Caveat on IR Spectroscopy of CO and NO

Corrections. The following error appears in the article by Chinhyu. Hur, Sally Solomon, and Christy Wetzel, “Demonstrat- ing Heat Changes on the Ove...
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Letters Caveat on IR Spectroscopy of CO and NO I read with great interest the article by H. H. R. Schor and E. L. Teixeira, “The Fundamental Rotational–Vibrational Band of CO and NO. Teaching the Theory of Diatomic Molecules” (J. Chem. Educ. 1994, 71, 771). Although the interest for this kind of question in the teaching laboratory is not new and has even been constant for over 30 years (see for example J. Chem. Educ. 1963, 40, 245; 1966, 43, 7, 357, 552, 645; 1970, 47, 2, 391; 1982, 59, 18, 683; 1983, 60, 522; 1994, 71, 621), the originality of the present paper is that it involves molecules that became quite famous these last years because of their importance in atmospheric chemistry and in ecology. Moreover, NO is a good example of a molecule with an angular momentum that involves, besides the rotational momentum, the contribution of orbital and spin momentum. This latter effect, however, cannot be resolved completely by the experimental techniques available in a teaching laboratory. Because of the general interest of the article, I would like to draw attention to some failures in the presentation: 1. In Figure 3, the abscissa is not “wavelength” but “wavenumber”; the scale of Figure 3b is incorrect.

2. Although the calibration of the spectrometer has been adjusted on the origin of the NO band taken from the literature, the position of the CO band, which is rather close to this calibration point, is in error by about 18 cm᎑1. 3. The values of B0 and B1 one obtains from the data in Table 1 using eqs 2 and 3 are 1.964 and 1.943 cm᎑1, respectively, instead of the author’s reported values of 1.9190 and 1.9101 cm᎑1. Moreover, using these latter values one gets Be = 1.923 cm᎑1 and αe = 0.0089 cm᎑1 instead of the values 1.928 and 0.018 cm᎑1 given in Table 2. I didn’t verify the NO data to the same extent. It is clear however, from the fact that lines II and III of Figure 6b don’t pass through the origin, that the data or their interpretation are in contradiction with eq 3. This will be rather confusing or misleading to nonspectroscopists, teachers, and students alike. 4. Finally, the theoretical introduction doesn’t lead to any clear experimental applications.

For all these reasons, this paper should never be put in the student’s hands without a major caveat. Jean Olbregts Université Libre de Bruxelles 50 av. F. D. Roosevelt - CP.160/09 B-1050 Brussels, Belgium

Letters continued on page 285

Corrections The following error appears in the article by Chinhyu Hur, Sally Solomon, and Christy Wetzel, “Demonstrating Heat Changes on the Overhead Projector with a Projecting Thermometer” (J. Chem. Educ. 1998, 75, 51). The first paragraph in the section “Chemical Reaction: Exothermic” correctly says sodium nitrite, but the equation immediately following has the formula for sodium nitrate. The correct equation is: NaNO2(s) + H2NOH• HCl(s) → NaCl(s) + 2H2O(g) + N2O(g) ∆H=-136.5 kJ/mol Sally Solomon Department of Chemistry Drexel University Philadelphia, PA 19104

* The following error appears in the article by Augustine Silveira, Jr., Michael A. Knopp, and Jhong Kim (J. Chem. Educ. 1998, 75, 78–80): The double bond in structures K and KB in equation (2) should be in the 1,6 position rather than the 1,2 position as shown. Augustine Silveira, Jr. Department of Chemistry SUNY at Oswego Oswego, NY 13126

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The following error appeared in the article by R. J. Tykodi, “The Gibbs Function, Spontaneity, and Walls” (J. Chem. Educ. 1996, 73, 398–403). Equation (20) should read: ∆U(composite) – To∆S(composite) + po∆V(composite) = –To(γη) ≤ 0 Ralph J. Tykodi Department of Chemistry University of Massachusetts Dartmouth North Dartmouth, MA 02747-2300

* The following errors have come to our attention in the article by David Todd, “The Three-Step Synthesis of 2, 6-Dinitro-4-methylaniline from p-Toluidine” (J. Chem. Educ. 1991, 68, 682): 1. At the end of third paragraph, the melting point should be 118 °C instead of 1183 °C. 2. At the end of fourth paragraph, the melting point should be 208–210 °C instead of 208–2103 °C. 3. The final sentence of the final paragraph should read: It is recrystallized from acetone-water to give, in about 90% yield, the desired dinitroamine as canary-yellow crystals, mp 171 °C.4

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continued from page 258

Why Balance Hypothetical Reactions? Olson defends his algebraic method of balancing equations implying that his three general conditions guarantee the chemistry (1). However two of his worked examples are not chemically possible even if the hypothetical reactions are balanced. The chlorate oxidation of the mineral orpiment cannot occur in acid solution because arsenic sulfides are insoluble in acids quite apart from the instability of chloric acid, which decomposes to evolve chlorine, oxygen, and chlorine dioxide. Alkaline conditions are required. It is regrettable that Group analysis has dropped out of curricula since it at least taught solubilities of sulfides and hydroxides as well as linking with mineralization of elements (2). The equation given for periodate oxidation in basic solution is also flawed because iodine, in solution as polyiodides, reacts with alkali forming an intermediate hypoiodite, which rapidly disproportionates to iodide and iodate. Balancing the equation under acid conditions only needs oxidation numbers. At pH 6–7 reduction is partial: I(VII) + 2I(–I) → I(V) + I2(0). In more acidic solution it is complete: I(VII) + 7I(–I) → 4I2(0). It does seem that authors tend to provide rather exotic examples to illustrate how good are their balancing methods. The emphasis should be on predicting the chemistry, knowing the reactant input. In redox reactions the products must be compatible with the redox potentials and concentrations used; in nonredox reactions relative acidities, basicities, and solubilities need consideration if feasible reactions are to be formulated and balanced. Literature Cited 1. Olson, J. A. J. Chem. Educ. 1997, 74, 538. 2. Philips C. S. G.; Williams, R. J. P. Inorganic Chemistry, Vol. 2; OUP: London, 1966.

A. A. Woolf Faculty of Applied Sciences University of the West of England Bristol BS16 1QY, UK The author replies:

The purpose of the article (J. Chem. Educ. 1997, 74, 538) was to introduce and illustrate a balancing method. Being trained in nonexperimental chemistry, my knowledge of practical chemistry is not extensive. The examples were chosen to be interesting illustrations of the method, not as illustrations of chemistry. I apologize if the use of hypothetical reactions offended any readers or distracted from the content of the article. In my opinion, the statement “Olson defends…implying that his three general conditions guarantee the chemistry” is a blatant misinterpretation of the article. It was stated that all balanced reactions satisfy the three conditions, which applies to both hypothetical and actual reactions. How this guarantees chemistry is baffling. Any balancing method requires both reactants and products and is not concerned with whether the reaction actually occurs. I agree that predicting chemistry knowing the reactants is important. But once a set of feasible products is predicted, it is still necessary to perform an analysis based on the second law of thermodynamics. This analysis requires the conditions (activities, temperature, pressure, etc.) and the balancing coefficients to predict if the reaction is spontaneous. The objective of the article was to obtain the balancing coefficients. Finally, should I infer, from the above letter, that only feasible reactions should be balanced? Perhaps a better way is needed to illustrate one of the important uses of the second law than applying it to hypothetical (unfeasible) reactions. John A. Olson Department of Chemistry Baylor University Waco, TX 76798

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Chemical Education Today

Letters We applaud John A. Olson (J. Chem. Educ. 1997, 74, 538) for advocating the “algebraic method” of balancing chemical reactions, and for refuting the criticism that it is “mathematics, not chemistry”. However, in his efforts to ease the solution of the linear equations involved by addition of the “oxidation-reduction” balance, he has provided an unnecessary condition. Furthermore, although two of his examples do not involve “a unique balanced reaction”, he does not obtain the complete solution, which is within the capability of the algebraic method without the extra condition. The following comments are prompted by Olson’s treatment. 1. The atom and charge balances by themselves provide a necessary and sufficient number (C) of algebraic equations to balance reactions. Implementation of these equations as conditions to obtain values of stoichiometric coefficients in balanced reactions requires (i) identification of the number of degrees of freedom in the equation set F = N – C ≡ R, where N is the number of substances and R is the number of independent chemical equations required for the reacting system; and (ii) obtaining a set of R equations by specification of the values of R sets of F coefficients, and solving for the remaining C values for each set. These features are evident in each of the six examples given by Olson. 2. In his second example, F = 7 – 6 = 1 ≡ R. We arbitrarily set the value of one coefficient and solve for the values of the remaining six, to obtain one balanced reaction. Thus, if we set a = 1, the coefficient set {a, b, c, d, e, f, g} is {1, 1/2, 1, 2, 1, {1, {1}; this is the same solution (apart from a factor of 2) obtained by Olson. His other examples, except the fourth and sixth, also have F = 1 ≡ R and can be treated similarly. 3. In his fourth example, F = 6 – 4 = 2 ≡ R. Since R = 2, there are 2 independent chemical equations, with coefficients, say, {a1, b1, c1, d1, e1, f1} and {a2, b2, c2, d2, e2, f2}. Since F = 2, we set values of two coefficients for each equation, in such a way as to ensure that the resulting chemical equations are independent. An easy way to do this is to use {1, 0} and {0,1} for the same two coefficients. Thus, if we choose {a1, c1} and {a2, c2}, we obtain the coefficient sets {1, 11, 0, 4, { 4, 8} and {0, {8, 1, { 3, 3, { 6}. The corresponding chemical equations can be written as IO4{ + 11I{ + 4H2O = 4 I3{ + 8OH { IO3{ + 8I{ + 3H2O = 3I3{ + 6OH { This set of equations is not unique (but the number of equations [two] is unique); the two equations may be linearly combined to obtain any number of equivalent sets of two independent equations. The fact that R > 1 in this case is the reason the system “does not have a unique balanced reaction”. Olson establishes the latter point, but does not provide a complete solution. A similar situation exists for Olson’s sixth example, the reduction half-reaction for ozone. The system has N = 5, C = 3, F = 2 ≡ R. A set of two independent chemical equations, corresponding to the two half-reactions given 286

by Olson, is O3 + 3 H2O + 6 e{ = 6 OH {

4.

5.

6.

7.

8.

O2 + 2 H2O + 4 e{ = 4 OH { The algebraic method yields this complete solution without the oxidation–reduction balance condition, and thus avoids the difficulty of assignment of oxidation states cited by Olson. He linearly combines these equations to yield a single so-called “correct balanced half-reaction”, which, however, is not unique. Furthermore, we are not sure in what sense it is “correct”. Lack of appreciation of the significance of a chemical system not being represented (stoichiometrically) by a unique balanced reaction can be a major source of confusion for beginning (and other) students. Unfortunately, examples of this nonuniqueness masquerading as uniqueness abound in the chemical literature (for a recent example, see J. Chem. Educ. 1996, 73, 1129). The additional algebraic equations provided by Olson’s oxidation–reduction balances are linearly dependent on those obtained from the atom and charge balances, and are thus unnecessary for writing chemical equations. Olson realizes the point about generating “more equations than are needed”, but does not draw the unequivocal conclusion about sufficiency of the atom and charge balances. We are puzzled by Olson’s statement that “there are reactions where these two conditions (atom and charge balances) do not generate enough equations…” He gives no example of this, and we are not aware of any. As indicated by Olson, the algebraic method he describes is a variation of the “matrix method” (see, e.g., R. A. Alberty, J. Chem. Educ. 1991, 68, 984). The matrix method is merely a systematic way of solving the linear algebraic equations involved, so as to generate the appropriate number of chemical equations. For many cases requiring treatment beyond inspection, such as the examples posed by Olson, the matrix method can be carried out by hand manipulation. For situations in which this becomes too tedious, computer software is available, but this need not be a consideration for beginning students. We agree with Olson that the algebraic method offers the best approach for beginning students to understand the fundamental basis for writing chemical equations and is well within the grasp of beginning students. However, we believe that this method should be unencumbered by additional and hence unnecessary concepts, such as oxidation states and half-reactions, whatever their value otherwise in chemistry pedagogy. R. W. Missen Department of Chemical Engineering and Applied Chemistry University of Toronto Toronto, Canada, M5S 3E5 W. R. Smith School of Engineering University of Guelph Guelph, Canada, N1G 2W1

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Chemical Education Today

The author replies:

I would like to thank Professors Missen and Smith for their comments concerning my article (J. Chem. Educ. 1997, 74, 588). For the most part, their comments are correct, although I fail to understand why they feel that my treatment of R = 2 reactions was not complete. After all, it is simple to show that their solutions are linear combinations of the reactions obtained in my treatment. Perhaps I should not have taken for granted that the readers were aware that there were only two independent solutions. I also did not mean to imply that the matrix method was not capable of producing the solutions for any reaction. What I meant to convey was that the oxidation reduction (OR) equations for a chosen OR scheme for R > 1 reactions gave sufficient equations to find a solution for that scheme as was shown in example 4. Changing the scheme determines the other independent reaction. The method they devised above works well, although I would choose any coefficient to be zero, find the solution, and use any non-zero coefficient in this solution to be the second choice (choosing the pair d and e in their method gives only one reaction). The rest of this letter will deal with what I feel are two important issues. The first is why the algebraic method has not become the standard technique for balancing reactions. The second is what additional information can be obtained from the OR condition. Missen and Smith are correct about, for R = 1 reactions, the OR equations being linearly dependent on the atom balance (AB) and charge balance (CB) equations. What they fail to consider is whether the AB and CB equations are the “simplest” set of equations. Given a computer program, this is not an important issue; but if balancing “by hand”, this could be an important point. To see this directly, consider the charge equation for my third example, which is a ({1) + b (0) = c ({1) + d (-2) + e({1) + f (0) + g (+1) This is not a “simple” equation, but rewriting the charges in terms of oxidation numbers, grouping the terms for each element and using the AB equations leads to [a(+5) – e ({1)] + [2b (+3) – c (+5)] + [3b({2) – d (+6)] = 0 Adding and subtracting a({1) and 2b (+5) (i.e., the final oxidation states) and using the AB equations leads to 6a = 28b, which was one of the OR equations. The other OR equations can be obtained in a similar fashion. The point here is that the charge equation can be transformed into a much simpler equation and when used with the AB equations solves the problem. It is simple to show that the CB equation is now a linear combination of this OR and the AB equations. One sees that the OR conditions bypass this procedure by furnishing a direct way to obtain these “simple” equations. The end result is the same in that a simpler set of equations can be used to solve the problem. A “purist” could mathematically construct the simplest set of linearly independent equations; but in my opinion, this is, as H. Goldstein would say, equivalent to cracking a peanut with a sledgehammer in that the simplest equations in the over-complete set would naturally be used anyway. Based on their comments, Missen and Smith prefer to ignore this simpler set of equations and live

with what AB and CB generates. I feel, however, that using a simpler set of equations could increase the popularity of the algebraic method and this is why the OR condition was introduced. In order to address the second issue, I would like to consider a class of reactions of the form +4

+3

+7

+2

aMX2 + bMY3 → cMX3Y + dM2Y4 which has the unique balancing coefficients a = 3, b = 4, c = 2, and d = 5, X and Y are nonmetals and have fixed oxidation numbers of {2 and {1, respectively, and M is a metal. Assuming that the total oxidation or reduction is the amount of electrons transferred, it would be important to know under what conditions this amount would be to obtain a certain voltage. Constructing again the CB equation in terms of oxidation states leads to a (+4) + b (+3) – c (+7) – d (+2) = 0 which does not lead to an OR equation. The problem here is that the balancing coefficients do not define the amount of oxidation or reduction, as is easily seen. Rewriting the coefficients as a = a′ + a″ etc. and using the OR condition for the reactant side gives 3a′ + 4b′ = 2a″ + b″ where the final oxidation numbers for a′, a″, b′, and b″ are 7, 2, 7, and 2, respectively. Using a′ + a″= 3 and b′ + b″ = 4 gives a′ + b′ = 2 which clearly shows that the amount of oxidation is not unique. If these coefficients are restricted to be positive numbers, the maximum oxidation would occur for a′ = 0, a″ = 3, b′ = 2, and b″ = 2 which would correspond to a transfer of eight electrons. The minimum oxidation would occur for a′ = 2, a″ = 1, b′ = 0, and b″ = 4 and would correspond to a transfer of 6 electrons. If one could control how much M in MX2 or MY3 goes into a given oxidation state, any voltage between the two values corresponding to maximum and minimum electron transfers could be obtained. Mathematically, negative values of these coefficients are also possible but their experimental interpretation is not obvious. The point is that the AB and CB conditions, which are sufficient to balance the reaction, give no further insight into the reaction. They give no understanding of what is occurring if a particular voltage is observed and they cannot predict what the conditions must be to give a desired voltage. In conclusion, Missen and Smith are against any additional concepts other than AB and CB in balancing reactions. It does not seem important to them whether the concept simplifies the problem or aids in further interpreting the reaction. I simply do not agree with them and have tried to show how useful the OR condition can be. Whether or not one agrees with this boils down to a matter of personal choice. John A. Olson Department of Chemistry Baylor University Waco, TX 76798

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