Air Pressure and Amontons' Law (Charles' Law)

Dec 12, 1998 - Department of Chemistry, University of North Carolina at Wilmington,Wilmington ... bined with Amontons' law involves putting a hard-boi...
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Chemistry Everyday for Everyone

The Egg in the Bottle Revisited: Air Pressure and Amontons’ Law (Charles’ Law) Louis H. Adcock Department of Chemistry, University of North Carolina at Wilmington,Wilmington, NC 28403-3297

“In any [ideal] gas whose volume and mass are kept constant, the same rise in temperature produces the same increase in pressure” (1). This is Amontons’ law. It is sometimes referred to as Charles’ law of pressures (2) or simply as Charles’ law (3) or Gay-Lussac’s law (4, 5), though the term Charles’ law is usually reserved for the temperature–volume relationship and Gay-Lussac’s law for his law of combining volumes. Guillaume Amontons discovered in 1699 that for a constant volume of air, the pressure increased by one-third when the air was heated from room temperature to that of boiling water. He also inferred from Boyle’s law (P ∝ 1/V at constant temperature and mass) that if the pressure is held constant then the volume would increase by that same amount. Lambert (1779) used Amontons’ results to calculate absolute zero as ᎑293.5 °C (6 ). A classic demonstration of the effects of air pressure combined with Amontons’ law involves putting a hard-boiled egg in a bottle whose opening is slightly smaller than the circumference of the egg. An even more spectacular demonstration is getting the egg back out intact. This demonstration is included in many popular books of chemical experiments aimed at young readers. The Demonstration

Needed 1 narrow-mouth 500-mL Erlenmeyer flask (or appropriate bottle) 1 medium hard-boiled egg (peeled) 1 heat gun (hair dryer)

Procedure First, demonstrate that the egg cannot be pushed into the flask. Point out that the “empty” flask is actually full of air; and since this air has no way out of the flask, it resists any pressure you exert on the egg. Next, clamp the flask to a ring stand and place the heat gun beneath the flask. Heat the flask with the heat gun for three minutes. Turn off the heat gun and immediately place the egg on the mouth of the flask. As the flask cools, outside air pressure forces the egg into the flask. When the flask was heated the temperature in the flask reached 63 °C. Using Ammontons’ law the difference in pressure can be calculated. P1 and T1 refer to the temperature and pressure in the heated flask and P2 and T2 to those quantities when the flask is cooled to room temperature: P1/T1 = P2/T2 where P1 = 760 torr; T1 = 336 K; T2 = 296 K. Then P2 = 670 torr, and ∆P = 90 torr (11% decrease). Turning the flask upside down and shaking or hitting it with the heel of your hand will not dislodge the egg. Now

turn the flask upside down so that the egg falls into the neck of the flask, clamp the inverted flask to the ring stand, and heat the bottom of the flask. The egg will pop out. A more dramatic method is to tilt your head back and blow strongly up into the flask. Be ready to catch the egg in your hand as the increased air pressure inside the flask forces the egg out. If the flask is clean, you can eat the egg. Kolb et al. (7) suggest a simple never-fail method for removing the egg: add a spoonful of baking soda, pour in a little vinegar, and swirl. The carbon dioxide thus formed causes the egg to pop out of the inverted bottle. Discussion How does the egg in the bottle demonstration work? Heating the flask causes the air inside to expand, forcing some of the gas molecules out of the flask. As long as the air is heated, the pressure of the fewer but hotter molecules inside is equal to that of the cooler more numerous molecules outside. Blocking the opening of the flask with the egg does not allow the expelled molecules of gas to return. Thus as the flask cools down, the reduced number of molecules inside do not exert enough pressure to equal the outside pressure. The greater external pressure forces the egg into the bottle. There are many ways to drive air out of the bottle. The demonstration is often performed by placing burning paper inside a bottle and putting the egg over the bottle’s mouth when the fire burns out (8–12). Gardner (13) used a match. Arthur (14 ) used alcohol-soaked cotton, and Markow (15) heated the flask with a Bunsen burner. Mandell (16 ) added boiling water to a ketchup or baby bottle and poured the water out quickly before placing the egg over the bottle’s mouth. Ford (8), Gardner (13), and Herbert (10) cite the partial vacuum inside the bottle as the reason the egg is forced into the bottle. Gardner (13) and Herbert (10) state that the air cools and contracts [?] to produce the vacuum. Church (11) states “When the air cooled, it shrunk and took up a lot less space.” This is impossible, since a gas will occupy the same volume (that of the flask) no matter what the temperature. Mandell (16 ) attributes the reduced air pressure to the condensation of residual steam. Kolb et al. (7), Van Cleave (9), and Walpole (12) state that as the paper burns, it removes most of the oxygen from the air inside the jar. The lack of this gas reduces the pressure of the air inside the jar. Since the combustion of cellulose (C6H 10O5)x actually produces more moles of gaseous products than there are moles of oxygen consumed, this is not the correct explanation, as De Lorenzo (17 ) and Moran (18) pointed out and Kolb (19) (in a letter of reply) concurred: (C6H10O5) x + 6x O2(g) = 6x CO2(g) + 5x H 2O(g) Arthur correctly states that heating causes the gas to expand and that part of it escapes from the bottle. As the re- • Vol. 75 No. 12 December 1998 • Journal of Chemical Education


Chemistry Everyday for Everyone

maining air cools, the pressure inside is decreased. Markow doesn’t give a detailed explanation, but states that this is an excellent demonstration of Charles’ law. Since heating the air in the flask well above room temperature enables the egg to be placed inside the flask, it seems logical that cooling the flask well below room temperature should have a similar effect. Place the egg over the mouth of the flask and place both egg and flask in a freezer. Within three minutes, the egg is forced inside the flask. (Alternatively, the flask could be placed in a salt–ice mixture (᎑ 4 °C), but this method is slow and not always successful). At room temperature, the molecules of gas exert a pressure equal to the external pressure. When the flask is cooled with the egg in place, the cooler air inside exerts a lower pressure and the egg is forced into the flask. If the flask is cooled in the freezer for 30 minutes, the egg is placed over the mouth of the flask, and the entire assembly is placed back inside the freezer, the egg will not be forced into the flask even after 10 minutes. (If left much longer than 10 minutes, the egg will begin to freeze and lose its elasticity.) The freezer temperature was ᎑11 °C. Using Amontons’ law, the decrease in pressure can be calculated as done above in the case of heating the flask: P 2 = 678 torr; ∆P = 87 torr (11% decrease). For people concerned about the high cholesterol content of eggs, the same experiment can be used to peel a banana (Drotar, ref 20). Use a 1-L flask and a banana whose diameter is a little larger than the diameter of the flask’s neck. Cut a 1.5-inch length off the banana, peel and all. Run the experiment but instead of the egg, place the banana section over the flask opening so that the peel overhangs the edge a little bit. The higher air pressure outside the flask will force the soft pulp into the flask leaving the peel outside. Drotar used the burning paper method in this experiment, but incorrectly stated that the cooling air occupies less space and thus has a reduced pressure.

Literature Cited 1. Ballentyne, D. W. G.; Lovitt, D. R. A Dictionary of Named Effects and Laws in Chemistry, Physics, and Mathematics, 4th ed.; Chapman and Hall: London, 1980; p 7. 2. Dictionary of Chemistry (from Oxford University Press Concise Science Dictionary); Warner: New York, 1985; p 63. 3. Steinbach, O. F.; Conery, G. F. J. Chem. Educ. 1944, 21, 216– 218, 227. 4. Joseph, A.; Brandwen, P. F.; Morholt, E.; Pollack, H.; Castka, J. A Sourcebook for the Physical Sciences; Harcourt, Brace, & World: New York, 1961; pp 397–398. 5. Wilbraham, A. C.; Staley, D. D.; Simpson, C. J.; Matta, M. S. Chemistry, teacher’s ed.; Addison-Wesley: Menlo Park, CA, 1990; pp 230-231. 6. Partington, J. R. A History of Chemistry, Vol. 3; Macmillan: London, 1962; p 771. 7. Kolb, D.; Grzanich, S.; Carrigan, P. J. Chem. Educ. 1995, 72, 527. 8. Ford, Leonard A. (revised by Grundmeier, E. W.) Chemical Magic; Dover: New York, 1993; p 28. 9. VanCleave, J. P. Teaching the Fun of Physics; Prentice-Hall: New York, 1985; p 17. 10. Herbert, D. Mr. Wizard’s Supermarket Science; Random House: New York, 1980; p 39. 11. Church, J. You Can with Beakman & Jax (syndicated comic strip); Wilmington Star-News, July 27, 1997; The Washington Post, July 27, 1997; comic section. 12. Walpole, B. 175 Science Experiments to Amuse and Amaze Your Friends; Random House: New York, 1988; p 65. 13. Gardner, M. Entertaining Science Experiments with Everyday Objects; Dover: New York, 1981; p 100. 14. Arthur, P. Lecture Demonstrations in General Chemistry; McGrawHill: New York, 1939; p 56. 15. Markow, P. G. J. Chem. Educ. 1980, 57, 307. 16. Mandell, M. Simple Science Experiments with Everyday Materials; Sterling: New York, 1989; p 72. 17. De Lorenzo, R. J. Chem. Educ. 1996, 73, A188. 18. Moran, M. J. Chem. Educ. 1996, 73, A189. 19. Kolb, D. J. Chem. Educ. 1996, 73, A189. 20. Drotar, D. L. Fun Science Learn and Discover Book; Playmore and Waldman: New York, 1986; p 45.

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Journal of Chemical Education • Vol. 75 No. 12 December 1998 •