In the Classroom
A Consistent Set of Oxidation Number Rules for Intelligent Computer Tutoring Dale A. Holder and Benny G. Johnson* Quantum Simulations, Inc., 5275 Sardis Road, Murrysville, PA 15668; *
[email protected] Paul J. Karol Department of Chemistry, Carnegie Mellon University, Pittsburgh, PA 15213
Many beginning students have difficulty learning the oxidation number model, as anyone who has taught introductory chemistry will attest. Oxidation numbers are values that are determined by the application of a set of conventional but somewhat arbitrary rules. The oxidation numbers do not strictly have a physical meaning. They may simply serve as a bookkeeping technique to keep track of electrons. We are engaged in a large-scale project for developing interactive artificial intelligence software for tutoring in chemistry. As part of this effort, we have developed an intelligent tutoring system for oxidation numbers.1 Though it would have been desirable for the tutor to use the same oxidation number rules found in the textbook, upon examination of several current textbooks2 we found that the rules were in fact not adequate to serve as the foundation for an intelligent tutoring system, owing to ambiguities and inconsistencies that may not be apparent on the surface. The focus of this paper is the development of a more rigorous method of assigning oxidation numbers that remains simple enough for beginning students. Pauling’s original definition (1) is an example of a rigorous method yielding unique and well-defined results. However, this approach has two potential drawbacks at the introductory chemistry level: it requires knowledge of molecular structure and electronegativity. Oxidation numbers are often introduced before one or both of these concepts. For this reason, in practice, rules are taught for assigning oxidation numbers from the chemical formula alone. Problems with Textbook Oxidation Number Rules No two textbooks have exactly the same set of rules. However, all rule sets we have examined contain the same basic information and suffer from the same weaknesses. Various limitations of oxidation number rules have been recognized many times, and several strategies for addressing them have been proposed (2–10). Most of these are primarily concerned with making the oxidation number values more “realistic” chemically, either in general or for specific problematic cases. Toward this end, many methods incorporate information from a Lewis structure or even more detailed chemical information (2–6 ); again, however, we must exclude such approaches from consideration here. Though the goal of chemically reasonable oxidation numbers is desirable to the extent it can be achieved, the issue addressed here is more elementary. We are focused on placing the oxidation number method on a more rigorous footing for beginning students. This paper deals with two problematic categories: (i) formulas having multiple solutions and (ii) formulas having no solution.
What is the best way to remedy the deficiencies in the rules? There are two common methods. One is to introduce exceptions in an attempt to cover problematic cases (such as peroxide) and also to increase the total number of rules (2, 6, 8–10). This approach cannot provide a satisfactory resolution. While peroxide is the most common counterexample to the rule for oxygen, for example, it is certainly not the only one, and more importantly is not the only one a student is likely to encounter. At least seven oxidation states of oxygen between ᎑2 and +2 occur in real compounds. Exhaustive identification of all possible exceptions to such a simplistic model is impractical, if not impossible. Proliferating rules and increasing their complexity by adding exceptions quickly makes the procedure unmanageable for the student. Another clear reason why this approach will fail is that making exceptions to one rule can do nothing to preclude an inconsistent solution using a different rule; sometimes different rules can produce different values for the same element. Successfully addressing inter-rule conflicts requires more than manipulating the rules separately. We will see that making peroxide an exception still does not prevent problems with hydrogen peroxide itself. A different approach is to recognize that if there is potential for numerous exceptions, then a heuristic such as the oxygen rule should in fact be viewed as on a lower level than, say, the summation rule, which is always obeyed. This leads to the introduction of priorities among the rules by stipulating a specific hierarchical order of application (6–8). This is usually considerably more robust. It comes at the expense, however, of being more complex than is likely to be practical for the student. Not only must the rules themselves be learned, but also their precise ordering with respect to one another. Furthermore, the student is not usually given the rationale behind the specific ordering, creating an impression of arbitrariness. Consistent Oxidation Number Rules We seek the advantages of a hierarchical rule set without assuming the complexity entailed. We have found that only two levels of priority are necessary to realize effectively all the practical benefit, while remaining substantially simpler than earlier schemes (6–8), which place each rule on a separate level of priority. This new rule set is given in Table 1. The advantages of the new rule set are illustrated in the following examples. Example 1. The simple example of hydrogen peroxide is one every student considers. Of the typical textbook rules, four are relevant here. One rule states that hydrogen should have an oxidation number of +1. Another directs that oxygen be
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In the Classroom Table 1. Consistent Oxidation Number Rules Name of Rule
Rule
Free element
The oxidation number of an atom of a free element equals 0.
Simple ion
The oxidation number of a monatomic ion equals the charge on the ion.
Fluorine
The oxidation number of fluorine in compounds equals ᎑1.
Hydrogen
The oxidation number of hydrogen in combination with nonmetals equals +1.
First Priority
Group 1 metal The oxidation number of group 1 metals in compounds equals +1. Group 2 metal The oxidation number of group 2 metals in compounds equals +2. Sum
The algebraic sum of the oxidation numbers of all the atoms in a chemical formula equals the net charge on the species.
Separate ions
In ionic compounds, the oxidation numbers in the cation and the anion are independent and can be assigned separately.
Oxygen
The oxidation number of oxygen in compounds equals ᎑2.
Nonmetal
In binary combinations of nonmetals, the element closer to fluorine on the periodic table is given a negative oxidation number, equal to the charge on its common monatomic ion.
Second Priority
Table 2. Oxidation Numbers for H2O2 Obtained with Conventional Rules
Rules Applied
Oxidation Number H
O
Hydrogen, Oxygen
+1
᎑1
Nonmetal, Hydrogen
+1
᎑2
Nonmetal, Sum
+2
᎑2
Common Formulas with No Oxidation Number Solution by Various Rule Sets No solution with conventional rules, has solution with new rules Transition metal compounds other than oxides, fluorides and hydroxides; e.g., Fe2(Cr2O7)3, AgNO3, CuSO4 Ammonium compounds other than oxide, fluoride and hydroxide; e.g., (NH4)2SO4, NH4Cl, (NH4)3PO4 No solution with conventional rules or new rules SCN ᎑, OCN ᎑, and their compounds, organics containing four or more elements; e.g., HCONH2
assigned a value of ᎑2, except in peroxides, where it is assigned ᎑1. A rule for binary compounds of nonmetals says the more electronegative element gets an oxidation number equal to the charge on its common monatomic ion. And finally, the oxidation number values are unified by the condition that their sum must be zero. Since there are only two elements to assign, several different rule combinations can be applied to solve the problem. Table 2 lists the oxidation numbers obtained for three different choices of rules. Surprisingly, three different sets of results are found. It is implicitly assumed, and rightly so, that the proper application of any of the rules should always lead to the same correct result. In practice, however, quite the
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opposite is found. Though it is possible to reach the correct solution, it is also equally possible to reach other incorrect solutions by legitimate application of the rules. It is therefore clear that students can reach a wrong answer through no fault of their own; this is unacceptable. The rules in Table 1 solve this problem with no difficulty. Hydrogen is first assigned +1 (by the hydrogen rule); then oxygen is assigned the correct value of ᎑1 by the sum rule, which is the only applicable first-priority rule. This is appropriate because charge conservation is the origin of the usual peroxide exception. In contrast with the results in Table 2, the correct values are now the only ones that follow by properly applying the rules, and they are obtained without the need for exceptions. Example 2. The second problematic category consists of compounds that cannot in fact be assigned a complete set of oxidation numbers by following the rules. The new rule set corrects this for a large number of “reasonable” formulas likely to be given to students. The box gives several examples of such compounds having no solution and shows how the new rule set affects these. Most of the rules in Table 1 have analogues in the textbooks, but one, the separate ions rule, is not frequently found. Its inclusion permits assignment of several common compounds that do not have a solution by the conventional rules. An example is ammonium sulfate, which cannot be completely assigned without exploiting the fact that this compound is composed of independent NH4+ and SO42᎑ ions. This makes use of structural information in a simple way and requires the students’ knowledge of the common ions, as typically assumed. Another innocent-looking example is the thiocyanate ion, SCN ᎑, and its compounds such as KSCN, often found in end-of-chapter and workbook problem sets. While numbers that appear reasonable can be written for each atom (᎑2, +4, and ᎑3, respectively), they are not obtainable from the rules. There are no rules that explicitly address these elements, and the rule covering nonmetals is for binary compounds only. In this case, the new rule set does not admit a solution either. After handling common ionic compounds, we decided this represented a reasonable point to compromise for the sake of keeping the rule set simple, before extending the rules too far into organic compounds for which oxidation numbers are much less appropriate. Attempting to make all possible formulas assignable is neither reasonable nor desirable. Again, the goal is to ensure that practical problems at the introductory level are handled consistently without confusion and contradiction, by a procedure that is simple enough to allow the student to focus clearly on the underlying concepts. An important part of this is pointing out that the oxidation number model may indeed sometimes fail owing to its limited approximate nature, and encouraging students to look for such cases and think about why the model fails when they do encounter them. Finally, we point out that our second-priority nonmetal rule is deliberately worded to avoid invoking electronegativity, which as mentioned earlier is not always taught before oxidation numbers. If electronegativity has been covered, the instructor may feel free to substitute “more electronegative element” for “element closer to fluorine on the periodic table” in the wording of the rule.
Journal of Chemical Education • Vol. 79 No. 4 April 2002 • JChemEd.chem.wisc.edu
In the Classroom
Summary We have developed a method for assigning oxidation numbers that eliminates the inconsistencies and ambiguities found in most conventional textbook rules, yet remains simple enough for beginning students to use. It involves imposition of a two-level hierarchy on a set of rules similar to those already being taught. We have used these improved rules as the basis for an intelligent tutoring program,1 which is available for evaluation and will be reported upon in a future publication. We further recommend underscoring that the oxidation number method is an approximation and cannot always be successfully applied. Clearly demonstrating to the students that they are in fact working with an approximate model that has limitations is of significant benefit in itself. When failure does occur, it will indicate the limitations of the oxidation number concept itself, rather than merely the failure of a poorly constructed set of rules. Our tutor specifically identifies and explains problems that are outside the scope of the model. The present approach should particularly be compared with prior work on oxidation number rules in the context of computer problem-solving or tutoring (8–10). These efforts have focused on extending the scope of the rules by adding special cases and exceptions and creating a significant number of additional rules. If the program is intended for teaching, in light of the considerations already discussed, we disagree with this approach as counterproductive for instructional purposes. Such a program should work with the same procedure the student is intended to learn. Forcing students to struggle with an overly complicated procedure clouds the view of the fundamental underlying concepts. Acknowledgments This work was partly supported by the Ben Franklin Technology Center of Western Pennsylvania through grant
number 98W.SC00647R-1. We are grateful to Paul E. Yeary and F. James Holler for helpful suggestions. A generous donation of twenty years of back issues of this Journal by Foil A. Miller is greatly appreciated. Notes 1. A demonstration copy of the tutor can be obtained by writing to
[email protected]. We welcome constructive feedback from JCE readers. 2. Based on a survey of 32 high school and undergraduate general chemistry textbooks from 15 publishers, comprising current textbooks exhibited by publishers at the ACS Fall 2000 National Meeting in Washington, DC, and books appearing on the Kentucky state textbook adoption list within the past six years.
Literature Cited 1. Pauling, L. C. The Nature of the Chemical Bond and the Structure of Molecules and Crystals; An Introduction to Modern Structural Chemistry, 3rd ed.; Cornell University Press: Ithaca, NY, 1960. 2. Stonestreet, R. H. J. Chem. Educ. 1971, 48, 625. Geanangel, R. J. Chem. Educ. 1972, 49, 299. Woolf, A. A. J. Chem. Educ. 1972, 49, 299. Smith, L. O. J. Chem. Educ. 1972, 49, 300. Stonestreet, R. H. J. Chem. Educ. 1972, 49, 300. 3. Kaufmann, J. M. J. Chem. Educ. 1986, 63, 474. 4. Woolf, A. A. J. Chem. Educ. 1988, 65, 45. 5. Packer, J. E.; Woodgate, S. D. J. Chem. Educ. 1991, 68, 456. 6. Calzaferri, G. J. Chem. Educ. 1999, 76, 362. 7. Holleran, E. M.; Jespersen, N. D. J. Chem. Educ. 1980, 57, 670. 8. Eggert, A.; Middlecamp, C.; Kean, E. J. Chem. Inf. Comput. Sci. 1990, 30, 181. 9. Eggert, A.; Middlecamp, C.; Kean, E. J. Chem. Educ. 1991, 68, 403. 10. Birk, J. P. J. Chem. Educ. 1992, 69, 294.
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