## Postlaboratory Problems And Questions

*1. The surface-ionization models (or surface-complexation models) account for the behavior of solid oxide suspensions, which usually behave as amphoteric substances. The most common are given in Table 1 (see Bourikas, 2005; Blesa, 1997; Davranche, 2003).

Table 1. Surface-ionization models (8 and e are fractional charges).

Equilibrium

Name Surface ionization model constants

One site/onepKa M - OH8+ <=* M — 0<1_8)_-|- H+ Ka

Multisite Mxj - OHyizi <=i Mxi - OHJ1"1, + H+ K,

As an example of calculation, let us analyze the first model. Here,

The point where the total sum of positive and negative changes is zero (i.e., the pzc) is achieved in this model when [M - 0(1"8)"] = [M - OH8+], since we assume that the protons diffuse away. Then, Ka — [H+] and pKa = pH = pzc.

Assuming again that the protons dissolve away and that electroneutrality must be achieved at the solid sphere, answer the following for the second model (i.e., one site/two pKa):

(a) How does [M - OHj ] compare with [M - O"]?

(b) Write the pH at which pzc is achieved, in terms ofp/sT0i andpKa2.

*2. In a real test, 10 g of a river sediment were added to a 0.1 M solution of a supporting electrolyte (e.g., NaNOs) to a final volume of 100 mL. The resulting suspension was titrated at first with HNO3 and then with NaOH. By ion exchange, the total surface sites were calculated as {S}tot = 0.00013 mol/g. Selected data points are given in Table 2. (See Davranche, 2003).

With this information,

(a) Calculate the value of Q at each point

(b) Plot Q vs pH and estimate the value of pzc

(c) Calculate the value of Ka\ at each point below the pzc

(d) Calculate the value of Ka2 at each point above the pzc

(e) Calculate the intrinsic values of pKa\ and pKa2

(f) With the values obtained from e), calculate the pzc and compare it with that obtained in (b).

*3. The surface acidity of a metal oxide may be considered as Lewis acidity, which is a result of the electron-accepting character of the oxide surface. The more acidic the surface, the fewer the acidic sites to neutralize and the lower the pzc of the oxide. Since the ionization of a metal M to form the metal ion Mz+ in the oxide can be written as

where / is the (total) ionization energy of the element (in kJ/mole), then it follows that the larger the /, the higher the acidity of the resulting cation since it will have a greater tendency to return to its original state by attracting electrons.

Test for this correlation with your own results by plotting your pzc vs. /. (Look up the different ionization energies in a handbook or elsewhere). For example, the following relationship was found in the literature (see Carre, 1992):

pzc = 12.2 - 0.00091 Student Comments and Suggestions

 V, mL HNO3 pH, meas. 0.1 5.33 0.2 4.86 0.5 4.47 0.8 4.02 1 3.72 V, mL NaOH pH, meas. 0.1 6.92 0.2 7.07 0.5 7.56 0.8 7.93 1 8.13

Literature References

Balderas-Hernandez, P.; Ibanez, J. G.; Godinez-Ramirez, J.J.; Almada-Calvo, F. "Microscale Environmental Chemistry: Part 7. Estimation of the Point of Zero Charge (pzc) for Simple Metal Oxides by a Simplified Potentiometrie Mass Titration Method," Chem. Educ. 2006,11, 267-270.

Barthes-Labrousse, M.-G. "Acid-Base Characterization of Flat Oxide-Covered Metal Surfaces," Vacuum 2002, 67, 385-392.

* Answer in this book's webpage at www.springer.com

Blesa, M. A.; Magaz, G.; Salfity, J. A.; Weisz, A. D. "Structure and Reactivity of Colloidal Metal Oxide Particles Immersed in Water," Solid State lonica 1997, 101-103, 1235-1241.

Bourikas, K.; Kordulis, C.; Lycourghiotis, A. "Differential Potentiometrie Titration: Development of a Methodology for Determining the Point of Zero Charge of Metal (Hydr)oxides by One Titration Curve," Environ. Sei. Technol. 2005, 39, 41004108.

Bourikas, K.; Vakros, J.; Kordulis, C.; Lycourghiotis, A. "Potentiometrie Mass Titrations: Experimental and Theoretical Establishment of a New Technique for Determining the Point of Zero Charge (PZC) of Metal (Hydr)Oxides," J. Phys. Chem. B, 2003, 107, 94419451.

Carre, A.; Roger, F.; Varinot, C. "Study of Acid/Base Properties of Oxide, Oxide Glass, and Glass-Ceramic Surfaces," / Coll. Interf. Sei. 1992,154, 174-183.

Davranche, M.; Lacour, S.; Bordas, F.; Bollinger, J.-C. "An Easy Determination of the Surface Chemical Properties of Simple and Natural Solids," J. Chem. Educ. 2003,80,76-78.

Hamieh, T. "Etude des Propriétés Acido-Basiques et Energie Interfaciale des Oxides et Hydroxides Métalliques," C. R. Acad. Sei. Paris ( Chim. Surf. Catal., in French) 1997,325 (Serie IIb), 353-362.

Healy, T. W; Fuerstenau, D. W. "The Oxide-Water Interface-Interrelation of the Zero Point of Charge and the Heat of Immersion," J. Coll Sei. 1965, 20, 376386.

Kraepiel, A. M. L.; Keller, K.; Morel, F. M. M. "On the Acid-Base Chemistry of Permanently Charged Minerals," Environ. Sei. Technol. 1998, 32, 2829-2838.

Mullet, M.; Fiebet, P.; Szymczyk, A.; Foissy, A.; Reg-giani, J.-C.; Pagetti, J. "A Simple and Accurate Determination of the Point of Zero Charge of Ceramic Membranes," De sal. 1999,121,41^18.

Reymond, J. P.; Kolenda, F. "Estimation of the Point of Zero Charge of Simple and Mixed Oxides by Mass Titration," Powder Technol. 1999,103, 30-36.

Preocanin, T.; Kallay, N. "Application of Mass Titration to Determination of Surface Charge of Metal Oxides," Croat. Chem. Acta. 1998, 71, 1117-1125.

Sahai, N. "Is Silica Really an Anomalous Oxide? Surface Acidity and Aqueous Hydrolysis Revisited," Environ. Sei. Technol. 2002, 36, 445-452.

Vakros, J.; Kordulis, C.; Lycourghiotis, A. "Potentiometrie Mass Titrations: A Quick Scan for Determining the Point of Zero Charge," Chem. Comm. 2002,19801981.

Yoon, R. H.; Salman, T.; Donnay, G. "Predicting Points of Zero Charge of Oxides and Hydroxides," J. Coll. Interf. Sei. 1979, 70, 483-493.

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