Derek A. Davenport, Mary Howe-Grant, a n d Viswanathan Srinivasan Purdue Unlverslty West Lafayene. Ind 47907
I
Musical Molecular Weights and Other N0n-Linear Propetlies of Gases
The fact that the classical gas laws are independent of the chemical nature of the gas is explicitly mentioned in all introductory texts and it is implicitly verified in many freshman laboratory experiments (1). Graham's Laws of Effusion and Diffusion introduce the experimental linear dependence of rate on the inverse square root of the molecular weight though theoretical derivations (2) and putative experimental verifications (I, 3-5) are more complex than is commonly allowed. More advanced freshman texts such as Mahan (6) treat also of the viscosity, thermal conductivity, and diffusion of gases as do some supplementary paperbacks snch as those by Cowling (7) and by Hildebrand (8). Experimental study of these phenomena is, however, commonly left to the physical chemistry lahoratory (9). This article describes simple ways in which the thermal conductivity, viscosity, and velocity of sound propagation of various gases can he semi-quantitatively measured (or demonstrated) a t the freshman level. Recognition of the complex and decidedly non-linear ways in which these properties vary with the chemical nature of the gas is both salutary and, with a little effort, insightful. In particular, transport properties provide a useful entry to relative molecular parameters and the velocity of sound propagation in various gases provides a valuable macroscopic feeling for the magnitude of the microscopic root mean square velocity of molecules in those same gases. Relative Thermal Conductivities of Gases Joseph Priestley (10) seems to have been the first to observe that a thermometer cools more rapidly in hydrogen than in common air. In his "New System of Chemical Philosophy" John Dalton devotes several pages to the subject citing new, and sometimes erroneous, data of his own (11). Later the thermal conductivity of gases was to attract the attention of, amongst others: Rumford, Davy, Dulong, Petit, Prout, Fourier, Audrews, Magnus, Tyndall, Clausius, Maxwell, Boltzmann, and Marie Curie. This early history has been admirably summarized by Burr (12). The experimental methods are authoritatively and exhaustively reviewed by Partington (13) and theoretical treatments may be found to any desired degree of rigor in standard texts. The present apparatus is simplicity itself. A 125-ml Erlenmeyer flask is flushed with the desired gas (where possible prepared by the student) and a one-hole rubber stopper carrying a thermometer is quickly inserted. The flask is then plunged stopper-deep into a thermostat maintained at, say, 50°C (or alternately into a large and vigorously stirred bucket of icelwater) and the rise (fall) in temperature (T) as a function of time ( t ) measured. The process being followed is of course the raising (or lowering) of the mercury level in the thermometer but this must be related ta the rate a t which heat is transmitted to (or from) the thermometer bulb. When log(T., - T,)is plotted against t, straight lines are obtained as is to be expected from Newton's Law of Cooling (14, 15). Figure 1shows results for several gases. From the slopes of snch plots one can ohtain a measure of the rate a t which heat is transmitted to (or from) the thermometer. This heat may he transmitted by conduction, convection, and radiation. The separation of these three factors is complex and lu a degree the problem remains unresolved even after two hundred years of investigation (16,17). In our case the contribution of radiation to the heating (or cooling) of the ther-
Figure 1.
Relative heat transmission of gases.
1.5r
t lsec) Figure 2. sure.
Relative heat transmission of air and helium as a function of pres-
mometer should not vary appreciably from gas to gas. Any convective contribution would be expected to diminish as the gas pressure is lowered. At first sight the conductive contrihution might also be expected to diminish and Dalton cites data to that effect (18). However. as Newton had first conjectured (19), thermal conductivity proves to he essential& pressure-independent exceDt a t extremelv low and verv.hieh u pressures (20j. This supe;ficially paradbxical behavior receives a ready explanationthrough kinetic-molecular theory. Figure 2 shows the effect of diminishing pressure with air and helium as the experimental gases. It would seem that convection can be ignored in an elementary context and the experimental slopes may be taken as semi-quantitative measures of thermal conductivitv. From a series of similar exneriments ~the following sequence of thermal conductivities was found: ~
~
.~
Hz > He >> CH4> NH3 >Air > Ar Z Con > SOn The method is sufficiently sensitive to establish the order: 02
>Air 2 N2
Volume 56. Number 8, August 1979
1 523
is pureed from the lunes. The even more strikine effect of hyhrogen gas was menti&ed as early as 1830 by siiiman (24, 25). He adds the cautionary footnote Pilatre de Rozier was accustomed, not only to fill his lungs with hydrogen gas, but to set fire to it as it issued from his mouth, where it farmed a very curiousjet of flame. He also mixed pure hydrogen gas with one ninth of common air, and respired the mixture as usual; "hut when he attempted to set it on fire, the consequence was an explosion so dreadful, that he imagined his teeth were all hlown out." The words of Jaques in As You Like I t are irresistibly brought to mind
.. .and his big manly voice, Turning again toward childish treble, pipes And whistles in his sound. Last scene of all, That ends this strange eventful history, Is second childishness and mere oblivion, Saris teeth, sans eyes, sans taste, sans everything.
Figure 3. Apparatus gases.
far
measurement
of
viscosity
of
water-insoluble.
Relative Viscosities of Gases The apparatus (Fie. 3) is similar to that used hv Faradav, .. Graham, and Bunsen in early invrstigatlms Ion rhe viscosity and eiiusion of rases 121I . :\ I~tlret(or chromatopravhv c d umn) with a ca$llary tube attached is inverted in a i000-ml graduated cylinder standing on an upturned wastehucket (or other suitable prop) in a sink. Water is run into the cylinder so that it gently and continuously overflows. The gas, which must he insoluble in water, is collected by downward displacement. When temperature equilibrium has been reached the time taken for a given volume of gas to flow through the capillary is measured. These values are readily reproducible to f 0 . 2 s and are compared with similar values for air. By analyzing the rate of change of flow with decreasing hydrostatic pressure it is possible to verify whether the particular gas involved is obeying Poiseuille's Law and undergoing regular viscous flow. The gases are of course saturated with water vapor and this fact renders direct comparison with accepted values difficult (Table 1). Alternate hut more complex methods of finding gaseous viscosities are readily available (22,231. Relative Velocities of Sound Propagation in Gases One of the most memorable of lecture demonstrations involves the attempt to talk after the lungs have been flushed with helium gas. The shrill tunes of a tenore castrato exponentially descend to the normal manly baritone as the helium Relative Viscosities of
Air N. 02
Hz He
CHI NO
Sulfur hexafluoride gives a profound deepening of the voice but even though i t is used clinically for shadowing the lungs in X-radioeravhv with that of hv.. . . its inhalation.. together .. drogcn, is not recommended e\.cn 111 those chrmiirs who h a w lotal faith in the precedence of kinetic over thermodvnamic control of spontaneous reactions. There are even those who question the breathing of helium and it is certainly unwise to feed xenon to goldfish (26). What is the cause of this frequency modulation? The physics of the human voice is extremely complex (27) hut there is little doubt that a major factor in the dramatic effect of helium is the much higher speed of sound in that gas as compared with air. In order to test the generality of the effect large hdloons containing various gases were allowed to sound through a small wwden organ pipe; in our case a "B FL D'Am pipe served admirably. The open-ended pipe was first flushed with a finger on the sounding slit. The end of the pipe was then closed and the sound Bllowed to stabilize. A musical ear can gauge the pitch directly; tin ears should store the sound on a tape-recorder and establish the pitch a t leisure using a standard pitch pipe. The results are shown in Figure 4. The distinctions are sharper (or flatter) than the coarsely quantized standard musical notation might suggest. Even the moderatelv tone-deaf can distinguish between air, nitrogen, and are sounded live again& the reoxygen when the pure corded standard air pitch. Some ears are sensitive to 0.04 semitones (28) and these would be able to detect 1%of oxygen in nitrogen or vice versa. The same principle has been applied as a whistle detector for gas chromatography using ultra-sonics in place of audible sounds with the obvious advantages of miniaturization and oiezo-circuitrv (29). The data in F i g u r e clearly show a qualitative relationship between molecular weieht and the pitch or freouencv of the sound. Such frequencies may he used togethe;withthe velocity of sound in air (331 m sec-') to derive values for the
a
Gases
Found
Literature
1 .OO 0.97 1.10 0.51 1.06
1.00 0.97 1.10 0.51 1.06
(line) Figure 4. Relationship between pitch of mte and molecular weigM of swnding gas.
524 / Journal of Chemical Education
velocity of sound in the different gases. These values are in generally poor agreement with literature values obtained by more sophisticated means. The problem would seem to be the back diffusion of air into the pipe. As early as 1829 Dulong attempted to minimize this by sounding an organ pipe inside a large chest filled with the gas (30).It is possible to sound a pipe inside a gas-filled glove-bag but the law of diminishing returns soon calls a halt. After all there are far better methods available for the accurate determination of the velocity of sound in a gas (31,32). Clearly such demonstrations are of little interest unless some considerable pedagogic advantage he forthcoming. Such, however, is indeed the case. How does the lecturer's voice reach the back row of the auditorium? Obviously it is "carried" there by the molecules of the air; in a non-McLuhan, bucket-handling sense the medium is the message. If the molecules are carrying the message, clearly they cannot do so more rapidly than they are, on the average, moving. Newton was the first to attempt the calculation of the speed of sound in air. The value he obtained using the isothermal (Boyle's Law) hulk modulus was substantially lower than the then crudely known experimental value. He attempted to adjust the discrepancy in ways described in an article engagingly titled "Newton and the Fudge Factor" and subtitled "Fiddling with Sound" (33).Much later, Laplace pointed out that the rapidity of sound-wave compressions and rarefactions necessitated the use of the adiabatic rather than the isothermal bulk modulus. A rather simple derivation leads to the following formula for the velocity of sound, U , of a gas of molecular weight, M
=,@ This is to be compared with the more familiar expression for the root mean square velocity of molecules of the same gas
-=e
Since y varies from about 1.15 to 1.66 for common gases a knowledge of U and the assumption of a value of 1.4 for y enables the molecular weight of an unknown gas to he estimated to about &lo%. The t.ifwt uf h y l r q t w #,rhelium upun the speaking voice is a iine examr,lv ,,it l w \,erssrilit\ of certain lecrurr drmonstrations. It may he dolie merely for effect, even for laughter. And why not? Cakes and ale have their place, even in chemistry. But with a little time and effort it may also he coaxed into yielding much insight into the interconnectedness of natural phenomena. Jaques again makes the distinction hetween the two approaches best
An hour
by hl's dial.
to which he counters And then he drew a dial from his poke, And looking on it with laek-lustre eye, Says, very wisely, "It is ten o'clock; Thus may we see," quoth he, "how the world wags."
Seeing how the world wags. There could be worse definitions for the scientific enterprise. Acknowledgment The authors wish to thank Rachel Britton and Wilbur Van Buren who at various times lent their musical ears to this project.
Literature Cited I11 Deal, W. J..J.CHEM. EDUC.52.405 (19751. (21 Mason. E. A.and Evans.R. B., J. CHEM. EDUC..46,359119691. (PI Weiner,S.andJohnson, D., J.CHEM. EOUC.,26,699(19491. (4) Dauenpxf,D.A., J. CHEM. EOUC.,39, 252 11962). 151 Rice. L.A.andChang,J. C., J.CHEM. EDUC.45.677 (19681. 161 Mshsn. B. H., "UniversityChemistry,"3rd Edition, Addison-Wesley,Reading. Massachusetri,1975, p 73. (71 Cowlin~,T. G.."Moleculer in Motion,"Harper and Brothers. New York, 1960,~. 48 et se4.
161 Hildehrand. J. H.. "An lntroduetion to Molecular Kinetie Theorv? Reinhold. New Y0.k. 1966,p. 71. Shoemaker, D. P., Gadand, C. W. and Steinfeld, J. I.., "Experiments in Physical Chemistry," 3rd Edition. MeGraw~Hill.New York. 1974. rriertley, ~ . . - ~ ~ ~ observations ~ ~ i on~Different ~ ~ ~ti "sd = o~~ A ~ ~d ~ ~ , " . I .~ Birmingham. 1790.p.457. Dalton. J.. "New System uf Chemieal Philorophy:volumeI,p. 117. (a1 Burr. A. C., Isis, 20. 246 119331. ihl Rurr,A. C.,Irin, 21, 169 (1934). Partington, J.R.,-An Advanced TmsfiseonPhynicalChomistry," Longmans. London. 1949. Volume I, p. 888-900. Nowtun. I.,Phil.Trans.. 824 117011. Kleiher, M., Scirncs. 178.1283 119721. Refemnee 113).p. 895. Rrurh. S. C.. Archive for Histurvuf the Exact Sciences, 11.38 11973).
(231 Reierenee 191.P. 102. (241 Silliman, B., "Elements oiChemirtq."Herekiah How*, New Haven. CO, 1830. Volume I. p. 206. . I m r p n W. R...I. CHEM. EDUC..54.39 119771.
1969.p. 113. (29) Brenner, N.,Callen,JE..snd weirs, M. D. ieditom),'~GarChmmatugrsphy: Academic PIDSS.New York. 1962. o. 183-8. 1301 seer&nee 1131, m i ' (31) See reference IlSI, p. 820-39. 152) white. J. M.;'Phyrical C h e m i s ~ yLaboratory Expenments."Prontice-Hall, Endewad cliffs,NH, 1975, p. 168. 118l Westfall. R. S.. Science. 179.751 119731.
b.
Volume 56, Number 8. August 1979 / 525
h
~
