Jerry A. Bell and William H. Snider University of California Riverside, 92502
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The Acetone-ChIoroform System
instructors
of undergraduate laboratory courses are continuously on the lookout for new and more interesting experiments for their classes. Ideas for new experiments come from a number of sources: the instructor's own research, reports in the research literature of another field, extensions of articles from journals such as THIS JOURNAL, or possibly the suggestions of enterprising students. We feel that occasionally the report of a new experiment should he prefaced by a few remarks on its genesis as a possible guide for ot,herteachers. The Genesis of this Experiment'
During the early part of 196.5 I (the senior author, J. A. B.) was casting about for spectroscopic experiments for a class of accelerated general chemistry students. The boundary conditions were: the interpretation of results should be relatively easy; the basis of the technique should he comprehensible to first year students; and the experiment should elucidate some interesting molecular interactions. After a fair amount of thought about the pedagogical content of such experiments, I decided that it was unnecessary for the students actually to carry out the experimental manipulations themselves. The range of techniques that could reasonably be considered was thus much increased. This conclusion is certainly not unique; an editorial ( 1 ) and a t least two recent articles (2)in THIS JOURNAL make the same point. While this problem was in the "mulling-over" stage, I attended a CACT meeting at which Dr. A. L. RlcClelIan spoke about his visits to secondary schools where he discussed his research on the hydrogen-bonding equilibria in the dimethylsulfoxide-chloroform system studied by nuclear magnetic resonance (NMR) (5). I was already aware that acetone and chloroform inter-
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This experiment, with 32 others, will be available in "Chemf cal Principles in Practice" (Editor: BELL,J. A.), Addison-Wesley Publishing Co., Reading, Mass., in press. A few of the other experiments also will be "dry-lab" types. ZISLOW,B., J. CHEM.EDUC.,37, 578 (1960). Inasmuch as hydrogeu bonding between chloroform molecules is not completely negligible, chloroform pres~rmablywill hydrogen band with carbon tetrachloride and hence will not act as an inert diluent. Perhaps for this reason cyclohexme should be substituted for carbon tetrachloride in this experiment. See also footnot,e 5 and reference (7). ' In fact, a. large number of hydrogen-bonding systems have been studied by NMR. See PIMENTEL, G . C., AND MCCLELLAN, A. L., "The Hydrogen Bond," W. H. Freeman & Co., San Francisco, 1960, pp. 142-157. Many more reports of hydrogen banding studies using NMR have appeared since this monograph was written. ' Zas~ow,B., o p . cit.
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acted strongly when mixed; this is readily observed in an experiment suggested by Z a s l o ~ . I~ presumed that the interaction is the same as in t,he dimethyl sulfoxidechloroform system. Indeed, a quick literature search revealed that Pimentel (4) had studied the acetonechloroform system during a relatively early period of NMR re~earch.~Since many of the students in the class go on directly to an organic course stressing the use of instrumental methods, including NMR, I felt that an NMR study of the acetone-chloroform system would be feasible and useful. Our first trial of the experiment began with :l calorimetric determination of the heat of mixing for an equimolar mixture of acetone and chloroform a la Z a ~ l o w . ~The students then read an introduction to NMR and afterwards spent two to three hours matching and asking questions as samples were run on a Varian A-60 NRlR spectrometer. Each student was given a copy of the NMR data (which had beeu obtained earlier) for a series of mixtures of chloroform and acetone a t 20°C and was asked to calculat,e an equilibrium constant for the reaction that. he understood was occurring. Using his equilibrium constant and the calorimetric heat of mixing, he then calculated the enthalpy change for the reaction. From the equilibrium constant, the free energy change for the reaction was obtained, and combination of the free energy and enthalpy changes yielded, finally, t,he entropy change for the reaction. The junior author of this article, one of the students during this first test of the experiment, has developed a much superior method of data reduction than had originally been used. He spent a summer and the past, academic year obtaining the much refined data that, are presented in this article. The data are given in detail here so that other classes, including those without access to an NMR spectrometer, can also perform this "experiment." Introduction to NMR
We introduce NMR as just another spectroscopic technique that is not different from other more fanliliar optical techniques except that the absorption or emission of radio frequency radiation by atomic nuclei occurs only when the sample is in a magnetic field. Students are told that the energy of the proton in a magnetic field is quantized and can take only two values. The energy separation between t.hese states is such that the frequency of radiation that mill be absorbed or emitted is v =
where P X
=
2#nH/h
magnetic moment of the proton
(1) =
14.1 X
10-z4 erg gauss-' and H is the magnetic field "felt" by the nucleus = about 14,000 gauss in many commercial NMR spectrometers. Thus v = 60 megacycles sec-' for protons, hydrogen nuclei. At t,his point the concept of chemical shift is introduced via the NMR spectrum of methanol, Figure 1. The appearance of t,wo absorptions rather than a single
increosinq
H
than those bonded to the less electronegative carbon. Appealing as this very simple picture is, it is marred by further experimental facts. When CH,OH is diluted by some nonpolar, NR4R-inert solvent such as CCL, the peak due to the OH hydrogen shifts to higher fields till it is actually found on the high field side of the CHa peak; under these circumstances the OH hydrogen is more shielded than the CHahydrogens. It seems certain that there must be intermolecular effects at mork as well as the previously discussed intramolecular effects. I n molecules containing the -OH grouping, the most obvious intermolecular interaction is hydrogen bonding,
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H external
Figure 1. NMR spectrum of CHIOH a t 60 mc with a magnetic fleld of about 14,000 gourr.
one is rationalized by the very schematic representation Figure 2, which indicates that the higher the electron density about the proton, (the more "shielded" it is) the greaterwill be the chemicalshift,i.e., the higher the external field will have to be to bring the proton into "reasonance" with the radiation and hence to detect the energy absorption. Chemical shifts are generally stated in terms of the difference between the field required to bring the interesting system into resonance and the field required for some standard substance. (A widely used reference standard is tetramethylsilane, (CHs)rSi, TILIS.)
(The 10' is put in to make the chemical shifts come out in the neighborhood of unity.) To convert the chemical shift in parts per million, ppm, to the difference in frequency between the sample and the reference, which would have been observed if we had varied v at const,ant H, we use the equation Av = 6vo
(3)
where vo, the frequency at which the NMR instrument operates, is given in megacycles but Au comes out in cycles sec-I because of the factor of lo6 in 6. (All of this background, together with much more material that is not directly relevant to this experiment, is contained in books by Roberts (6) and Jackman (6). Almost all the very recent organic and physical chemistry textbooks have a section on the NMR technique and students are sent to the library to consult as many of these references as they wish to improve on the sketchy picture given in their laboratory notes.) Now let us examine the NIVIR spectrum of CH,OH in a bit more detail. The lower shielding of the OH hydrogen is the result of a lower average electron density about this hydrogen nucleus than about the CHa hydrogen nuclei. Qualitatively, perhaps, this is understandable, since oxygen is more electronegative than carbon, and it might be expected that the electron density distribution making up the bond between 0 and H would be shifted toward 0, leaving that H less shielded
Mognetic field lines produced by the mowing e l e c t r o n , f i e l d strength = H e l e c t r o n Figure 2. shielding.
The resultant field, H. a t t h e p r o t o n
A schematic representation of the origin of nuclsar magnetic
which we know has such a profound effect on the physical properties of water, alcohols, and organic acids. When a hydrogen bond is formed, the hydrogen nucleus is drawn a bit further away from the atom to which it is bonded, because of the electrostatic interaction of its positive charge with the negative "charge cloud" of the atom (usually oxygen or nitrogen) with which the bond is formed. If the proton is actually drawn slightly further out of its bonding electron density distribution, it will be less shielded from external magnetic fields and will be in resonance at lower fields. Why does just one peak that shifts upon dilution occur and not two, one because of hydrogen-bonded and the other nonhydrogen-bonded hydrogens? If a changing interaction of a hydrogen puts it in two different magnetic environments (e.g., H-bonded and non Hbonded), and the rate of change from one environment to the other is fast compared with the time resolution of the NMR technique, then the instrument will detect only an average of the signals from the two different environments. The averaee will be weighted bv the average mole fractions oflhydrogens in each of tge two environments, and the observed chemical shift will be given by 6 = Xl& X& (4) where X is the mole fraction of hydrogens in a given environment denoted by subscripts, and 61 and 62 are the shifts that would be observed if all the hydrogens were in environment 1 or 2, respectively.
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Figurer 3.4, and 5. The NMR spectra for the mcetone-chloroform mixtvrer ot 2 0 . 0 , and -20DC, rt~prctively,ore given on the next three paget. The number on the bareline of eoch spectrum mrrerpondr to the mixture number in the table. Al4hough the artist's rendition of the spectra is somewhat rtylired, the peaks are accurately located; the relative rirer of the peaks are indicative only and are not meant to represent the true values.
NMR and the Acetone-Chloroform System
Suppose that the hydrogen in chloroform, C, can interact to form a hvdrocen bond with the electronezative " oxygen atom in acetone, A, hut that there is little interaction between chloroform molecule^.^ I n this circumstance we will probably find that the NMR chemical shift, 6,, of the chloroform hydrogen in pure chloroform is different from the shift, 6, in a mixture of c moles chloroform and a moles acetone. Figures 3, 4, and 5 show that snch differencesdo indeed exist. Let us describe the proposed hydrogen bonding interaction by equilibrium reaction:
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The equilibrium constant for eqn. (5)-in terms of mole fractions-is:
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where X is the hydrogen-bonded complex, and use eqn. (4) to analyze the interaction. Eqn. ( 4 ) may be rewritten for our system as:
The experimentally observable properties of the system are 6, 6,, a, and c. Thus we have two eqns., (6) and (7), in three unknowns, 6,, x,and K . We might try making up a new and different mixture of acetone and chloroform which would yield another equation like (G) with a different value of 6, but, of course, x will also be different in this new situation since it varies with changes in the ratio a a: c. This is, however, the correct approach toward solving our dilemma. We make up a number of mixtures of A and C with varying ratios of a t o c, plot ( 6 - 6,) vs c / ( a c) and extrapolate to get ( 6 - 6,) in the limit as c goes
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where x is the number of moles of the hydrogen-bonded complex and 6, is the chemical shift of the proton in the complex. (What criterion must be met by the reactions in eqn. (5) in order that eqn. (4) be applicable to this system?) 202
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6 The latter supposition is made to simplify the mathematical treatment of this problem. The results of experiments snch as those suggested by Zaslow can he used as evidence to refute or support this assumption. See also the third from last paragraph of this article.
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0 CPS
1
1111111111111111111111
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to zero, i.e., the intercept at c/(a c) = 0 on our plot. Let us call this extrapolated value (6 - 6,)o-referring to the fact that "zero c" is present at this point. As c approaches zero, (a c - x) will approach (a - x) and we can write:
(6) and (lo), solving the resulting equation for x, suhstituting into eqn. ( l l ) , and solving the quadratic for K (dropping zero and negative roots of equations). The result (which the reader should work through for himself) is:
which can (in the limit) he arranged to give:
where
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Substitute eqn. (9) into eqn. (6) to get:
This substitution is proper because we have used the value for (6 - 6,) at zero limit to which eqn. (9) refers. The succeeding computations will be easier if we vary the ratio a: c while holding the sum, a c, constant; this is conceptually easy to do. Thc simplest choice for the sum is unity. With this choice you can show that eqn. (7) becomes
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Now we see that eqns. (6), (lo), and (11) are independent equations containing our three unknowns, and we should be able to solve them simultaneously to obtain the values of these three unknowns. We obtain the solution for K by eliminating (6, - 6,) between eqns.
Thus, once we have obtained a value for (6 - 6J0 by extrapolating the (6 - 6,) data for a series of mixtures, we can calculate N and M for each mixture from the appropriate values of a and c (whose sum is unity) and (6 - 6,) and hence get as many values for K as me have mixtures. The Data
Acetone and chloroform were purified by the methods suggested by Pimentel (4) and a series of mixtures mere made up as follows: a capped NMR sample tube was weighed; the desired volume of chloroform was added; the capped tuhe and contents were reweighed; the desired volume of acetone was added and the capped tuhe reweighed; a very small drop of TMS, tetramethylsilane, mas added; and the capped tube was reweighed. Volume 44, Number 4, April 1967
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The contents of the tube were frozen in liquid nitrogen; the tube was attached to a vacuum system, evacuated, and sealed off with a torch. Finally, the sealed tube and contents, the cap, and the small remaining piece of glass tubing were weighed and any sample whose final weight did not correspond within 0.3 mg with that hefore sealing was discarded. The composition of these samples is given in the table. The amount of TMS in each sample is of the order of 0.1% by weight. The NMR spectra of these mixtures were taken a t three temperatures, 20, 0, and -20°C, with a Varian A40 NMR Spectrometer. Temperature control was good to *loC. Four spectra of each mixture were taken at each temperature; the spectra were taken in random order. The four spectra for each mixture at a particular temperature were averaged, and these averages are shown in Figures 3, 4, and 5. The spread of values for any one mixture is *0.5 cycles/sec. Since this is just about the reading error in the figures, the results obtained from them will be just as good as those from the original data.
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to c/(a c) = 0 to obtain (6 - a,),, and then calculate the values of A t and N, eqn. (12), for each mixture and hence a value of K for each mixture. The following questions and suggestions are then posed to the students: Inwhat concentration range are the values of K most consistent? Average these values to obtain a "best K." Choose about ten arbitrary values of c/(a c) in the range zero to unity and calculatex, the number of moles of hydrogen-bonded complex, for each value using eqn. (10). (What is a,? Does this make sense?) Finally, compute a theoretical value of (8 - a,), eqn. (6), for each of the chosen c/(a c ) values and plot these theoretical points on the same
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The Composition of the Acetone-Chloroform Mixtures Used in This Experiment.
Mixture
Acetone, o' (moles)
Chloroform, c" (moles)
Computdions a n d Complications
The data analysis is begun by measuring the chemical shifts for the chloroform hydrogen in each mixture at each temperature. (We usually have students work in groups of three, each working on a particular temperature.) The students compute (8 - 6,) for each of the mixtures and plot (6 - 6,) us c/(a c). They draw a smooth curve through the points, extrapolate the curve
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a The values for the acetone and chloroform fractions have c = 1. already been reduced to the common reference state a
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Figure 6 shows the data from Figure 5 plotted as suggested previously. The dotted line represents the theoretical curve that would be observed for K = 3.0. I t is easy to see that the theoretical curve and the experimental data do not correspond at all well at high chloroform concentrations. The deviation of the experimental points at high chloroform concentrations is in the direction that indicates that more of the chloroform is hydrogen-bonded than we have accounted for theoretically. Why? Two possibilities spring readily to mind: chloroform molecules may hydrogen bond with each other or a second complex containing two chloroforms and an acetone may be formed. The equilibria me might have to account for would be:
M O L E FRdCTlON CHC13 Figure 6. The open circler are the doto at 20°C plotted as suggested in the article. (The sire of the circler is on indication of the error limits of there dota.) The dashed cune is the theoretical c v n e for K = 3.0. The solid c u n e is o theoretical curve accounting for the equilibria in eqnr. 1501, 1131, and 1141.
graph with the experimental data. Draw a smooth curve through the theoretical points. Do the theoretical and experimental curves agree? If not, where is the disagreement worst? For what reasons might the theoretical and experimental values disagree? Do these hypotheses explain the direction of any discrepancy between the experimental and theoretical curves? (On this subject one might cogitate profitably upon the results of direct calorimetric measurements.) From the "best" values of K for each temperature compute AH", AGO, and ASo for the reaction occuning in these mixtures. Compare the AH" obtained indirectly here with the direct calorimetric value;l the existence of an equilibrium constant smaller than infinity will have to be taken into account to compute the "direct" value. Perhaps other questions or suggestions have occurred to the reader: e.g., could the same analysis he applied to the shift of the proton resonance in the acetone?
' Z a s t o x , R., op. cit
The results of McClellan (3) and Jumper (7) support the inclusion of all three of these equilibria in a full treatment of this system. Indeed, when all three equilibria are accounted for, the theoretical curve shown as a solid line in Figure 6 is obtained. (8) The authors would he happy to corrcspond with anyone about his problems or suggestions for improvement of this experiment. Acknowledgments
We should like to thank the University of California and the National Science Foundation, Research Grant GP-4939 for financial support of this work; the junior author was a National Science Foundation Undergraduate Research Participant. Also we are grateful to the UCR Computer Center for assistance in some details of the computer calculations we performed with these data and especially to Dr. A. L. McClellan for furnishing us the program for the analysis reported in reference (8). Literature Cited ( 1 ) Editorially Speaking, J. CHEM.EDUC.,42, 63 (1065). (2) BOER,F., AND JORDAN, T. A,,J. CHEM.EDUC.,42, i G (lOti5); LITTLE,R., J. CHEM.EDUC.,43, 2 (1066). ( 3 ) MC~LELLAN, A. L., NICKSIC, 8. W., AND GUFFI., J. C., J . Mol. Spertr., 11, 340 (1063). ( 4 ) HUGGINS, C. M., PIMENTEL, G. C., AND SCHOOLERY, J. N., J . Chem. Phws.. 23. 1244 (19551. . . ( 5 ) ROBERTS, J. D., "N~~clear Magnetic Resonanre," 11cG1.m~Hill Book Co., New York, 1959. ( 6 ) J.~CKMIN, L. M.,"Applicatiom of Nuclear Magnetic Reelname Spectroscopy in Organic Chemistry," Pergamon Press, Ine., London, 1959. ( 7 ) JUMPER,C. F., EMERSON, M. T., I N D HOW.(RD, B. B., J . Chem. Phl/s., 35, 1911 (1961). (8) BELL,J. A,, .4ND SNIDER, W. H., to be published.
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