# Graham's law

Procedure. Remove the several cubes from rhe ice cube tray. Place at least one tap water cuhe into the water in the 250-mI. bea- ker, and obsenre that...
Procedure Remove the several cubes from rhe ice cube tray. Place at least one tap water cuhe into the water in the 250-mI. beaker, and obsenre that it floats. Place the deuterium oxide cubeinto the same water, andobserve that it sinks. Optional: The two cubes may be removed and placed into a smaller 150-mL beaker containing liquid D 2 0 to show that both cubes will float in this liquid. If the contamination of one isotope with the other is to be minimized, the ice cubes should be removed and allowed to melt in separate vessels as soon as the demonstration's point has been made. Alternatively, if re-use of materials is not a concern, liquid DzO can be added t o the beaker of ordinary water to increase the liquid's density, thereby causing the deuterated ice cube to rise from the bottom of the beaker. All of these experiments can readily be shown to a large audience by projecting the image of the rectangular plastic container using the overhead projector on its back.4 Dlscusslon An ice cube floatine in water is a natural phenomenon with which students &e well acquainted. TI;^ density of frozen H?O varies sliehtlv with temperature. but at the temperatureof many hokehold freeze& (--20 "C) it is about 0.9 e/mL and does not vary much up t o its melting point. ~ i q i i dwater has a density approximately 1.0 g / < ~from room temperature down to its freezinc point of 0 "C, so the less dense-ice is expected and observed to float in water. Substitution of water with deuterium would be expected to increase the densities of the solid and liquid by -1170, to 1.0 and 1.1 gImL, respectively, if only mass changes are considered: Each atom of deuterium, possessing a proton and neutron in its nucleus, is about twice as heavy as the hydrogen atom, which has only aproton in its nucleus. Thus, while the molecular mass of Hz0 is approximately 18 g/mol, the molecular mass of D20 is approximately 20 glmol, an -11% increase. Volume changes contributing to the density cannot be com~letelvienored. but thev are small bv comnarison: In the liquid stat;, the molar voiumes of HZOand ~~0 are 18.02 and 18.09 mL.. resnectivelv. . .. at 20 O C 5 in the solid state, oxygen-oxygen distances in hexagonal ice and "heavy"iee are virtually identical6 The effect of isotopic substitution is thus that the D20 ice cubes have a slightly greater density than the ordinary liquid Hz0 in which they are placed. Consequently, they sink. Addition of some liquid D20 to the hath increases the liquid's density, tuning the buoyant force to the point where theD20 ice cube will now float. Liquid D20 provides a sufficiently dense medium that ice cubes prepared from either isotope will float in it.

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Hazards Deuterium oxide is a relatively safe material to handle. I t is not radioactive. I t should, however, not be ingested, as large doses have proved toxic to animals.7

melts, its liquid may be stored in an appropriate bottle. Likewise, i t is inevitable that floating a normal ice cube in pure liquid deuterium oxide will result in some contamination of the liquid due to the melting ice, but, if the contact is minimized, the contaminated deuterium oxide may he reused a number of times. , Deuterium oxide is hygroscopic. If its container is not well sealed, the compoundwill exchange with ordinary water vapor in the air. I t may be appropriate to weal a once-opened bottle with melted candle wax. Acknowled~ment We thank L. F. Dahl, M. Hoffmann, M. H. O'Leary, and F. Weinhold for helpful discussions. A. T. Jacob is thanked for providing the photograph.

A Simple Apparatus To Demonstrate Differing Gas Diffusion Rates [Graham's Law] SUBMIITEO BY

Phlllp C. Keller Unlversny of Arizona Tucson, A2 85721

CHECKED BY

The apparatus described in this note dramatically demonstrates relative diffusion rate effects for commm gases like methane (natural gas) and carbon dioxide and can be constructed easily from common laboratory glassware. I t represents an improvement over earlier demonstrations of this tme.' If several eases are available. semiouantitative measkements can be-made to illustratethe incerse relationship between molecular mass and diffusion rate (Graham's )awl. The apparatus requires a 500-mL separatory funnel, a 4-ft length of 8-10-mm glass tubing, clear Tygon tubing, a small stopcock, a 600-mL beaker, water with food coloring, an unglazed battery cup2,and a few rubber stoppers. The demonstration is set up in two configurations: the first (Fig. 1) serves to illustrate the higher diffusion rates of gases with molecular masses less than air (e.e.. methane. helium.. and hydrogen). The second arrange*elt'(Fig. 2) shows the lower diffusion rates of gases with molecular masses ereater than air (carbon dioxid;, freons, etc.). The functionof the small stopcock is to equalize the pressure rapidly before the start of the demonstration. ~

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Dlsposal Deuterium oxide is not cheap (at the time of this writing, 100 mL costs about \$50), and i t may be appropriate to recover as much as possible a t the conclusion of this demonstration. I t is inevitable that some solid deuterium oxide will melt when placed in water. hut if the cube is withdrawn quickly from the liquid and placed in a separate container, relatively little contamination will take place. As the cube

Operation for Low-Molecular-Mass Gases The configuration used for gases like methane (natural gas), helium: and hydrogen is Shown in Figure 1. A p(mus porcelain cup of the type uned for Galvanic cell demonstrations'is fitted to the tou of a 500-mL senaratorv funnel with rubber stoppers and ashort lengthof glass tubiAg. An inverted 500-mL beaker rests on top of the cup. The separatory funnel is connected with clear Tygon tubing to a vertically clamped 4-ft length of 8-10-mm fad.) elass tubine. The systek is filled to within 1in. of the topVof the sep&atory funnel with water containing a food colorine- or dye for easv visibility.

The Merck Index, 8th ed.; Merck: Rahway, NJ. 1968: p 334. BPimentel. G. C.; McClellan, A. L. 7'fm hydrogen Bond; W. H. Freeman: San Francisco, 1960; p. 294. Katz, J. J.: Crespi, H. L. In botopeEffectsin ChemicalReactions: Collins. C. J.; Bowman. N. S., Eds.; Van NostrandReinhold: New York, 1970: pp 286-363.

Alyea, H. N.; Dunon, F. B., Eds. TestedDemonstmtions in Chem istry, 6thed.; Journal of Chemical Education:Easton, PA, 1965: p 204. Cylindrical porous porcelain cups can be obtained from SargentWelch Scientific Company (Cat. No. 2202). Frey ScientificCompany (Cat.No. 1780),Central Scientific Company (Cat. No. 79286).or other suppliers.

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T o show pas diffusion through a porous barrier, a hose connected t b a source of methane, heiium, hydrogen (high13 inflammable!),or any other available yas with a molecular mass less than air is ciirected inside theinverted beaker, the pressure is equalized with the stopcock, and the gas is then allowed to flow. This is best done after first discussing the molecular diffusion phenomenon with the class, explaining the apparatus, and asking what is going to happen when the gas is turned on. The rise in the vertical water column resulting from the faster inward diffusion of the lighter gas molecules is dramatic and is easily ohserved even in large lecture halls. If more than one light gas is available for the demonatration, the inverse relationship between column height and the molecular mass is clearlv demonstrated. Suitable follow-up discussion could center bn the use of this phenomenon to measure molecular mass and to separate gases of differing molecular mass (e.g., isotope separation). Once the maximum pressure rise has been achieved, i t is effective t o ask the class what will h a n ~ e nwhen the eas flow ceases, the beaker is removed, and tie lighter gas bigins to diffuse back out of the porous cup. Withagaslike helium the height of the vertical water column drops rapidly and temporarily falls well below the starting point of the experiment because helium diffuses out of the cup faster than air can diffuse in. This effect is also observable using.methane hut is not as dramatic. Operatlon for Hlgh-Molecular-Mass Gases T o demonstrate the effect with cases denser than air. the system can be modified as shown i n - ~ i y r e 2 .The porouscup is sealed with a ruhber stopper and connected to a 3- or 4-ft length of clear Tygon tub& leading to the same separatory funnel and vertical glass tube. The cup is lowered into a beaker containing carhon dioxide gas. This can be more effectively dramatized by pouring the denser carbon dioxide gas from another beaker. The water column quickly drops below its original level because of the faster diffusion of air out of the system. If other heavier gases like Freons are available, the inverse relationship between diffusion rate and moIecular mass can again be demonstrated. Once the pressure reaches its lowest point, the demonstrator can again ask the class what will happen when the cup is withdrawn from the beaker and placed in the open air. When this is done, the water column rises to its original level and continues to rise for a short time because of the faster diffusion of the lighter air molecules into the system.

Figure 1. Apparatus cantigured to shew higher diffusionrate of gases with molecular masses less than air.

Dlscusslon The use of water rather than rnercurv to show Dressure changes allows a magnification of the Gessure difierential by a factor of 13.5 (the specific gravity of mercury). With colored water the pressure changes can be seen in the largest classr~wms.Tvpicnl pressure differences obtained with sev.. era1 common gases are Hydrogen

Helium

Methane

Air Carbon Dioxide Freon-3a3

in. in. 8 in. 0 in. -8 in. -18+ in. 30+ 22

Freon-38 is perflwropropane (C.F,). A more readily available Freon isusedtofiliautomobiie air conditioners, e.g.. "Refrigerant 12" (CCi2Fd;it can be purchased in small cans from automotive supply Stores.

Figure 2.

Apparatus

configured to show lower diffusionrate of gases whh

rmIezuW masses geater thm air.

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February 1990

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