mdlad by W A L T E R A. WOLF Colgnte Vnlvenlty HBmllton. New York
Le Chateller's Principle: A Laboratory Exercise Frederiea Friedman The Brandeis School Lawrence, New York 11559
Le Chatelier's Principle can be demonstrated to nonscience oriented students by showing how water can boil at temperatures below 100 'C, due to reduced vapor pressure. In a c h e d water-water vapor syst&condensation occurs as the vapor cools. With cooling, pressure on the surface . vapor . . of the liquid decreases. The system reacts to the stress of the lowered vapor pressure by the water boiling. A new equilibria can be established at temoeratures well below 100 OC. A 500-ml Florence flasi half filled with water is heated to a rolling boil for about 5 min. Using a one-holed stopper with a thermometer inserted, the tlask is immediately corked, and inverted on a ring stand. A Petri dish or watch g l w containing ice cubes is placed on top of the inverted flask. An ice cube mav he mhhed around the Dart of the flask containine the vapor (not the water). Bubbles of water vapor soon rise from around the rubber stopper to the surface of the water in the inverted flask. Boiling may continue as temperatures drop to as low as 28 "C.
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Lennard-Jones Potential and the Posslblllty of Bound Vibrational Levels in Ar2 and He, Xf2,+ J. R. Riter. Jr. University bf Denuer 80210 Dmuer. Col~~rado For beginning chemistry majors we have attempted to establish at least a slender connection between the topics of molecular orhital theory, vibrational spectroscopy,and nonbonded forces between atoms and chemically saturated molecules by means of a simple computational exercise. One compares the likelihood of finding hound vibrational lev~lain the eround electronicstatesof the Ar., and He, molecules by usLg the familiar Lennard-Jones 6 1 2 p o t e k l in the harmonic oscillator approximation. The force constant turns out to be 72 t/re2. With typical values' for the well depth r and re of 83.2 cm-' and 3.82 A (Ard and 7.10 cm-' and 2.87 A (He?). one finds harmonic frequencies of 26.3 and 32.3 cm-"res&tively. Thus the ratios of zero-point energy to well depth become 0.158 (Ar2)and 2.28 (He2)in this approximation, leading the student to anticipate several hound vihrational levels in Ar2 and none in He2 in accord with the log21au*2configuration. Experimental results2show 5 or 6 bound vibrational levels in 236 1 Journal of Chemical Education
Ar2,with values of De (91.6 cm-') and o. (30.7 cm-l) similar to the Lennard-Jones oarameters. The argument can be carried a bit further in an advanced course. Second-order uerturhation theory ~rovidesan expression for the anharmonic coefficient w&; in terms of the cubic and quartic terns in the potential enerw. which in turn can he easily evaluated from-u(r) above when cast into a Taylor's expansion. The o,x. values determined in this way turn out to he 2.63 em-' (Arz) and 46.6 cm-1 (Hez).This Arz result matches the experimental value2 of about 2.6 very nicely, but in this appriximation He2 now indicates a singre bound vihrational level, perhaps generating some interest in determinine the second~anh&moniccoefficient w.v. . from higher ter& A discussion of the well known auantitative deficiencv of the Lennard-Jones 6 1 2 potenthi could then be in order, which in any case is much easier than the computation.
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' e.g. Hill. T. L. "Introduction to Statistical Thermodynamics", Addison-Wesley,Reading, Mass., 1960. Appendix IV. 'Tanska. Y. and Yoshino, J. C k e m Pk)r, 53,2012 (1970). Chemical Oscillations as an Undergraduate Experiment B. M. Deb Indian Institute of Technoloev -" Bombay 400 076, india
230 first-year undergraduates were asked to observe for 6 hours, using a given list of materials, the delightful BriggsRauscher oscillating system [J. CHEM. EDUC., 50, 496 (1973)l. Each student was to gather information systematically, explain every observation, and submit a complete report. The following hitherto unreported facts were collected: (1) Oscillation period and intensitv of hlue color increase with time. (2) he end of the oscillaiion iw marked hy iodine precipitation and warming up of the reaction mixture. (3) Oncillaiions can he prolonged by adding small amounts of malonic acid towards the end of the reaction. (4) HzSOl can he replaced hy HN03, but not by HCI as C1- acts as an inhibitor, MnSOa can he replaced by Ce(SOd2,hut malonic acid cannot he replaced by citric acid. (5) Oscillation parameters (induction period, average time period, average amplitude, total number of oscillations) depend rather sensitively on temperature and each reactant concentration; for each of these there is a narrow ranee outside which no oscillations are ohserved. (6) HCOOH i d C02are among the reaction products. (7) When the reaction mixture is thorouehlv shaken and poured into a petri dish or a large beaker, and then left undisturhed. the hlue color occasionallv develons in beautiful space patterns. If the mixture is poured into a long narrow tube then. after a few oscillations. the hlue color develom first either at the top or the bottom &d then advances like wave through the solution.
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Interestingly, only one student claimed to have observed temperature oscillations in this system. Nobody thought about possible oscillations in p H or gas (02 plus COZ)evolution. Only 38 students proceeded with a clearly set out plan, 6 speculated about the thermodynamic implications of chemical oscillations, and 5 tried to utilize their knowledge of chemical kinetics for explaining the phenomenon.
A New Expression for Relating Solvent Extraction Efficiency to Experimental Parameters
= (1
Taking the log of both sides yields log f,, = -n log (1
+ DV,,IVaq)
This expression can be read "the log of the fraction not extracted in nsteps is equal to the negative of the number of steps times the log of the extractability where the extractability is one plus the distribution ratio times the ratioof the organic volume to the aqueous volume." This expression relates the extraction efficienry to the experimentafparameters more clearly than the usual formulas and permits solutinn for an unknown parameter more readily.
D. C. Ailderbrand South Dakota State Uniuersity Brookings, 57006 Mathematical expressions for relating the efficiency of solvent extraction processes to the distribution ratio, solvent volumes, and number of steps are often unclear and cumbersome to use. This paper presents a new expression which is easier to use and retain by students. The derivation follows.
1 + D V . d V , )" = (I + DVOdV&"
NMR Resolution Analogy Sheton Bank State University of New York a t Albany Albany, 12222 The power of high resolution nuclear magnetic spectmscopy is seldom grasped by noting that one can resolve peaks of approximately one H e n with an applied frequency of 60 mega Hew.
where f l is the fraction not extracted in one step and [A].,, [A],, V,, and Vaq represent the formal concentrations of the species being extracted in and the volume of the organic and aqueous phases. Dividing the right side by [A].,V,, and setting [A],d[A]., = D, the distribution ratio, yields
For n steps
Some years ago Dr. James Dawson, then a graduate student with Professor L. M. Venanzi, and I performed some calculations (making reasonable assumptions) to provide a stimulating visual analogy for the reiolving power of the nmr spectrometer. Imagine atelescope focused on the moon. The resolution associated with nmr chemical shift translated to the visual would enable the observer to see a pair of horses. The resolution associated with a nmr coupling constant would enable the observer to determine which horse is the gray stallion.
Volume 54. Number 4, A ~ r l 1977 l / 237
