Questions and How To Differentiate Prediction and Explanation in

In the Classroom

Questions and How To Differentiate Prediction and Explanation in Chemistry Teaching and Learning Victor M. S. Gil Department of Chemistry, University of Coimbra, Coimbra 3000-015 Portugal ~ o Carlos Paiva* Joa Centro de Investigac-~ ao em Química, Department of Chemistry and Biochemistry, Faculty of Science, University of Porto, Rua do Campo Alegre, 687, P-4169-007 Porto, Portugal *[email protected]

It is widely accepted that the establishment of a climate of questioning plays a key role in current science education. Thus, any inquiry-based approach to the teaching of chemistry soon calls for “whys” over the “whats” (including other interrogative expressions like “how many” and “how much”) on the nature, properties, and changes of matter. Understanding in chemistry begins when facts and phenomena, observed and organized in a systematic manner and eventually correlated, are interpreted in terms of atoms and their associations. Both in the process of converting the results of observations into a scientific language and in the meaning-making mechanisms involved, various concepts are invoked. Some are more fundamental and common to other sciences, such as the central concepts of energy and probability. Others are more specific to chemistry, such as pH, oxidation, electronegativity, or reaction rate. Many concepts, of similar status, are shared with other traditional disciplines, especially physics or biology: color and light, electrical behavior, changes of state, and so forth. Raising Questions and Question Levels But “whats” and “whys” in conceptual learning are usually intermingled, leading to a cascade of generative activity. If a first “why” aims at the nearest reason for a given fact or phenomenon, the more profound reason implies further “whys” and often also another set of facts or phenomena at a deeper level; so more “whats” as well as some “hows”; for example, “how do we know?”. Some recent studies (both in general discourse contexts and in scientific discourse) on question generation (1-7) have focused on these interrelated topics: question taxonomies; the effects of questioning on students' thinking and as an attempt to construct frameworks of understanding; and the ability to ask good thinking questions as an important component of scientific literacy that allows individuals to become critical consumers of scientific knowledge. Figure 1 shows a sequence detailing an example cascade of “whats” and “whys” focused on a simple chemical example: the blue color of copper sulfate aqueous solutions. Beginning with the fact (the blue color of copper sulfate aqueous solutions), we end up invoking quantum mechanics, where the more fundamental “whys” lie. At this stage, a possible question could be: can quantum mechanics obtain, through calculation, the energy levels for Cu2þ(aq), hence predicting the blue color of the copper sulfate solutions? In fact, correct prediction is not only a necessary condition for the validity of a theory, but a way of attaining 1324

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additional intellectual comfort at the level of the application of the theory. In the case above, the answer is yes, followed by further questions like “how is it done?”, which may have to wait for a future moment (from the point of view of the learner) or may need to be left to others' expertise. But questioning is not ended: besides practical questions, for example of the “what if” type (e.g., what color change is predicted if water molecules surrounding Cu2þ are replaced by NH3 molecules?), one can think of more profound “whys” that rely on the nature of quantum mechanics itself. Quantum mechanics would ultimately also be invoked had the initial problem concerned the solubility of copper sulfate as compared with barium sulfate, for example. Here, an intermediate phase in the questioning sequence would involve the fundamental concept of probability related to entropy and the second law of thermodynamics, associated with the concepts of lattice energy and solvation energy. Again, theoretical prediction would provide the intellectual comfort of comprehension. Leaving aside the philosophical considerations around the validity of theories, it is clear that if the soundness of a given theory or theoretical model depends on its predictive power this is not a sufficient condition. Explanatory power necessarily implies predictive power, yet the reverse is not true. This is not always made clear, and students may be led to take as a correct or final explanation what can be only a simplistic, nonexplanatory model of high predictive power. This is not to say that such models are not useful: they are not only an important practical tool, but also a preliminary contribution to rationalization and justification. Chemistry and the teaching of chemistry are full of examples. What should be made clear is that if a practical mind uses predictive considerations when dealing with new situations, an inquiring mind does not stop there and certainly does not identify high predictive capacity with full understanding. Below, we briefly discuss popular models in the field of chemical bonding and molecular structure, clearly distinguishing between predictive power and explanatory power. In addition, we address the main reasons for their practical success, which is not coincidence. Because these situations may be regarded as particular manifestations of a more general confusion between what we could perhaps call “fundamental whys” and “operational whys”, the latter in the sense of “how can I arrive at the right answer” or “justify your answer”, we first recall a variety of examples of operational “whys” of special relevance in chemistry, divided into three categories: (i) application of systematized data; (ii) deduction

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Vol. 87 No. 12 December 2010 pubs.acs.org/jchemeduc r 2010 American Chemical Society and Division of Chemical Education, Inc. 10.1021/ed100531b Published on Web 10/15/2010

In the Classroom

Figure 1. Example of a cascade of “what”, “how” and “why” questions.

of a particular case from a generalized statement (law, principle); and (iii) correlations of facts and variables. Fundamental “Whys” versus Operational “Whys” Application of Systematized Data The use of tables of Ka and Kb values for acids and bases, respectively, is well known for rationalizing and predicting acid-base behavior. But to the question of “why is acetic acid a weak acid whereas hydrochloric acid is a strong acid?” we (perhaps provocatively for some readers) state that the acceptable answer cannot be “because the former has a small Ka value”. The reference to Ka only adds a quantitative dimension to the original statement. Instead of the word “because”, expressions such as “in accordance with” would be more appropriate (for a more detailed discussion, see ref 8). The same criticism is applied to the use of tables of Ksp values for sparingly soluble salts in order to rationalize and predict dissolution

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and precipitation reactions; for example the inappropriate use of “because” in “calcium carbonate is less soluble in water than magnesium carbonate, because the former has a lower solubility product” (8). Another example comes from Hess's Law. The use of a table of standard enthalpies of formation is a rapid way to calculate the ΔH° value of any reaction, but that does not offer an explanation for the sign and size of this value. Chemical equations, with the corresponding ΔH° values, can be usefully related but not as a cause-effect relationship. Deduction The application of Le Ch^atelier's principle to alterations of the equilibrium state of a particular system provides a good example of deductive use of a generalization supported both by experiment and theory. To invoke the principle to answer the question “What is the effect of compression on the system N2(g) þ 3H2(g) / 2NH3(g)?” is acceptable, but to the question

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“Why does the yield of the reaction N2(g) þ 3H2(g) / 2NH3(g) increase upon compression?” one cannot answer, for example, “because Le Ch^atelier's principle so requires”. One may involve a calculation of the reaction quotient for comparison with the equilibrium constant, but as with the previous examples on chemical reactivity, full intellectual satisfaction cannot avoid thermodynamic considerations in turn tied up with molecular structural considerations. Correlation One well-known case of correlation is provided by the interpretation and prediction of the extent of redox reactions in terms of the standard electrode potentials associated with the respective half-reactions. The extent of any reaction is related to the corresponding ΔG° value, according to basic thermodynamics, and it is this same value that determines the cell potential of the standard cell based on the reaction being studied. The existence of a correlation, instead of a cause-effect relation, enables one to say that, for example, magnesium reacts more extensively with water, leading to the production of hydrogen, than does copper, “in accordance with”, not “because of”, a greater tendency of Mg to be oxidized, as shown by a smaller electrode (reduction) potential for Mg2þ(aq) þ 2e- f Mg(s). Accordingly, it can be predicted that Mg(s) reacts with Cu2þ(aq) but Cu(s) does not react with Mg2þ(aq). The Predictive Power of Simplistic Models Chemical Bonding The atoms of the noble gases are well known to be the most stable in the sense that each atom does not associate easily with other atoms (in particular, the noble gases are monatomic). This is usually attributed to having complete electron energy levels or shells: 2 electrons for He, 2 þ 8 electrons for the first and second energy shell of Ne, 2 þ 8 þ 8 for Ar, .... The idea of completeness as equivalent to stability is often taken too much for granted: for example, it is not found surprising that, in ionic compounds, the element sodium appears as Naþ, the element magnesium as Mg2þ, the element oxygen as O2-, the element fluorine as F-, all the ions possessing an electronic structure similar to that of Ne atom. The interpretation of the stability of the noble gases is predicated on the fact that they have high ionization energies (maximum for the corresponding period in the periodic table, corresponding to maximum nuclear charge) and low electron affinities (an additional electron would require a higher energy level): no stable compounds are known having Neþ or Ne-, for example. In the case of ionic compounds, although some energetics must be considered (after all, to go from an atom Na to the stable ion Naþ requires energy, which happens to be larger than the energy liberated in the conversion of an atom Cl into Cl-), we can think essentially of a correlation model between elements such as Na, Mg, O, F, and others (namely of the third period such as K, Ca, Al, Cl) and the atoms of noble gases (Ne and Ar, in particular). In covalent molecules, atoms are considered to “attain the electronic structure of a rare gas atom” (the nearest rare gas in the periodic table) by sharing electrons in chemical bonding, hence, the single bond involving H atoms, the single bond in F2, the double bond in O2, the triple bond in N2. The predictive power of this model, the Lewis model, is very high, especially with atoms of low atomic number. One refers to 1326


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the octet rule (doublet, in the case of H), although for atoms of the third and higher periods this rule is not, in general, expected to hold. PCl5 and SF6 are two well-known examples, as well as many coordination compounds of transition metals. On the other hand, the enormous number of organic compounds have molecular structures in accordance with the rule: four lines around each C, N, O ... symbol, each line representing two valence electrons. An efficient development of this model is provided by the cases when more than one structural formula obeying the octet rule is possible. Then, the notion of hybrid structure can be introduced, and fractional bond orders can be established, as is the case of the ozone and benzene molecules or the carbonate and nitrate ions. Also, providing we stick to atoms of the second period (besides H), the inexistence of a structural formula obeying the octet rule is a clear indication that such a molecule very likely does not exist. Thus, the inexistence of molecules such as Ne2, H3O, OH, NH4, and F4 as stable species can be interpreted, whereas species F2, H3Oþ, OH-, NH4þ, and P4 do exist with structures in agreement with the octet rule. The great success of the Lewis model as a predicting model should be acknowledged, in spite of its limitations at the explanation level. There are several reasons why (in the way it is usually applied in chemistry teaching) it must be regarded as a simplistic model. First, it is simply not correct to say, as it is often stated or implied, that in F2, for example, only two electrons are shared. In fact, all 2 7 = 14 valence electrons are shared between the two atoms. In N2, all the 2 5 = 10 valence electrons are shared. Also, the use of the word “stability” both for atoms of rare gases, such as Ne and Ar, and for molecules, such as F2 and N2, for example, deserves some consideration. In both cases, it is taken as being equivalent to saying “preferred existence” compared to associations like “Ne2” and “Ar2” and to individual atoms F þ F and N þ N. In both situations, one is concerned with bond orders in diatomic molecules. For the noble gases, it also means an absent or small tendency for association with atoms of other elements, related to the stability of the atoms with respect to the addition and removal, hence sharing, of electrons. However, reference to stable molecules like F2 and N2 does not necessarily mean chemically inert species. In fact, if N2(g) is comparatively inert (see, however, the study of the synthesis of NH3 as a central example in chemistry teaching), F2(g) is a very reactive substance. The answer to “why” questions in the field of chemical bonding lies, at an approximate level, with orbital theory (quantum mechanical wave functions in general). In fact, this not only provides a deeper understanding of chemical bonding and bond orders, but also gives a justification for the octet rule. For example, the shared 14 valence electrons in F2 are divided into antibonding and bonding molecular orbitals: 8 bonding and 6 antibonding electrons, equivalent to a net result of 2 bonding electrons. The reason for formulas with four lines around each symbol for atoms of the second period (just one in the case of bonding to H) is traced to a maximum of four atomic orbitals and eight electrons for the second electron shell in any atom (quantum numbers n = 2, l = 0 and l = 1). This maximum is attained precisely with the noble gas Ne. Accordingly, there is no line for two Ne atoms, no Ne2 molecules, corresponding to a zero bond order: eight bonding and eight antibonding valence electrons.


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In the Classroom

At an introductory level, the octet rule is a useful tool to rationalize and predict (common) bond orders, but instead of referring (wrongly) to the number of shared electrons, one should admit the complexity of any case, besides H2, stressing that a balance should be made of the multiple forces (attractions and repulsions) being present. A rapid way of predicting the balance is by distributing the number of lines (half of that of valence electrons) around the symbols according to the rule: one line for H and four lines for C, N, O or F. Only later, this rule can be properly justified. For a review on the use of Lewis structures beyond common bond orders, see refs 9-11. There is, indeed, another simple way of rationalizing and predicting bond orders in simple cases, at an introductory level, which uses analogical reasoning related to the old notion of valence. It assumes single bonds when H is involved and is illustrated below: • The O atom in the molecule H2O is bonded to two atoms, whereas in the molecule O2, it is bonded to just one. Thus, the OO bond in O2 should have a “value” twice that of the O-H bond in H2O, hence OdO. • The N atom in the molecule NH3 is bonded to three atoms, whereas in the molecule N2, it is bonded to just one. Thus, the NN bond in N2 should have a “value” three times that of the N-H bond in NH3, hence NN. • The C atom in the molecule CH4 (and in C2H6) is bonded to four atoms, whereas in the molecule C2H2, it is bonded to just two. Thus, the CC bond in ethyne should have a “value” three times that of the C-H bond (or C-C), hence, H-CC-H.

The bond order two for the CO bonds in carbon dioxide is also accommodated in this manner: a double bond for each O atom and two double bonds involving C. In the case of carbon monoxide, with the O atom needing bond order two and the C atom bond order four, the balance points to a triple bond CO. The rule of bond-order conservation in chemical reactions (12) is directly related to the octet rule: in any balanced chemical equation (involving species whose structures follow the octet rule), the sum of the bond orders in reactants equals the sum of bond orders in products. Thus, an unknown bond order can be obtained if the remaining ones are known. Molecular Geometry The simplicity with which it is usually presented, coupled with its high predictive power, accounts for the immense popularity of the VSEPR model (valence-shell electron pair repulsion) for teaching molecular geometry (13-17). In practical terms, what is usually applied is a model based on the lines which, in a Lewis representation of AXm-type molecules or molecular fragments, correspond to valence bonding and nonbonding electron pairs: the geometric arrangement around A is that which maximizes interpair (interdomain) separation, multiple bonds being regarded as a single domain. Fine changes in molecular geometry are accommodated by considering A lone pairs as corresponding to larger and broader domains, multiple bonds as corresponding also to larger domains, and the size of bonding AX domains taken as decreasing with increasing electronegativity of X. In spite of the large amount of evidence in favor of the predictive power of the VSEPR model, which can hardly be just a mere coincidence (see below), it can be argued that the model


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lacks sufficient explanatory power. In fact, if the interaction between electron pairs is taken as Coulombic repulsion, as is often implied or even explicitly declared, the model acquires a qualitative explanatory nature, but it is clear that it ignores other important contributions to the total molecular energy, hence, to the molecular geometry, especially the electron exchange energy and the very attractions (electron-nucleus Coulombic attractions) that contribute to maintain the atoms associated into molecules. In this version of the VSEPR model, it is not uncommon that electron-pair domains are identified with localized (or quasilocalized) molecular orbitals or valence-bond functions, based on hybrid orbitals, ignoring residual delocalization contributions and wrongly taking atomic orbital hybridization as a physical phenomenon. As a matter of fact, it is ironic that such a popular use of the VSEPR model is largely at variance with the argument insistently advanced by Gillespie (17), one of the authors of the model, that the simplistic version usually applied is not in agreement with a correct understanding of the physical basis of the real model. It is true that the VSEPR model was developed by Gillespie and Nyholm (13) and Gillespie (14) on the basis of a natural extension of the electron-pair model of Lewis made by Sidgwick and Powell (18) who suggested that the main contribution to the difference in energy between different geometric configurations of the nuclei of a molecule would arise from the repulsion of the valence-shell electron pairs. However, Gillespie (17) has insisted that the electron-pair repulsions should not be regarded as Coulombic interactions but as repulsions associated with spin correlation, hence, with the Pauli principle. This interpretation follows a model developed by Linnett (19) in which the orbital concept is largely ignored in favor of spin correlation, which is a consequence of the antisymmetrization of the total wave function demanded by the Pauli principle. Accordingly, electron-pair domains will have nothing to do with orbitals. In any case, insofar as it remains essentially qualitative, the VSEPR model (in any version) is, by far, much more powerful as a predictive method than as an explanatory theory. From a more quantitative point of view, it has been found that the consideration of localized pairs of electrons (having opposite spins) is at variance with the topological properties of the charge density F(r) as determined by the accepted theories and, in particular, the theory of Bader (20) of atoms in molecules (AIM). It is interesting, though, that the work of Bader invoked above to criticize VSEPR as an explanatory model, does indeed offer some physical interpretation of the high predictive power of the method. This can be found not in the topology of the charge density F(r) but in the corresponding second derivatives, the so-called laplacian of F(r) (20). This corresponds to the idea of regions where the function F(r) is said to be “locally concentrated” (or depleted), in a sense that does not imply the existence of maxima (or minima) in the charge density. It has, indeed, been demonstrated that the total energy of a molecule is minimized for the geometry that maximizes the separations between the valence-shell charge concentrations defined in terms of the laplacian of F(r) (21). For a more detailed discussion see ref 22. Thus, the high predictive power of the VSEPR model, obviously not a coincidence, has some physical basis but on a much more sophisticated level than usually implied in chemistry teaching or explicitly taught.


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Conclusion The development of inquiring attitudes and the encouragement of questions by students in the teaching and learning of chemistry requires a proper distinction among the different types of questions. In particular, it is important to distinguish between “fundamental whys” and “operational whys”. Examples of “operational whys” of special relevance in chemistry organized in three categories are provided by: (i) the application of systematized numerical data; (ii) the deduction of a particular case from a generalized statement; and (iii) correlation of facts and variables. The confusion between fundamental and operational “whys” is also related to the misuse of some theoretical models, namely by taking high predictive power as equivalent to high explanatory power. If explanatory power necessarily implies predictive power, the reverse is not true. This is not to say that a more or less simplistic nonexplanatory model of high predictive power is not useful. There are many examples in chemistry teaching. We have mainly discussed popular models in the field of chemical bonding and molecular structure, clearly distinguishing between predictive power and explanatory power in discussing the Lewis model and the octet rule for the establishment of structural formula and the VSEPR model for predicting molecular geometries. It is hoped that this reflection will contribute to make the teaching of chemistry more honest and learning chemistry more effective. Acknowledgment Thanks are due to Christopher Brett, Department of Chemistry of the University of Coimbra, for reading and commenting on the manuscript, and to the referees for their comments and suggestions. Literature Cited 1. Graesser, A. C.; Lang, K.; Horgan, D. A Taxonomy for Question Generation. Questioning Exch. 1988, 2 (1), 3–15. 2. Anderson, L. W.; Krathwohl, D. R., Eds. A Taxonomy for Learning, Teaching and Assessment: A Revision of Bloom's Taxonomy of Educational Objectives; Longman: New York, 2001. 3. Pedrosa de Jesus, M. H.; Almeida, P.; Watts, M. Questioning Styles and Students' Learning: Four Case Studies. Educ. Psychol. 2004, 24 (4), 531–548.

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4. Watts, M.; Pedrosa, M. H. Enhancing University Teaching through the Use of Questioning, SEDA Special 19; Staff and Educational Development Association Ltd: London, U.K., 2006; and references therein. 5. Chin, C. Students' Questions: Fostering a Culture of Inquisitiveness in Science Classrooms. Sch. Sci. Rev. 2004, 86 (314), 107–112. 6. Chin, C.; Osborne, J. F. Students' Questions: A Potential Resource for Teaching and Learning Science. Stud. Sci. Educ. 2008, 1 (44), 1–39and references therein . 7. Millar, R.; Osborne, J. F. Beyond 2000: Science Education for the Future; King's College: London, U.K., 1998. 8. Gil, V. M. S. University Students' Assessment of the Explanatory Content of Justification Statements. Int. J. Sci. Educ. 1988, 10, 581–588. 9. Purser, G. H. J. Chem. Educ. 1999, 76, 1013. 10. Weinhold, F. J. Chem. Educ. 2005, 82, 527. 11. Purser, G. H. J. Chem. Educ. 2005, 82, 528. 12. Gil, V. M. S.; Formosinho, S. J.; Cardoso, A. C. Bond-Orders in Molecular Chemical Reactions and the Teaching of Multiple Bonding. Educ. Chem. 1988, 25, 11–12. 13. Gillespie, R. J.; Nyholm, R. S. Q. Rev. Chem. Soc. 1957, 11, 339. 14. Gillespie, R. J. Molecular Geometry; Van Nostrand Reinhold: London, U.K., 1972. 15. Gillespie, R. J.; Hargitai, I. The VSEPR Model of Molecular Geometry; Prentice Hall: London, U.K., 1991; and references therein. 16. Gillespie, R. J. VSEPR Method Revisited. Chem. Soc. Rev. 1991, 21, 59. 17. Gillespie, R. J. J. Chem. Educ. 2004, 81, 298and references therein . 18. Sidgwick, N. V.; Powell, H. M. Stereochemical Types and Valency Groups. Proc. R. Soc. London 1940, 176A, 153. 19. Linnett, J. W. The Electronic Structure of Molecules; Methuen: London, U.K., 1964. 20. Bader, R. Atoms in Molecules: A Quantum Theory. In International Series of Monographs on Chemistry; Clarendon Press: Gloucestershire, U.K., 1995; and references therein. 21. Bader, R.; Gillespie, R. J.; MacDougall, P. J. A Physical Basis for the VSEPR Model of Molecular Geometry. J. Am. Chem. Soc. 1988, 110, 7329. 22. Gil, V. Orbitals in Chemistry; Cambridge University Press: Cambridge, U.K., 2000.


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Questions and How To Differentiate Prediction and Explanation in

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