrated, for each temperature, by standard NBS buffers: aqueous solution of potassium hydrogen phthalate, m = 0.05 mol k g l , and the aqueous solution of potassium dihydrogen phosphate, m = 0.025 mol kg', and sodium hydrogen phosphate, m = 0.025 mol kg'. The properties of these buffers are precisely known in the wide temperature range.23 The pH value of the suspension, at each temperature, was calculated from the electromotive forces for two buffers and that for the suspension.16 The results are presented on Figure 1. The linear regression resulted in A f l - AaH" = 14.6 kJ mol-' and AbS" - A a s o
179 kJ K-' mol-'
Point of zero charge of Ti02 suspension at 20 "C was found to be at 5.96. Calorimetry. Calorimetric measurements with Ti02 concentrated suspension (y = 370 g dm-3) were performed by an isoperibol reaction calorimeter constructed by Simeon et al.24 Thirty grams of powder was dispersed (stirring under ultrasound) in 80 cm3 of aqueous solution of HN03. After equilibration the pH was 5.56. The suspension (70 cm3) was transferred into a calorimetric vessel and thermostated at 20 "C. In the course of the experiment 0.34 cm3 of NaOH solution (c = 0.5 mol dm-3) was added. By means of separate potentiometric titration, the amount of base was chosen so that a "symmetric" condition was achieved as defined by eq 19. Accordingly, the final value of pH, measured after reaction, was 6.36. The measured heat was found to be -8.34 J. The extent of neutralization, calculated by eq 13,was 1.72 X 10-4 mol. Experiment was designed so that extents of surface (22) Zalac, S.; Kallay, N. J. Colloid Interface Sci. 1992, 149, 233. (23) Definition of pH Scales, Standard Reference Values,Measurement of pH and Related Terminology. Pure Appl. Chem. 1985,57,531. (24) Simeon, V.; IviEM, N.; TkalEec, M. 2.Phys. Chem. 1972, 78, 1.
3460 Langmuir, Vol. 9,No. 12, 1993
Kallay et al.
deprotonation and protonation reactions were equal in magnitude (eq 19)so that Ata = -A[b = 8.592 X 106 mol. The difference in standard reaction enthalpies AJP) was calculated by means of eq 21, taking the literature value%for A J P = -55.84 kJ mol-'
(Am
A,,H"
-A
F = 14.7 kJ mol-'
Discussion This study deals with the enthalpy changes of surface reactions takiig place at the TiOdwater interface. In such reactions the relationship between surface charge and extent of surface reactions is not simple. When a base is added to an aqueous (acidic) oxide suspension in a calorimeter, at least three reactions are taking place. Any sound data interpretation should resolve the measured overall heat into the contributions of individual reactions. This task is further complicated by the electrostatic contribution to the enthalpies. Calorimetric results in this area, published in the literature, did not provide a convincing answer to these questions. In this study we have proposed a design of the calorimetric experiments which avoids most of these problems. If the point of zero charge is located in the middle, between the initial and the fmal pH ("symmetrical" design), it is possible to obtain the difference in standard enthalpies of deprotonation and protonation reactions. The so obtained enthalpy difference is a standard one, which means that it corresponds to the processes in the absence of the electrostatic effect. Thus, it is directlycomparableto the value obtained from P.Z.C. dependency on temperature. Indeed, the observed agreement supports the proposed approach. An inevitable side-reaction seriously affecting the accuracy of the calorimetric experiment is the reaction of neutralization which is accompanied by a large heat effect. In order to have a significant contribution of surface reactions, one should perform the experiments with concentrated suspensions. However, there are limitations due to several other reasons, e g . the viscosity which is related to the heat produced by operating the stirrer. In the experiments, described in this study, the extent of surface reaction was approximately '12 of the extent of neutralization, so the heat of the surface reactions was about 15% of the total heat which is satisfactory. The
compensation of the electrostatic effect will be more accurate if the initial and final pH values are closer to P.Z.C. However, the accuracy of pH adjustment and evaluation of the extents of reactions require thisdifference to be high. In the described experiment the difference of about half of a pH unit was found to be a reasonable compromise. The "symmetrical" design was necessary to obtain the proper extents of surface reaction and also to achieve the compensation of the electronic effects. This effect is related to the so-called Nernstian behavior of the surfacem according to which the slope in the surface potential us pH should be -58.2 mV at 20 OC. The interpretation of the adsorption data at the TiOdwater interface resulted2' in a lower value of the slope, -36 to -41 mV, which was later confiimed by direct measureConsequently,to achieve &J& = -1,the second factor in the exponential term in eq 17 had to be zero as it was achieved in the experiments. The application of the "mass titration concept- to the P.Z.C. measurementswas found to be suitable owing to its simplicity and accuracy. It is simple to keep electrodes immersed in one suspension and to change just the temperature. On other hand, if all necessary requirements are met, the accuracy of the P.Z.C. measurement isjust the accuracy of the pH measurements. The value of the difference in standard reaction enthalpies obtained from calorimetric measurements (14.7kJ mol-') agrees well with the value obtained from potentiometric measurementsof the temperature dependenceof pH, (14.6kJ mol-') and is comparable with the literature values for the rutile/ water interface: 13.8 kJ mol-' (Berube and de Bruyn);'' 17.6 kJ mol-' (Fokkink et al.);'S 22 kJ mol-' (de Keizer et al.);a 15-30 kJ mol-' (Machesky and Anderson).s The latter two resulta were obtained by calorimetric measurementa. The presented theoretical model used for the design of the calorimetry experiment, used in this study, is based on the "2-pK" concept. The analysis based on a "1-pK" approachn is in progress and will be published elsewhere.=
Acknowledgment. The authors are grateful to Professor Vladimir Simeon for helpful discussion. (26) Avena, M. J.; Camara, 0. R.;
(26) Wagman, D.D.;Evans, W.H.;Parker, V. B.; Halow, I.; Bailey, S. M.; Schumm, R. H.Selected Value8 of Chemical Thermodynumic Properties;NBS TechnicalNote,Institute for Bmic Standards, National Bureau of Standards: Washington, DC,1968.
De Pauli, C. P. Colloid Surf. 1998,
--.(27) Van R i e d i j k , V. H.;Bolt, G. H.;Koopal, L. K.;Blackmeer,J.
69. 217.
J. Colloid Interface Sci. 1986, 109, 219. (28) Kallay, N.;h a c , 5. Submitted for publication in Croat. Chem. Acta.
