Research: Science & Education
Optical Basicity: A Practical Acid–Base Theory for Oxides and Oxyanions J. A. Duffy Department of Chemistry, University of Aberdeen, Aberdeen, Scotland, UK Acid-Base Theories
Lux–Flood Theory
Inorganic chemistry textbooks for undergraduate students devote many pages to acid–base theory. Much attention is given to interactions in aqueous solution, and the subject is covered in such a way as to convey many useful insights (1). Coverage extends to protonic systems in which the water content is low or absent, and a discussion of the Hammett acidity function is usually included. When it comes to dealing with acid–base theory of nonprotonic nonaqueous systems, examples are usually chosen from molecular species such as BF3, POCl 3, amines, and so on. Acid–base reactions involving ionic compounds such as the alkali or alkaline earth oxides, or “network” materials such as SiO2 (silica), P4O10, or B2O3 receive slight treatment. Indeed, considering the technological importance of these reactions, the treatment is inadequate.
Many oxides can be classified as basic or acidic from their behavior with water. For example, CaO and Na2O react with water to give alkaline solutions, whereas SiO2 and P4O10 produce silicic and phosphoric acids. From the chemistry of the group II elements, MgO would be regarded as a basic oxide but less so than CaO, whereas Al2O3, in view of the amphoteric nature of aluminium hydroxide, would be regarded as less basic than MgO and less acidic than SiO2. In the theory developed by Lux and Flood (2), an oxidic network system, such as a molten silicate, is regarded in terms of the following dissociations:
Oxide Systems Acid–base reactions occur in the molten state at high temperatures in several important processes: for example, in the production of iron and steel, in glass making, and in certain geochemical reactions. In the blast-furnace, as well as the series of reactions leading to the production of molten iron from Fe2O3, silica-containing materials react with limestone to give a mixture of silicates. Writing the reaction of silica with calcium oxide as eqs 1 and 2 indicates different extents of neutralization: CaO + SiO2 → CaSiO3
(1)
CaO + CaSiO3 → Ca 4SiO4
(2)
Usually the ratio of CaO to SiO2 is not a simple number; and if it is between 1:1 and 2:1, then the extent of neutralization corresponds to the formation of a calcium silicate having a composition between CaSiO 3 and Ca2SiO4. The molten silicates constitute a “slag”, and in practice this also contains other oxides such as MgO and Al2O3. The chemical composition of a molten slag is responsible for the extent of acid–base neutralization. A vitally important property of the slag is its ability to extract impurities such as sulfur and phosphorus from the molten iron, and it is the state of neutralization that determines optimum performance. Hence the composition of the slag is very important. This is also true for glass in the molten state in order to ensure the desired properties. For example, the refractive index of a glass depends largely on the polarized “state” of the oxygen atoms and this, in turn, is determined by the extent to which acid– base neutralization has occurred while in the molten condition.
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SiO 32{ → SiO 2 + O2{
(3)
SiO44{ → SiO 32- + O 2{
(4)
The basicity of the medium is then expressed in terms of the oxide ion activity. It is important to realize that the above dissociations occur to a very limited extent. Indeed, for most silicate compositions of practical importance, addition of an ionic oxide such as CaO results in the O2{ ions being incorporated into the silicate network by the action of “bridging” oxygen atoms changing into “nonbridging”: \ / \ / O2{ + —Si—O—Si— → —Si—O{ + { O—Si— / \ / \ In effect, this action serves to “store” oxide ions, making them available when required for participation in a chemical reaction. The basicity of the silicate melt can therefore be regarded as its tendency to liberate oxide ions. This principle extends to other systems that form anionic networks, such as phosphates, borates, and aluminosilicates. Most textbooks describing the Lux–Flood theory neglect to point out its severe limitations. Problems arise, for example, in comparing a calcium silicate melt with a magnesium silicate melt; the oxide ion activities are not single ion activities but activities of CaO and MgO, and no comparison is possible. Indeed, in network oxide media generally the concept of oxide ion activity produces so many difficulties that the theory degenerates so that it can be used only in an empirical way. For example, in dealing with a calcium magnesium aluminosilicate slag, previous workers (3) have regarded the oxide ion activity as proportional to a “basicity ratio”, R:
Journal of Chemical Education • Vol. 73 No. 12 December 1996
R=
c CaO + 12 c MgO c Si O 2 + 13 c Al 2O 3
(5)
Research: Science & Education where the fractions (1⁄2 and 1⁄3) were introduced arbitrarily to take account of the lesser basicity of MgO and the lesser acidity of Al2O 3. Although empirical expressions of this type have been found to be useful, from a chemical point of view they are not satisfactory. Optical Basicity Let us consider the two calcium silicates, CaSiO3 and Ca2SiO4, in the molten state. It is important to note that eq 3 (SiO32{ → SiO2 + O2{) is schematic; the formula SiO32{ represents stoichiometry and not structure. Both Ca2SiO 4 and CaSiO3 contain SiO4 tetrahedral units, but in CaSiO3 two of the four oxygen atoms are shared between two silicon atoms (the silicon atom “owns” the two nonbridging oxygens and has half-shares in the two bridging oxygens, corresponding to the stoichiometric ratio of 1:3 for Si:O). The average negative charge borne by the oxygen atoms in CaSiO3 is less than in Ca2SiO4. (The charges differ from the formal charges of { 1⁄2 and {1 owing to electronegativity differences and delocalization effects.) Since Ca2SiO4 is more basic than CaSiO3 (it contains more of the basic CaO), it is reasonable to associate basicity with the average negative charge borne by the oxygen atoms in an oxide-containing system. After all, the tendency for the release of oxide ions is expected to increase with increasing negative charge on the SiO4 unit. So how can this overall negative charge borne by the oxygen atoms be measured? One approach is to regard oxidic network systems in terms of Lewis acid–base theory (4). Here, an acid, A, is an electron pair acceptor and a base, B, is an electron pair donor: A + :B → A:B acid
base
(6)
product
Thus, on being introduced into an oxidic medium a metal ion behaves as a Lewis acid, while the anionic network behaves as a Lewis base. The oxygen atoms of the network surrounding the metal ion donate the negative charge, and this reduces the positive charge on the metal ion. The greater the negative charge borne by the oxygen atoms the greater will be the electron donation, and if the metal ion can signal the extent to which its positive charge falls, then there is the possibility of using it as a probe for the quantitative measurement of basicity. From a practical point of view, it is important that the probe ion behaves in an “innocent” manner by selecting sites that reflect the overall average charge on the oxygen atoms rather than forming specific complexes that may not correspond to the stoichiometry of the medium. It is possible to make measurements of this kind with certain probe ions using ultraviolet absorption spectroscopy. Many oxide-containing systems have been studied over the last 20 years, especially by chemists primarily interested in extraction metallurgy or glass-making. The most successful probes are the p-block ions Tl +, Pb2+, and Bi 3+ (with the outer 6s2 electronic configuration). Furthermore, these yield results that are consistent with each other (5). The ions have a prominent 6s → 6p ultraviolet absorption band, the frequency of which indicates the energy separation between the 6s and 6p levels, and from the spectra it is possible to calculate the positive charge borne by the metal ion (although, as we shall see presently, this particular calculation is not required). As the positive charge on the probe ion falls with increas-
Figure 1. The ultraviolet spectrum of a sodium silicate glass plate (Na2O:SiO 2 ratio, 3:7) showing the 6s → 6p absorption band of the Pb 2+ probe.
ing basicity of the oxidic medium, so the 6s–6p energy separation decreases and the frequency falls. The relevant theory, which we shall not deal with here, involves consideration of orbital expansion [the nephelauxetic effect (6)], which is well known in the field of coordination chemistry. In principle, ultraviolet spectra could be measured for the molten medium (which might be at a temperature of 1000 to 1600 °C), but it is more practical to quench the melt and make measurements on the glass. Figure 1 shows the spectrum of the Pb2+ ion in a glass obtained from molten sodium silicate where the Na2O:SiO2 ratio is 3:7. The wave number of the absorption maximum, ν, is measured in cm{1 (the ultraviolet region is ca. 25,000 cm{1 to 50,000 cm{1). For Pb 2+ in Figure 1 this is at 42,200 cm{1. For a series of sodium silicate glasses, the absorption band moves to lower wave number as the Na2O content is increased, and vice versa. The 6s → 6p wave number for Pb2+ in the gas phase can be obtained from atomic spectroscopy tables and is found to be 60,700 cm{1. For this condition, the lead ion bears a charge of exactly +2. Thus, the wave number falls by (60,700 { 42,200) cm {1 (i.e., 18,500 cm{1) when the lead ion is taken from the gas phase and placed in the sodium silicate glass. When the Pb2+ ion exists under very basic conditions (e.g., when it replaces a small proportion of Ca2+ ions in a crystal of calcium oxide), the wave number shift is much greater, amounting to 31,000 cm{1. From a practical point of view, it is convenient to choose calcium oxide as the standard medium for high basicity, since it can be obtained in a pure state (much more so than the more basic Na2O, for example). Relative to calcium oxide, the basicity of a medium such as a sodium silicate glass can be expressed as the ratio of wave numbers: (60,300 cm{1 { ν)/31,000 cm{1, where ν is the s–p frequency
Vol. 73 No. 12 December 1996 • Journal of Chemical Education
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Research: Science & Education of the Pb2+ probe in a particular medium. This ratio is known (5) as the “optical basicity”, Λ:
Λ=
60,700 cm –1 – ν 31,000 cm –1
(7)
Table 1. Basicity Moderating Parameters, γ, of Some Elements in Oxides, and Optical Basicity Values, Λ, of Some Oxides, Fluorides, and Sulfides Oxides Flourides Sulfides Elements a Λ Λa γ Λ Cesium(I)
0.60
1.7
Potassium(I)
0.73
1.4
0.60
Sodium(I)
0.87
1.15
0.50
Lithium(I)
1.0
1.0
Barium(II)
0.87
1.15
Optical Basicity and Chemical Composition
Strontium(II)
0.91
1.1
0.48
1.35
Spectroscopic studies of the probe ions Tl+ , Pb2+, and Bi3+ have provided data for many oxide-containing systems. Careful examination of these data shows that Λ can be calculated simply from the chemical stoichiometry of the material. It has been pointed out previously that in a silicate such as CaSiO3, the oxygen atoms bear fractional charges owing to delocalization and differences in electronegativity. However, if a formal oxidation state of {2 is assumed, it is clear that the total negative charge borne by the oxygen atoms is balanced one third by the Ca2+ ions and two thirds by the Si4+ atoms (ions). It might be expected that the optical basicity of CaSiO3 incorporates this balancing of charge by the constituent cations Ca2+ and Si4+ together with some feature that these ions have for moderating the basicity of the O2{ ion (expressed by a parameter, γ, possibly related to the electronegativity). An expression of the type:
Calcium(II)
1.00
1.00
0.43
1.30
Iron(II)
1.0
1.0
Manganese(II)
1.0
1.0
Magnesium(II)
1.3
0.78
0.34
1.25
Aluminium(III)
1.65
0.60
0.26
Silicon(IV)
2.1
0.48
0.21
Boron(III)
2.36
0.42
0.18
Hydrogen(I)
2.5
0.40
Phosphorus(V)
3.0
0.33
Sulfur(VI)
4.0
0.25
For example, the glass in Figure 1 would have an optical basicity value of (60,700 cm{1 { 42,200 cm{1)/31,000 cm{1 = 0.60. By definition, eq 7 yields Λ = 1.00 for calcium oxide.
Λ = 1 × γ1 + 2 × γ1 3 3 Ca Si
(CH3CO)2O
0.72
1.30 0.50
0.47
Values of Λ are expressed to the nearest 0.05 for oxides of formula M2O and MO(except CaO and MgO) and for sulfides. a
XA [= ax/(ax + by)] and XB [= by/(ax + by)]. The optical basicity is then given by:
(8)
might be expected to apply. For many alkali and alkaline earth silicates, phosphates, borates (usually as glasses), and also certain compounds, expressions of this type work well and yield values of γ consistent for each element. For obvious reasons, γ has been termed the “basicity moderating parameter” (5). Some values of it and of Λ are given in Table 1 for a variety of oxides. It may be noted that γ does increase roughly in line with electronegativity except for the transition elements, the oxides of which are more basic than aqueous solution chemistry might suggest. Equation 8 is a specific form of a general expression for the optical basicity of a system comprised of oxides [which includes, as well as network systems, specific compounds, e.g. Na4SiO4 or Ca3(PO4)2]. Suppose the system comprises two oxides, oxide(A) and oxide(B), in the proportion of x:y; then the proportion of total formal negative charge neutralized by the two oxides can be calculated by taking into account the oxidation states of the elements in the two oxides (+a and +b, respectively). These proportions are “equivalent fractions”denoted by
Λ = X A γ1 + X B γ1 A B
(9)
Taking the Na2O–SiO2 system as an example, a melt where the molar ratio is 3:7 has XA = 3/17 and XB = 14/17. With γ Na = 0.87 and γSi = 2.1 (Table 1), the optical basicity is (3/0.87 + 14/2.1)/17, or 0.60. Taking another example, Ca3(PO4)2, Λ = (3/γ Ca + 5/γP)/8, or 0.58. It can be seen that for a single oxide the optical basicity is simply 1/γ; for example, for SiO2, Λ is 1/2.1 = 0.48. Equation 9 then becomes: Λ = XA × Λ[oxide(A)] + XB × Λ[oxide(B)]
Borates
Λ
Silicates
Λ
Na2B4O7
0.52
Na2Si2O5
0.61
Phosphates
Λ
1:1
Na2B2O4
0.62
Na2SiO3
0.70
NaPO3
0.47
2:1
Na4B2O5
0.71
Na4SiO4
0.82
Na4P2O7
0.56
Protonic acids
H3BO3
0.41
H4SiO4
0.44
H3PO4
0.36
Sulfates
Λ
Na2S2O7
0.38
Na2SO4
0.48 NaCH3CO2 0.64
H2SO4
0.29 CH3CO2H 0.45
Λ is calculated from γ values in Table 1 using eq 9. Acetate data from ref 7.
a
1140
(10)
Expressions similar to equations 9 and 10 can be derived for three-component and higher systems. Optical basicity values of some simple substances, calculated using equation 10, are given in Table 2. It can be seen how the Λ values of salts are between those of the parent acid and base; for example, sodium metaphosphate (NaPO3) has Λ = 0.47—between 1.15 for Na2O and 0.33 for P4O 10. Also, in a series of salts with an increasing proportion of basic oxide, there is an increase in op-
Table 2. Optical Basicities, Λ, of Some Substances a Oxide ratio basic/acidic 1:2
1.40
Journal of Chemical Education • Vol. 73 No. 12 December 1996
Acetates
Λ
Research: Science & Education
tical basicity—for example, on going from Na 2Si 2O 5 (Λ = 0.61) to Na2SiO3 (Λ = 0.70) to Na 4SiO4 (Λ = 0.82). It should be noted how the mineral acids phosphoric and sulfuric have the lowest Λ values, which are less than for water [Λ(H 2O) = 0.40]. The slightly greater values of Λ for the weak acids boric acid and silicic (0.41 and 0.44, respectively) do not conflict with these acids being stronger protonic acids than water. It must be remembered that the optical basicity model is concerned with the electron donor power of oxygen atoms; and although this is expected to be related to the tendency for proton attraction (by the conjugate base of an oxyacid), there will also be unknown entropy effects. It is possible to make optical basicity measurements in organic oxidic media such as molten metal carboxylates (7). Tables 1 and 2 show that acetic anhydride and acetic acid have Λ values close to those for silica and silicic acid, respectively. Practical Applications Optical basicity has been used in the iron and steel industry for optimizing the refining power of slags (8), for example, for removing sulfur from the molten metal. The action of the slag can be expressed as follows: S2 + 2O2{ → 2S2{ + O2 (metal) (slag)
(11)
(slag)
Figure 2. Variation of the [Fe2+ ]/[Fe3+] equilibrium ratio in the alkali silicate glass system M2O–SiO2. The upper oxidation state is favored by increasing the glass basicity by either (a) replacing the alkali oxide (Li 2O < Na2O < K2 O) or (b) raising its content. Plotting log ([Fe 2+]/[Fe3+]) against the optical basicity of the glass unifies the three trends. (Although the points lie closer to a curve, their proximity to the straight line simplifies the application of this relationship to redox problems in glass chemistry.)
This behavior for a series of slags can be expressed quantitatively as the “sulfide capacity”, CS, and this quantity correlates very well with optical basicity. It is found that log Cs increases linearly with Λ, making good chemical sense when considered with equation 11. In glass research, optical basicity rationalizes the behavior of molten glass for stabilizing and destabilizing oxidation states of certain ions. Figure 2 shows, for example, how (the logarithm of) the [Fe2+]/[Fe 3+] ratio in the equilibrium 4Fe3+ + 2O2- → 4Fe2+ + O2
(12)
varies in three alkali silicate glass systems where the alkali oxide component is Li2O, Na2O, or K2O. It is apparent that the equilibrium moves to the left with increasing alkali oxide content and also that there are three distinct trends in accordance with the increasing basicity on going from Li2O to Na2O to K2O. By plotting log ([Fe2+]/[Fe3+]) against optical basicity instead of the alkali oxide content, the three trends are unified into a single trend (Fig. 2). Generally, the advantages of the optical basicity model can be summarized as follows. 1. In the context of Lewis acid–base theory, it provides a numerical scale for oxides and oxide-containing materials where the assigned Λ value can be related to a standard base, CaO, for which Λ is defined as unity. 2. Optical basicity values (Table 1) rank the oxides of the elements in what appears to be a sensible order. Thus K2O > Na2O > (CaO = FeO) > MgO > Al2O3 > SiO2 > B2O3 > H2O > P4O10 > SO3. Other oxidic materials, for example oxysalts, can be placed within this ranking order. For example, Na2O–SiO2 (1:2) has almost the same basicity (from eq 10, Λ = 0.61) as Al2O3. 3. For binary (and higher) systems, e.g. CaO–SiO2 or Na2O–B2O3, it indicates the quantitative trend in basicity with continuous change of composition (see eq 10). 4. Reactions between oxide ceramic materials can often be rationalized in terms of acids and bases (9). For
Figure 3. Variable parameters of oxygen in its compounds. Changes in (a) its electronic polarizability, αO 2-, and (b) its electronegativity, xO, in oxides, with optical basicity for the oxide designated.
Vol. 73 No. 12 December 1996 • Journal of Chemical Education
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Research: Science & Education
example, in the reaction Na4SiO 4 + Na 4P 2O7 → Na2SiO 3 + 2Na 3PO 4
(12)
which occurs on heating, Na4SiO4 is the base (Λ = 0.82) while Na4P2O7, because its optical basicity is much less (Λ = 0.56), is the acid. It should be noted that the optical basicity difference between the products (0.70 { 0.64) is much less, indicating that acid–base neutralization is a major driving force. 5. Optical basicity provides an insight into the chemical nature of oxygen. Unlike most other elements, oxygen shows a wild variation in some of its parameters. For example, its (Pauling-type) electronegativity, x o, is between 3.4 and 3.6 in covalent oxides such as SO3 or SiO2, but falls to much lower values when it is combined ionically in CaO or Na2O. Further, its electronic polarizability, αo2{, is low in covalent compounds but increases with increasing ionicity (e.g. 1.41 Å3 in SiO 2 but 2.49 Å3 in CaO). Optical basicity is related to both of these parameters in a very simple way (Fig. 3). 6. The optical basicity model has been extended to fluorides and sulfides (10), and the Λ values (Table 1) indicate an overall ranking for oxides, fluorides, and sulfides. It can be seen, for example, that KF is as basic as Al2O3; AlF3 is more acidic than P4O10; and MgS is more
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basic than BaO. These rankings do not necessarily extend to aqueous solution. However, the availability of these Λ values allows optical basicity to be calculated for technologically important materials such as oxidefluoride glasses and metallurgical fluxes containing, for example, calcium fluoride. Literature Cited 1. For example: Douglas, B.; McDaniel, D.; Alexander, J. Concepts and Models of Inorganic Chemistry, 3rd ed.; Wiley: New York, 1993; Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry, 4th ed.; Harper Collins: New York, 1993; Butler, I. S.; Harrod, J. F. Inorganic Chemistry, Benjamin Cummings: Redwood City, 1989; Moeller, T. Inorganic Chemistry; Wiley: New York, 1952. 2. Lux, H. Z. Elektrochem. 1939, 45, 303; Flood, H.; Forland, T. Acta Chem. Scand. 1947, 1, 592. 3. Bodsworth, C.; Bell, H. B. Physical Chemistry of Iron and Steel Manufacture, 2nd ed.; Longmans: London, 1972, pp 177, 445. 4. Lewis, G. N. J. Franklin Inst. 1938, 226, 293. 5. Duffy, J. A.; Ingram, M. D. J. Am. Chem. Soc. 1971, 93, 6448; J. Non-Cryst. Solids 1976, 21, 373; Duffy, J. A. Bonding, Energy Levels and Bands in Inorganic Solids; Longmans: London, 1990, Chapters 6, 8; Porterfield, W. W. Inorganic Chemistry—A Unified Approach; Addison–Wesley: Reading, MA, 1984; Chapter 6. 6. Jørgensen, C. K. Orbitals in Atoms and Molecules; Academic: New York, 1962; Chapter 4. 7. Blair, J. A.; Duffy, J. A. Phys. Chem. Glasses 1993, 34, 194. 8. See, for example, several papers in 3rd Int. Conf. Molten Slags and Fluxes, Glasgow, 1988; Institute of Metals: London, 1989, pp 29, 60, 86, 91–94, 107, 146–149, 150–153, 154–156, 157–162, 166–168, 241–245, 277–282, 313–316. 9. Dent-Glasser, L. S.; Duffy, J. A. J. Chem. Soc. Dalton Trans. 1987, 2323. 10. Duffy, J. A. J. Non-Cryst. Solids 1989, 109, 35; J. Chem. Soc. Faraday Trans. 1992, 88, 2397.
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