Chemical Education Today
Letters Generation of HCl, DCl, HBr, and DBr The article “Vibration-Rotation Spectra” (J. Chem. Educ. 1993, 70, 1035) describes the preparation of gaseous DBr, its related halides HCl, DCl, and HBr, and their IR spectra. The reagents involved are liquid Br2 and D8-toluene catalyzed by FeCl3. These materials are toxic, corrosive, flammable, and expensive. It should be noted that there are two previous articles in this Journal deals with the same subject (M. Bader, “Molecular Properties of Diatomic Molecules from IR Spectra”, J. Chem. Educ. 1969, 46, 206, and J. L. Hollenberg, “Energy State of Molecules—Resource Paper VIII, J. Chem. Educ. 1970, 47, 2). In 1969, trying to teach molecular spectroscopy, I discovered that DBr fell in the most sensitive region of the common Perkin-Elmer IR instruments of that day. The individual spectral lines were so well resolved that using a measuring microscope we could measure them, in principle, to 0.01 wave number. DBr then became a routine gas for undergraduate experiments. The synthesis I suggest, which is safer and simpler than the one proposed, is to place a small volume, ca. 1 mL, of liquid PBr3 in a vertically clamped sidearm test tube (hood!) and cover with an equal volume of D 2O without mixing so, that two layers result. The reagents are very slow to react. A slight tickle with a Bunsen burner will initiate a self-sustaining reaction that will generate copious amounts of DBr at a fairly constant rate. (The system must be open to the atmosphere somewhere.) The gas can be dried over anhydrous CaBr2. HBr is generated using ordinary water. To our surprise we discovered that passing the wet DBr or HBr over CaCl2 allowed sufficient exchange that significant amounts of the corresponding chlorides were obtained. One cautionary note: since PBr3 is exceedingly hygroscopic, whenever we opened a fresh bottle we resealed it in ca. 2 mL portions in simple glass vials made from 6 mm Pyrex tubing having a small bulb blown on one end and leaving a 4–5 cm length of bare tubing. This vial is easy to crack without spilling and in this way students were always guaranteed equal amounts of fresh reagent for their experiments. Morris Bader Department of Chemistry Bethlehem, PA 18018
ion. It makes people trying the experiment be more conscientious about safety, waste disposal, and pollution. In addition, they gain insight into an interesting reaction, namely a Lewis acid-catalyzed electrophilic aromatic substitution. Bader’s procedure calls for PBr3 that needs to be handled carefully. Bader’s procedure is also valid, but I would like to stress once again that my procedure simultaneously leads to HCl, HBr, DCl, and DBr in a single experiment, which in my opinion is quite a desirable feature. N. Ganapathisubramanian Department of Chemistry Yale University New Haven, CT 06520-8107
Beer–Lambert Law The experiment described in “Discovering the Beer– Lambert Law” (1994, 71, 983), by Ricci, Ditzler, and Nestor, is a very cleverly designed exercise that demonstrates elegantly the physical basis of the Beer–Lambert law, but the thought experiment as described therein leads to results students will likely find puzzling. Students are asked to consider what will happen as a collection of 1000 marbles is rolled down an inclined plane that has many holes drilled randomly into its surface. The edge of the plane is marked off in 10 equal intervals and there are enough holes in each interval so that any one BB has a one-in-10 chance of falling through a hole as it traverses any one interval. On this basis it is suggested that after the marbles have traveled one interval, there will be 900 marbles left; after two intervals; 810, and so on. A similar process is followed for an inclined plane for which the probability of a marble dropping through a hole is one in 20. Clearly, the number of marbles decreases exponentially with the distance traveled down the ramp; the number of marbles left after a distance L has been covered is given by N = No e{PL where P is the probability per unit length that a marble falls through a hole. Differentiating this expression and solving for P, we find
N. Ganapathisubramanian replies: I get the impression from Bader’s letter that he completely missed the thrust of my article (J. Chem. Educ. 1993, 70, 1035), which is the simultaneous generation of all the four gases of interest. I apologize for not having cited his 1969 note (J. Chem. Educ. 1969, 46, 206) in my article, but that note does not contain any experimental procedure. It is true that the procedure in my article calls for two toxic/dangerous substances (toluene–d8 and bromine liquid). But that should not be a deterrent, in my opin-
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dN = {NoPe{PL dL = {PNdL Rearranging gives us { (dN/N)/dL = P which is the slope of a graph of ln(Remaining BBs) versus path length. If one plots the data of Ricci et al. for both of the examples they discuss, the slopes one obtains differ from what they predict, i.e., (negative) slopes of 0.100 and 0.0500; the data for a one-in-10 chance yields a slope of 0.1055, and that for a one-in-20 chance a slope of 0.05129.
Journal of Chemical Education • Vol. 73 No. 11 November 1996
Chemical Education Today
The reason for this discrepancy is that Ricci et al. are using (∆N/N)/∆L to approximate (dN/N)/dL. While using algebra rather than calculus is appropriate for a freshman laboratory exercise, one can avoid what may be a troubling discrepancy by simply choosing a smaller interval; for example, making the interval length 0.1 units rather than 1.0 units gives slopes of 0.1005 and 0.05013 for probabilities of .10 and .05, respectively. By having students choose appropriate numbers of decimal places for their answers, these values will be represented as 0.10 and 0.05, consistent with the probabilities chosen. Jonathan Mitschele Saint Joseph’s College Windham, ME 04062
Ricci and Nestor reply: Mitschele’s letter correctly points out that in our thought experiment we are only approximating an exponential decrease. We point out the approximate nature of our calculation to our students during the presentation and it is worthwhile to remind the readers as well. We selected one chance out of ten for our presentation to the student for two reasons. First, it makes for simple arithmetic in calculating the number of BBs remaining after each interval and second, it leads to a rapid decrease in the number of remaining BBs. For example, after only five intervals almost half the BBs are lost. Choosing one chance in one hundred would approximate the exponential a little better but would result in only a fifteen percent loss in BBs in five intervals. Robert W. Ricci and Lisa P. Nestor College of the Holy Cross Worcester, MA 01610
Chemical Equilibrium The article by A. C. Banerjee on teaching chemical equilibrium (J. Chem. Educ. 1995, 72, 879) touches on a number of interesting aspects of equilibrium. However, item 7, about the graph of Gibbs energy, G, versus extent of reaction, x, may deserve a fuller answer than was given to it. For the interconversion A = B, it is essential to know the phases of these two species. If both are solids, then the straight-line plots of G against x, which students were said to offer, are in fact correct. Banerjee seems to assume, but omits to state, that A and B are in one homogeneous phase. If they are both gases or are both in solution, the plot of Gibbs energy against x should show a dip and a recent paper (1) explored the correlation of this with the entropy of mixing of A and B. However, Banerjee, like some other authors, does not quite do justice to the relationship between G and x for a homogeneous equilibrium, in that his limiting
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Chemical Education Today
Letters slopes are far from being sufficiently steep. At x = 0, the slope should be {µ and at x = 1 it is +µ. Consequently, even where the difference, (G A { G B) is extremely large, whether positive or negative, there must always be a minimum in G at some value of x between zero and unity. Banerjee also insists that the true criterion of equilibrium is not the minimizing of G for the system, but the maximizing of the entropy of the universe. But since both occur as the system moves towards equilibrium, how can one tell which is fundamental and which incidental? The pragmatic answer for teachers of undergraduates must be to use a criterion of equilibrium which can easily be shown to be true and which can readily be applied. One can, with equal facility, show that G will be a minimum when P and T are constant or that S will be a maximum when U and V are constant. However, for the gas phase system A = B, at constant T and P, it is much easier to deduce the state of equilibrium using the first statement than it is from the second.
Kudos for September Issue I just received my September issue and like very much what I see. I especially like the Reports from Other Journals, Selected Articles from Education in Chemistry. I had forgotten about this journal but already checked out several articles of interest to me. I also checked the subscription cost of Education in Chemistry. It turned out surprisingly high, $203 for an annual subscription for those of us in the U.S. How does your journal maintain its affordable cost? Continued success. Paul Poskozim Northeastern Illinois University Chicago, IL 60625
Literature Cited 1. Logan, S. R. Educ. Chem. 1988, 25, 44.
S. R. Logan University of Ulster Coleraine, N. Ireland BT52 1SA
Anil Banerjee replies: I appreciate the comments of Logan on my article “Teaching Chemical Equilibrium and Thermodynamics in Undergraduate General Chemistry Classes” (J. Chem. Educ. 1995, 72, 879). It is true that for item 7, it is necessary to specify that both the reactant (A) and the product (B) are in one homogenous phase. The argument of Logan regarding use of free energy (Gibbs function) as a criterion of defining equilibrium state is well known and followed in most textbooks. However, it is necessary to appreciate that entropy is a more fundamental concept then free energy. The origin of all thermodynamic effects lies in entropy. Entropy accounts for changes in free energy and the reverse is not true. Most common textbooks on general and physical chemistry over emphasize free energy and under-emphasis entropy. Mathematically speaking, both free energy and entropy would produce similar results for deducing the state of equilibrium. It is true that Gibbs free energy, particularly in the form of chemical potential, has been a very useful concept in chemistry. However, it is necessary to emphasize that many properties, for example, osmotic pressure, depression in freezing point, and elevation in boiling point, are explained in terms of only chemical potential; and the actual reason in terms of entropy effects is not usually mentioned in most textbooks and during teaching.
Correction I just discovered an unfortunate error in our article “Nonlinear Dynamics in the BZ Reaction…” in the September issue of J. Chem. Educ. (1996, 73, 868): the last line of the caption of Fig. 5 should read [malonic acid]0 = 0.3 M, instead of 0.44 M. The concentration 0.44 M applies to the supercritical Hopf bifurcation of Figs. 3 and 5 a, b. Anybody who wishes to duplicate the subcritical Hopf bifurcation of Figs. 5 c,d would not be able to do so with the information given. To obtain a subcritical Hopf bifurcation, the malonic acid concentration quoted in the caption of Figure 5 should be [malonic acid]0 = 0.3 M, instead of 0.44 M (the latter results in supercritical Hopf bifurcation). I am sorry for this error which is entirely mine. Michael Menzinger University of Toronto Toronto, ON M5S 1A1 Canada
About Letters to the Editor Letters to the Editor may be submitted to the editorial office by regular mail (JCE, University of Wisconsin–Madison, Department of Chemistry, 209 North Brooks, Madison, WI 53715-1116), by FAX (608-2627145), or by email (jce@chem. wisc.edu.). Be sure to include your complete address, your daytime phone number, and your signature. Your letter should be brief (400 words or less) and to the point; it may be edited for style, consistency, clarity, or for space considerations.
Anil Banerjee Regional Institute of Education, Ajer 305 004 India
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Journal of Chemical Education • Vol. 73 No. 11 November 1996
