Communication Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX
pubs.acs.org/jchemeduc
Introducing a Simple Equation To Express Oxidation States as an Alternative to Using Rules Associated with Words Alone Piotr Minkiewicz,* Małgorzata Darewicz, and Anna Iwaniak Department of Food Biochemistry, University of Warmia and Mazury in Olsztyn, Plac Cieszyński 1, 10-726 Olsztyn-Kortowo, Poland S Supporting Information *
ABSTRACT: A simple equation to calculate the oxidation states (oxidation numbers) of individual atoms in molecules and ions may be introduced instead of rules associated with words alone. The equation includes two of three categories of bonds, classified as proposed by Goodstein: number of bonds with more electronegative atoms and number of bonds with less electronegative atoms. Formal charge of a given atom is also taken into account in agreement with IUPAC recommendations. The equation provides a new (not described to date) way to work with the commonly used rules of oxidation state calculation, and presents an interesting opportunity for studying the redox reaction.
KEYWORDS: High School/Introductory Chemistry, First-Year Undergraduate/General, Organic Chemistry, Oxidation/Reduction, Oxidation State, Communication/Writing
O
recommended by Paik et al.4 and Generalić,9 especially for calculation of oxidation numbers of atoms in organic molecules. According to Goodstein, the bonds formed by a given atom may be divided into three categories: bonds with more electronegative atoms, bonds with equally electronegative atoms, and bonds with less electronegative atoms. The equation including number of bonds belonging to the first and third category, together with the formal charge at a given atom, is as follows:
xidation and reduction reactions are important topics in chemistry teaching, both from a theoretical and practical point of view.1−4 Calculation of the oxidation states (oxidation numbers) of particular atoms in a molecule is a crucial step in processing and understanding redox reactions, especially in the case of organic compounds. Functional groups of organic compounds are classified, e.g., according to oxidation state of carbon atoms included in these groups.5 Reaction converting one functional group into another may be thus explained in terms of change of oxidation state. This issue is usually explained in handbooks5−7 and on Web sites8,9 using sets of rules associated with words alone. The most recent overwiew of rules applied is provided in the article of Paik et al.4 and references cited therein. The exploded structure method (ESM)/Lewis structure method of oxidation state calculation is an exception. This method has been first described by Kauffman10 using rules associated by words alone. Jurowski and co-workers2 have expressed these rules using the equation
Z = n + − n− + z
Z is an oxidation state (oxidation number). n+ is defined as a number of bonds formed by a given atom with more electronegative atoms (number of electrons from a given atom involved in pairs assigned to more electronegative atoms). n− is defined as a number of bonds formed by a given atom with less electronegative atoms (number of electrons from less electronegative atoms, involved in electron pairs assigned to given atom). z is defined as formal charge at a given atom. Taking into account formal charge is in agreement with general chemistry rules and the IUPAC recommendation.8 The required information includes the molecule or ion structure (including assignment of formal charge to individual atom in
[oxidation state] = [valence electrons] − [assigned electrons]
(1)
4
As discussed by Paik et al., rules associated with words alone are difficult to remember, and there are also difficulties in their implementation in computer programs calculating oxidation states (such as an Oxidation Number Calculator9).
■
FORMALISM USED FOR OXIDATION NUMBER CALCULATION Rules for oxidation state calculation, as proposed by Goodstein,1 are simple and general. The same or similar rules are also © XXXX American Chemical Society and Division of Chemical Education, Inc.
(2)
Received: May 10, 2017 Revised: November 28, 2017
A
DOI: 10.1021/acs.jchemed.7b00322 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Communication
calculation of oxidation states of atoms in fragments remaining unchanged during the reaction. Trifluoromethanethiol (compound in part c) in Figure 1 possesses a carbon atom forming four bonds with more electronegative atoms (fluorine and sulfur). The oxidation state of this atom is thus +4. The thiocyanate anion (compound in part d in Figure 1) forms resonance structures (see Figure 1 and Table 2).
the case of ions) and electronegativity values of particular atoms. The latter are recently available via the Internet.9,11
■
ADVANTAGES OF THE PROPOSED METHOD The equation based on the rules proposed by Goodstein1 makes calculation of oxidation numbers easier compared to rules associated with words alone, especially for organic compounds, which do not contain oxygen. Methanethiol (compound in part a of Figure 1) may serve as an example
Table 2. Oxidation States of Particular Atoms in Two Resonance Structures of Thiocyanate Anion (NCS−), Calculated on the Basis of Electronegativity Atom
Pa
N C S
3.04 2.55 2.58
N C S
3.04 2.55 2.58
n+
n−
Resonance Structure 1b 0 3 4 0 0 1 Resonance Structure 2b 0 2 4 0 0 2
z
Z
0 0 −1
−3 +4 −2
−1 0 0
−3 +4 −2
a
P is the Pauling electronegativity according to the periodic table, published at the ChemWiki Web site.11 bResonance structures from Figure 1d.
Resonance structures 1 and 2 possess a different number of bonds formed by nitrogen and sulfur atoms, and thus different localization of the −1 formal charge (on S in d1, vs on N in d2). Taking both the number of bonds and formal charge into account, we can find that oxidation states of corresponding atoms in both structures are the same (Table 2, but see the comparison to Paik et al.’s results below). Simplicity is the major advantage of the equation as compared with rules associated with words alone. This opinion is in agreement with results published by Jurowski et al.,2 showing that calculation of oxidation states using the method based on the equation (eq 1) gave better results in learning than methods based on rules associated with words alone (e.g., IUPAC rules8). We believe that our eq 2 is simplier than Kauffman’s ESM/ Lewis Structure Method. Our proposal does not utilize all terms and definitions required to understand eq 1. We do not need to take into account the number of valence electrons. As shown in the explanation of symbols used in eq 2, it is also possible to avoid the term “assigned electrons”, although not for all compounds. For instance, calculation of the oxidation state of nitrogen in nitro compounds requires the use of explanations of eq 2 given in parentheses. On the other hand, our equation includes the formal charge at particular atoms. Additional explanations concerning the formal charge are not required. Reduction of number of definitions used may be considered as an advantage of our proposal in light of remarks published by Silverstein.12
Figure 1. Examples of oxidation states in (a) methanethiol (CH3SH); (b) dimethyl disulfide (CH3SSCH3); (c) trifluoromethanethiol (CF3SH); (d) thiocyanate anion (NCS−), 1 and 2 are resonance structures indicated in Table 2. (e) Two example resonance structures of furan.
Table 1. Oxidation States of Particular Atoms in Methanethiol (CH3SH), Calculated on the Basis of Electronegativity Atom
Pa
n+
n−
z
Z
C H S
2.55 2.20 2.58
1 1 0
3 0 2
0 0 0
−2 +1 −2
a
P is the Pauling electronegativity according to the periodic table, published at the ChemWiki Web site.11
of calculations (Table 1). Although it appears controversial, even the smallest differences between electronegativities of particular atoms are included. Electronegativity values used in this text are stipulated to the hundredth’s place. Rounding to the tenth’s place may change results of calculation of oxidation states (for details see Supporting Information). Dimethyl disulfide (compound in part b in Figure 1) is a product of the first step of methanethiol oxidation. Oxidation of methanethiol to dimethyl disulfide leads to replacing two S−H bonds by one bond between two sulfur atoms. The S−S bond is not taken into account in the calculations. The reaction leads to a change in the oxidation state of two sulfur atoms from −2 to −1. The oxidation states of carbon and hydrogen atoms are the same in both compounds. It is possible to omit the
■
LIMITATIONS OF THE PROPOSED METHOD Occurrence of resonance may complicate the calculation of oxidation states of atoms in molecules. Thiocyanate anion may serve as an example of such complications. Our oxidation state calculations (Table 2) differ from these of Paik et al.4 This difference is an artifact occurring due to rounding of electronegativity values to the tenth’s place (see Supporting Information). This example shows that even slight differences B
DOI: 10.1021/acs.jchemed.7b00322 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Communication
ORCID
in electronegativity may play an important role in oxidation state calculation. Oxidation states of individual atoms, calculated according to eq 1, may be different in different resonance structures (independently from rounding of electronegativity values). This can occur if there is more than one atom of the same element in a molecule or ion. Calculation of average oxidation states according to Menzek13 may serve as an alternative solution in that case. Average oxidation state of atoms of the same element, e.g., carbon atoms in furan (compound in part e of Figure 1) or in ion C5H5−, discussed by Paik et al.,4 remains the same in different resonance structures. This finding is in agreement with the fact that a true distribution of electrons is a superposition of resonance structures. The average oxidation state of atoms of a given element in a molecule or ion may be calculated on the basis of oxidation states of atoms in all individual resonance structures, using eq 1 proposed here; however, the above algorithm would be complicated and timeconsuming as compared with the one proposed by Menzek.13 Oxidation states have some general limitations reported by Woolf14 and Gupta et al.15 Calculation of oxidation states using electronegativity values of individual atoms does not take into account changes of bond polarity caused by neighboring atoms. Woolf14 has discussed some examples of experimentally determined bond polarization, which cannot be explained on the basis of formal oxidation states. Gupta et al.15 have pointed out that electron density at some atoms may be independent of formal oxidation states using carbon atoms in aldehyde and ketone groups as an example. A similar remark concerns carbon atoms in alkanes. The occurrence of the limitations mentioned above does not depend on the manner of calculating oxidation states. An alternative solution is necessary to address these challenges. For instance, the program MolCalc16,17 allows the calculation of partial charges at particular atoms in molecules and the prediction of the true polarization of bonds between them. The results obtained using this program are consistent with the findings discussed by Woolf14 and Gupta et al.15
Piotr Minkiewicz: 0000-0003-0481-1196 Notes
The authors declare no competing financial interest.
■ ■
ACKNOWLEDGMENTS This work has been financed by the University of Warmia and Mazury in Olsztyn (Project No. 17.610.014-300).
■
CONCLUSION We propose a simple equation for the calculation of oxidation states of individual atoms in molecules and ions based on Goodstein’s and IUPAC rules. It seems to be an interesting opportunity to study the redox reactions of organic compounds. Moreover, it offers a systematic algorithm allowing the calculation of oxidation states of all atoms in a molecule or ion step by step.
■
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.7b00322. Examples of oxidation states of atoms, calculated on the basis of electronegativity values rounded to the tenth’s place, and students’ opinion about comparison of eq 2 and rules associated with words alone (PDF)
■
REFERENCES
(1) Goodstein, M. P. Interpretation of Oxidation-Reduction. J. Chem. Educ. 1970, 47 (6), 452−457. (2) Jurowski, K.; Krzeczkowska, M. K.; Jurowska, A. Approaches to Determining the Oxidation State of Nitrogen and Carbon Atoms in Organic Compounds for High School Students. J. Chem. Educ. 2015, 92 (10), 1645−1652. (3) Saloranta, T.; Lönnqvist, J.-E.; Eklund, P. C. Transforming Undergraduate Students Into Junior Researchers: Oxidation−Reduction Sequence as a Problem-Based Case Study. J. Chem. Educ. 2016, 93 (5), 841−846. (4) Paik, S.-H.; Kim, S.; Kim, K. Suggestion of a Viewpoint Change for the Classification Criteria of Redox Reactions. J. Chem. Educ. 2017, 94 (5), 563−568. (5) Clayden, J.; Greeves, N.; Warren, S.; Wothers, P. Organic Chemistry; Oxford University Press: Oxford, U.K., 2004. (6) Brown, T. E.; LeMay, H. E. H.; Bursten, B. E.; Murphy, C.; Woodward, P. Chemistry The Central Science; Prentice-Hall: Upper Saddle River, NJ, 2012. (7) Karty, J.; Organic Chemistry. Principles and Mechanisms; W. W. Norton & Company Inc.: New York, NY, 2014. (8) Oxidation States at the IUPAC Gold Book Website, http:// goldbook.iupac.org/html/O/O04365.html (accessed Nov 2017). (9) Generalić, E. Oxidation Numbers Calculator. EniG. Periodic Table of the Elements; KTF-Split, http://www.periodni.com/oxidation_ numbers_calculator.php (accessed Nov 2017). (10) Kauffman, J. M. Simple Method for Determination of Oxidation Numbers of Atoms in Compounds. J. Chem. Educ. 1986, 63 (6), 474− 475. (11) Electronegativity Values ChemWiki Website, University of California Davis; https://chem.libretexts.org/Reference/Reference_ Tables/Atomic_and_Molecular_Properties/A2%3A_ Electronegativity_Values (accessed Nov 2017). (12) Silverstein, T. P. Oxidation and Reduction: Too Many Definitions? J. Chem. Educ. 2011, 88 (3), 279−281. (13) Menzek, A. A. New Approach to Understanding OxidationReduction of Compounds in Organic Chemistry. J. Chem. Educ. 2002, 79 (6), 700−702. (14) Woolf, A. A. Oxidation Numbers and Their Limitations. J. Chem. Educ. 1988, 65 (1), 45−46. (15) Gupta, V.; Ganegoda, H.; Engelhard, M. H.; Terry, J.; Linford, M. R. Assigning Oxidation States to Organic Compounds via Predictions From X-Ray Photoelectron Spectroscopy: a Discussion of Approaches and Recommended Improvements. J. Chem. Educ. 2014, 91 (2), 232−238. (16) Jensen, J. H.; Kromann, J. C. The Molecule Calculator: A Web Application for Fast Quantum Mechanics-based Estimation of Molecular Properties. J. Chem. Educ. 2013, 90 (8), 1093−1095. (17) Program MolCalc (Molecule Calculator); http://molcalc.org/ calculation (accessed Nov 2017).
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. C
DOI: 10.1021/acs.jchemed.7b00322 J. Chem. Educ. XXXX, XXX, XXX−XXX
