Chemical Education Today
Letters Boiling Point and Molecular Weight
The author replies:
It was good that Ronald L. Rich (J. Chem. Educ. 1996, 73, A294) pointed out once again that molecular weight is not a factor in determining boiling point of molecular compounds. However, in 1979 I published an article (1) delineating the four factors which determine the boiling point of nonpolar compounds: polarizability (molar refraction, R), size (molar volume, V), ionization potential (I ), and shape. The shapes are spherical, linear, and flat. For example, for (roughly) spherical molecules the relationship is
R. Thomas Myers and I agree that polarizability, or molar refraction, R, is a major determinant of boiling points. We differ on how to apply this, and on other factors. He uses R for the whole molecule—as opposed to the outer, exposed parts (1)—and, partly as a consequence, has to fit several types of spherical, “cylindrical”, and flat molecules to separate straight lines or curves which, additionally, do not extrapolate to the origins; also, the flat ones show very slight correlation. Apparently his method is not yet applicable to a wide variety of other nonpolar or slightly polar substances, of which carbonyls, metallocenes, heterocycles, and most transitional-metal halides are examples, nor have higher multipole moments or quantum effects been recognized. His highest Tb is 506.5 K, for TiBr4, as opposed to my 838 K, for As4S4. We probably agree that small multipole moments don’t matter, but what would his limits be? I still find that certain substances, especially the elemental halogens, require separate fitting (1, 2), and this may be why Myers omits them without identification, explanation, or rationalization. Myers’ formula is a function of R/V. Isn’t there any partial theoretical justification for this? R and V are correlated (1), so this puts a major burden—too much, I believe—onto I. Nevertheless, as Harold Urey used to say, in a semi-empirical theory it is best to emphasize the empiricism (although Einstein’s different view is also of interest); let us therefore judge more by the results than by any theoretical elegance. I add that my method predicted the Tb for As2(CH3) 4—estimated at 438 K and later found to be already known at 439 K, that it has given 29 other public (probably less accurate!) predictions, that it gives numerous useful statistical data including constants for further predictions plus low standard deviations, and that the latter are obtained without Myers’ arbitrary exclusion of benzene, for example, while retaining my own worst case of WCl6. My printed letter, cited by Myers above, stated somewhat confusingly, “then no quantitative function relation” where the manuscript had had “when no quantitative functional relationship” (italics added here).
Tb ∝
2
R I V
2
The rare gases are truly spherical, the tetrahedral hydrides of group 14 are approximately spherical, and these fall on one line. The tetrahedral halides fall on another. I chose the straight-chain hydrocarbons as linear compounds. But neither I nor the reviewer realized that they are not actually rodlike, but flexible. Consequently these data give a curve. I used actual molar polarizabilities. The method of Rich for estimating these will expand the usefulness of my procedure for correlating boiling points with physical properties. I have completed a second article on the boiling point of polar compounds. The results show that some polar compounds (halides of group 14) do not have an elevated boiling point caused by the polarity. (The possible exception is CH2F2, but this deviation may be due to an error in the measured properties.) Anyone wishing a copy of that article can write to me at the address below. Literature Cited 1. Myers, R. T. J. Phys. Chem. 1979, 83, 294. R. Thomas Myers Department of Chemistry Kent State University Kent, OH 44242-0001
Literature Cited 1. Rich, R. L. Bull. Chem. Soc. Jpn. 1993, 66, 1065–1078. 2. Rich, R. L. J. Chem. Educ. 1995, 72, 9–12, a summary of the above. Ronald L. Rich 112 S. Spring St., Bluffton, OH 45817-1112 email:
[email protected] Letters continued on page 410
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Letters continued from page 394
A University President’s Perspective I would like to call attention to an error in John Kenkel’s article entitled “A University President’s Perspective on Recruitment, Retention, and Quality” (J. Chem. Educ. 1997, 74, 377). Robert Krienke is the president of Lamar University Institute of Technology, not of Lamar University–Beaumont. Rex Cottle is the president of Lamar University–Beaumont. While these two institutions have similar names and both are members of the Texas University System, they are independent of one another. Lamar University Institute of Technology is a two-year technical college, whereas Lamar University–Beaumont is a Ph.D. granting university. Shawn B. Allin Department of Chemistry Lamar University–Beaumont Beaumont, TX 77710
. Masses of the Fundamental Particles in the Bound State I realize that it is politically correct to ignore defects, but to refuse to say “mass defect” relative to nuclear properties is going too far. Subramaniam, Goh, and Chia (J. Chem. Educ. 1996, 73, 663–666) calculate the mass of e + p + n, frequently commenting that it is less than this sum for the free particles. Yet they refuse to subtract one from the other and call the difference the mass defect. Why? Plots of their e + p + n values versus mass number have the same shape as plots of mass defect per nucleon versus A (with a sign change). Their attempts to distribute the bound mass between e, p, and n are unconvincing and, as far as I can see, not useful. I guess I missed their point. What is it? Roy W. Clark 1615 Jupiter Place Murfreesboro, TN 37130
The authors reply: The principal objective of our paper is to show that the masses of the fundamental particles in the bound state are lower than in the free state. In the process of addressing this, we have developed a simple mathematical formalism that does not require knowledge of the mass defect values for the various elements. On Clark’s comments about our approach in distributing the bound mass among e, p, and n, we maintain that the approach is reasonable. When an ensemble of electrons, protons, and neutrons come together to form atoms of the various elements, the extent to which each particle’s mass is annihilated in the process is difficult to determine accurately because of the complexity in the mature of the interaction. We used an approach based on the relative mass distribu410
tions of the fundamental particles in the theoretically computed atomic mass values of the elements, as our objective here is basically to obtain some indication of their respective masses in the bound state, since such data do not seem to be available in the literature. And more importantly, our approach yields data that are in consonance with theoretical requirements. That is, the masses of the fundamental particles in the elements are lower than in the free state. As for their utility, the pedagogical potential should not be overlooked. There is a common misconception among students that the masses of the fundamental particles, since they feature in tables of fundamental constants, cannot assume other values. The results clearly reiterate the point that the mass values of the fundamental particles in the elements are not only lower than in the free state but are also different for the various elements. Also, it can be stressed that without this seemingly negligible, but not insignificant, diminution of the mass values from the free state, it would not be possible for the fundamental particles to form the various elements. R. Subramaniam Singapore Science Centre, Science Centre Road Singapore 609081 N. K. Goh and L. S. Chia Division of Chemistry, Nanyang Technological University 469 Bukit Timah Road Singapore 259756
. This and That Now that I have taught university chemistry for many years, I would like to share some items with fellow chemists:
Brønsted's Concept of Acids and Bases I wish that textbook authors and chemistry teachers would stop giving credit of Brønsted's concept to Lowry. Bell's reminder (1) made it very clear that Lowry himself did not claim credit to Brønsted's concept. Electron Affinities I wish that textbook authors would stop defining electron affinity as the opposite. If they insist on stating that the electron affinity of fluorine is –328 kJ mol-1, then they should name it “electron antiaffinity”, or the “electron attachment enthalpy change”. Equilibrium Constants I wish that textbook authors would stop mentioning Kc at all, regardless of whether or not they include units for equilibrium constants. It is historical, unnecessary, and misleading, thus causing confusion when Kp and Ka are introduced. Exam Question Exchange The simple question (1) below tests the students’ understanding of basic concepts more than one might think on the surface. Question (2) can be used as an optional or take-
Journal of Chemical Education • Vol. 75 No. 4 April 1998 • JChemEd.chem.wisc.edu
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home question to get more out of the better students. You can give whatever conversion factors and numerical data as you see fit. Question (1): Nitric acid is a strong acid and calcium hydroxide is a strong base. Calculate the pH of the following solutions: (a) 50.0 mL of 0.000600 M HNO 3 solution (b) 200.0 mL of 0.000100 M Ca(OH)2 solution (c) The final solution prepared by mixing the solutions in parts (a) and (b) and allowing for the acid–base neutralization to occur. Question (2): A weather report reads as follows: Barometric pressure 30.0 in. mm Hg Current temperature 86o F Relative humidity 55.1% Dew point 68o F Calculate the heat of vaporization of water.
Valence-Bond (VB) and Molecular Orbital (MO) Concepts Most textbooks introduce the concept of bonding the H2 molecule or its cation. This example leads to confusion when VB is contrasted with MO because the bonding region is so closely related to the MO region. A far better example is the H3+ molecular ion. It involves only two electrons and therefore the singlet spin function can be factored out as in H2. Resonance structures can be introduced for VB and the contrast with MO description is much clearer. For more advanced levels, symmetry labels of the MO’s for C2v and D3h symmetry point groups can be introduced as well as the relationship of VB and MO and of unpaired spatial orbitals (2) to the simple-minded two-term configuration interaction (CI). Numerical comparison with the energy of H in the some basis set and analogous CI results for H2 would introduce the students to computational thermochemistry. As indicated above, this example spans from freshman to graduate students. Literature Cited 1. Bell, R. P. The Proton in Chemistry; Cornell University Press: Ithaca, 1959; p 7. 2. Linnett, J. W. The Electronic Structure of Molecules; Methuen: London, 1964. Delano P. Chong Department of Chemistry University of British Columbia Vancouver, B.C., Canada V6T 1Z1
. Am I Doing the Right Thing? The editorial in the March 1997 issue of the Journal (1997, 74, 253) struck a familiar chord of experience when I read it. I too have noticed that many students in general chemistry classes are familiar with the material, but have little understanding of it in any context other than the high school classroom. I agree that a dialogue must be started between high school and college teachers of chemistry.
However, I would urge caution on the idea of covering certain topics only once—and particularly on the matter of choosing such topics. As a student, I have noticed that seeing a topic more than once extends my understanding of the topic, especially if exposed to it in different contexts. Perhaps an example from personal experience will help me illustrate this. Since high school, I have encountered the subject of thermodynamics in many classes, but each experience has fleshed out and developed my knowledge of it beyond simply classifying reactions as “exothermic” or “endothermic.” In the first quarter of general chemistry, I learned for the second time about the thermodynamics of reactions, and for the first time about kinetics and entropy. I was familiar with the classic cases, but not with the calculations involved and with analyzing systems qualitatively with respect to their thermodynamics. Furthermore, I learned more about the significance of thermodynamics in the third quarter chemistry course covering electrochemistry—and again the next quarter in lab with an electrochemistry experiment. Just this quarter, I learned about thermodynamics again in physics— however, the context was much different this time. I went into that chapter thinking I would know everything already; but when I tried to work some problems in the physics book, I was taken by surprise! I had never really thought of systems where chemical changes weren’t going on, I had always assumed that either pressure or volume would be constant, and I never imagined that problems could be solved using calculus. But after being exposed to this context, I became more comfortable with solving thermodynamics problems with either a physics or chemistry approach. I now have many modes of access to knowledge about this topic, spanning two broad disciplines. There are other benefits to being exposed to topics multiple times. Confronted with the fast pace and demanding workload of a general chemistry class, a student fresh out of high school may be tempted to study “for the test”, rather than attempting to unify his understanding; this is particularly true if the student is not familiar with the symbolism, rules, models, etc., of each new topic. But exposing a student to some of the easier-to-grasp aspects of a subject will better prepare her to extend her knowledge in the college classroom, linking new concepts to older, more familiar ones. I would wholeheartedly support a move to form some understandings between the high school and college chemistry teaching communities on what material to present to their students. And I agree that some topics need not be rehashed and served to a lecture hall of students who have “seen this all before”. But before we make such a move, we need to consider carefully how concepts are formed and how they evolve, and then identify topics that are complex and that require a good deal of familiarity and practice. Simon Garcia 3076-A Via Alicante La Jolla, CA 92037
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Letters Units of Concentration in Chemistry and in Chemical Kinetics For many years, chemists working with solutions used for concentration the molar unit which is designated by M, standing for mol l-1 or mol dm-3. This symbol for concentration simplifies all the units of terms which involve concentrations. Thus the units for bimolecular rate constants were given in M-1 s-1. In recent years, an international committee for SI units which probably did not have any solution chemist, didn’t include any unit for concentration and forced the use of mol dm-3 as a unit for concentration. Thus bimolecular rate constants were expressed in mol dm-3 s-1. The committee, having a sufficient number of physicists, allows the use of short units not only for basic terms, such as energy (J), but also for less commonly used terms, such as the unit used in radiation physics for absorbed energy, the Gray (Gy), instead of using J kg-1 or m2 s-2. Having a special unit for concentration is at least as justified as a special unit for absorbed energy. I would like to urge all solution chemists to fight for the recognition of the molar unit as the SI unit for concentration, and thus return to the comfortable M-1 s-1 unit in chemical kinetics for bimolecular constants. Zeev B. Alfassi Department of Nuclear Engineering Ben-Gurion University of the Negev Beer-Sheva, Israel
Corrections In the article “The Gibbs Energy Basis and Construction of Melting Point Diagrams in Binary Systems” by Norman O. Smith (J. Chem. Edu. 1997, 74, 1080– 1084), the value for ∆fus HA in the footnote of Table 1 on page 1081 should be 21,250 J/mol instead of 23,250 J/mol.
❖❖❖ The following are corrections to the article “Computer Algebra in Chemical Education: Illustrations in Molecular Spectroscopy” by J. F. Ogilvie (J. Chem. Educ. 1994, 71, A223–A227): 1. The fourth equation on page A223 should read: 5: b(j+1)(j+2) – d(j+1) 2 (j+2) 2 + h(j+1) 3 (j+2) 2 + (j+1)4 (j+2)4(j 2m + 3jm + 1 + 2m) 2. The last equation on page A224 should read:
NJ = N0(2J + 1)e –[hBJ(J + 1)/(kT)] 3. The final equation on page A225 should read:
Jm = √[(kT)/(2Bh)] – /2 1
4. Reference 2 on page A227 should read: 2. Ogilvie, J. F. Comput. & Chem. 1982, 6, 169–172.
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Getting the Egg Out of the Bottle “Getting the Egg Out of the Bottle” (J. Chem. Educ. 1995, 72, 527; 1996, 73, A189) is a welcome demonstration in physical science class. For students in Taipei Municipal Chieh-Shou Public Junior Middle School, a simple and easy way was developed to do the experiment. The glass bottle containing a hard-boiled egg was held upside down, and the egg could easily drop out after a small amount of hot water had been poured over the bottle. The principle is the reverse of the one for sucking the egg in. It is easy for students aged 13 to 14 to understand, and they can do it by themselves. Kwang-Ting Liu Department of Chemistry National Taiwan University, Taipei, Taiwan, ROC Meei-ling Wu Taipei Municipal Chieh-Shou Public Junior Middle School Taipei, Taiwan, ROC
. What Good Is (Journal of) Chemical Education? We occasionally read useful articles in which we are encouraged to implement the conclusions reached by education research (1). Unfortunately, these articles often describe how to teach simple concepts. If you are not an education specialist, what should you do when it comes to teaching fundamental but difficult concepts? (e.g. Why does there exist an ORD? What is the difference between a singlet and a triplet?) In connection with my humble efforts (published in J. Chem. Educ.) concerning the teaching of difficult concepts, I received interesting comments from a very senior staff member of my Department. Comment A “... it is not necessarily true that staff who engage in chemical education research make better teachers. In fact, many don’t make good teachers because there are a few ideas that are new, and they beat the few ideas around to death. The best people to do this kind of research are the ones interested in educational psychology. The rest are simply dilettantes.” Comment B “... as for the staff publishing in the Journal of Chemical Education, we do not encourage it too strongly because of the ‘low level image’ associated with it...” The “low level image” refers to the Science Citation Index impact factor which is currently 0.309. Literature Cited 1. Johnstone, A. H. J. Chem. Educ. 1997, 74, 262. Igor Novak Department of Chemistry National University of Singapore Singapore 119260
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Wöhler’s Synthesis of Urea The article by P. S. Cohen and S. M. Cohen (1) on the synthesis of urea from ammonium cyanate by Wöhler in 1828 noted that the Vital Force theory persisted long after Wöhler’s work was published. As they point out, the theory was still generally accepted until at least 1845, when Kolbe synthesized acetic acid from purely inorganic sources. Why did Wöhler’s work not demolish the Vital Force theory, as many texts incorrectly imply? The answer was given by Partington (2) who stated that Wöhler’s achievement was not a real synthesis of urea: it did not produce an organic compound (in the original sense) from inorganic materials. Wöhler’s cyanate came from cyanide which was made from ferrocyanide which in those days was obtained from the wastes from tanning factories. Thus, to an adherent of the Vital Force theory, the urea had not been derived from nonliving sources and the theory had not therefore been disproved. Literature Cited 1. Cohen, P. S.; Cohen, S. M. J. Chem. Educ. 1996, 73, 883. 2. Partington, J. R. A Short History of Chemistry; Macmillan: London, 1948.
Dice-Shaking as an Analogy for Radioactive Decay and First-Order Kinetics The recent article by Emeric Schultz (1) entitled “DiceShaking as an Analogy for Radioactive Decay and First-Order Kinetics” is very interesting. But unfortunately, the statement that the half-life for four-sided dice is 2.7 shakes is in error. The correct value is 2.41 or, more precisely, 2.40942084 shakes. I obtained this value by trial and error using the xy function on my calculator, (0.75)2.40942084 = 0.5. It can also be obtained from the general formula τ = ln(2)/ln(n/n-1) where n is the number of sides of the dice. The student experimental data in Figure 2 of the article is sufficient to show that τ is about 2.5 and definitely less than 2.7 shakes. This calculation can be followed by beginning students and can be used in an interesting exam question testing both the concept of half-life and the correct use of calculators or graphing: “If dice ‘decay’ every time the number one is rolled, what is the half-life in shakes of four-sided dice?” I would give the answer of 2.7 only 80% partial credit, about what I would assign to 1.5 = ln(2)/(ln(4)/3). Literature Cited
Sidney Toby Rutgers University Piscataway, NJ 08855
1. Schultz, E. J. Chem. Educ. 1997, 74, 505–507.
The authors reply: Sidney Toby is correct in noting that some adherents to the Vital Force theory saw a weakness in experiment, which was corrected by Kolbe. If, however, that is why these chemists did not credit Wöhler with the downfall of Vitalism then they should have given such credit to Herman Kolbe’s acetic acid synthesis in 1845 (1). Not until 1891 do we find an appropriate recognition of the relationship between Wöhler and Kolbe’s work, in a speech by Odling (2). Thus, we contend, the real reason Wöhler, along with many scientists, made no claim to upsetting Vitalism is that they did not want to offend Berzelius, the most famous scientist of his day, a man who was known to have a sharp tongue and strong pen against those who challenged him. Literature Cited 1. Kolbe, H. Liebigs Ann. Chem. 1845, 54, 145. 2. Odling, W. “On the Development of Chemical Theory since the Foundation of the Society,” in The Jubilee of the Chemical Society of London’s Record of the Proceedings, 1891; London: 1896; p 27. Paul S. Cohen and Stephen M. Cohen Department of Chemistry Trenton State College Trenton, NJ 08650-4700
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Reed Howald Department of Chemistry and Biochemistry Montana State University Bozeman, MT 59717
The author replies: The point made by Howald is correct, and I thank him for it. The intention of the article was to show how dice shaking could be an analogy for radioactive decay and first order kinetics. I believe that the article still does that. When I mentioned in the article that the level of treatment could be extended for different audiences, I did not specifically address the possibility of comparing the theoretical values for different sided dice (as Howald does for the 4 sided case) to the values obtained experimentally (and graphically). The value of 2.7 was a ball park value that was “read” off the graph instead of one that was calculated. In reviewing the other data, it is gratifying to find out that the “experimentally” determined values for other dice fall close to the theoretical values (if calculated in the way described by Howald). I regret any confusion that may have arisen between exact values and approximate ones. I'll accept the 80% partial credit, but I would have given only about 40% for the missed calculation used as an illustration. Emeric Schultz Department of Chemistry Bloomsburg University Bloomsburg, PA 17815
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