A Systematic Experimental Test of the Ideal Gas Equation for the General Chemistry Laboratory Luis H. ~ l a n c o and l Carmen M. Rornero Facultad de Ciencias Universidad Nacional de Colombia, Bogota, Colombia Experimentation with air or other gases to show ideal gas behavior is a common practice in the General Chemistry Program. Most laboratory manuals have descriptions of relevant ex~eriments. Thc suhjcct is of permanent interest to teachers, and one it. See fbr instance ( 1 , . In frequently finds new ~ d e a about s (21,there is a description of a a recent issue of lhrsJ~~urrto1 eood demonstration ofCharles'law. 'The authors have cited 14 references, corresponding to material that appeared from 1962 to 1990. We have found that most of the experiments stand alone illustrating a single feature of the ideal gas equation. They may measure P versus T, or Vversus P and so on, but it's not easy to find a set of measurements designed to study each of the terms of the equation. For one of our courses we have developed a set of experiments that fulfills the purpose of showing ideal gas behavior in an integral way. I t bas been nsed for several years, having had good acceptance by other teachers and specially by the students. The following is a description of the set of experiments. They may be complemented with some others that can be considered applications of the gas laws ( 3 , 4 ) .
obtained for both temperature and length of the enclosed air, the data are recorded. The temperature is then set at another value, and the procedure is repeated until at least six pairs of values are obtained. Table 2 and Figure 4 are samples of student results. I
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Boyle's Law: Vversus P The method described by Hermens (5)is used for the purpose. A glass capillary is closed a t one end and an amount of air is trapped with mercury, which a d s as a piston. Using the setup shown in Figure 1, the pressure on the air is varied by changing the angle of the tubing with respect to the horizontal. This is accomplished by rotation as indicated. The lengths of the air columns and the corresponding angles are recorded. Up to 12 readings can be obtained in a very short period of time. Table 1and Firmre 2 are the results of a h i c a l eweriment. v&es of the The pressures o i the air are computed &;the angles and of the lengths of the mercury columns. Charles-Gay Lussac's Law: Vversus T For this experiment the same principle of the preceding one is nsed. The apparatus is adapted so that the temperature can be controlled and measured. The setup is shown in Figure 3. It is interesting to note that more than one of the gas cells can be connected to a single circulating thermostated bath. It should be remembered, nonetheless, that a small temperature gradient will develop, so that it is necessary to use a thermometer for each gas containing capillary. Also, because the scale used to measure the length of the air column is placed outside the water jacket, the students must be cautioned about the importance of maintaining a constant zero position, i.e., the closed end of the capillary. The tube is placed so that i t is horizontal. At all times the Dressure of the e n t r a ~ o e dair will be atmos~heric.In a typical run the tempe;&nre is made to vary some 30 degrees in 4- or 5-degree intervals. Once stable values are 'Corresponding author.
Figure 1. Boyle's law apparatus:A. Glass capillary, B. Meter stick, C. Thermometer,D. Pivot, E. Mercury slug. Table 1. Results Obtained by a Group of Students for Boyle's Law Experiment Measurement Number
9 10 11 12 13 14 15 16 17 18 19
Length of Air Angle of Capillary Total Pressure Degrees mm Hg Column mm
40.6 41.4 42.8 43.5 45.2 46.3 47.2 48.2 48.6 49.0 49.1
10 0.0 -1 0 -20 3 0 -40 -50
575 560 545 530 517 504 494 40 485 -70 479 -80 475 -90 474 Note: Temperature = 17 'C, Atmasphetic Pressure = 560 mm Hg (Bogota is located at about 2600 m above sea level. The atmospheric pressure vanes amund an average of 560 mm Hg.).Length of the Mercury Column = 86 mm.
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Figure 4. ChariesGay Lussac's law: Length of the air column in millimeters versus temperature in K. Figure 2. Boyle's law plot: Pressure in millimeters of mercury versus inverse of length in mm-'.
Figure 3. Charles' law cell: A. Glass jacket, B.Capiiiary, C. Millimeter scale, D. Mercury slug, E. Thermometer graduated in 0.1 "C. F. Water inlet G. Water outlet. Table 2. Data for Charles' Law Experiment: Length of the Air Column as a Function of Temperature
No.
Temperature K
Length of the Air Column mm
1 2 3 4 5 6 7 8 9 10
295.8 300.9 304.3 304.7 309.1 312.3 315.6 317.4 321.0 322.5
250 255 259 260 264 266 269 270 273 275
Note: Total pressure 560 mrn Hg.
If one wants to obtain more than one isobar, i t is a rather simple procedure to change the angle of the capillary from the horizontal position, and repeat the entire experiment a t the new pressure. The plots can be made on the same 934
Journal of Chemical Education
Figure 5. Experimental setup for the determination of Pversus Tbehavior: A. Mercury manometer, 8. Plastic syringe,C. Three way stopcock, D.Therrnostated cell (see Fig. 3). piece of paper to establish a good basis for discussion of the effect of pressure. Amonton's Law, Pversus T
The same idea of having air entrapped in a capillary by means of a slug of mercury a s in the preceding experiments is used. This time the volume or the length of the air column will be kept constant with changing temperature by adjusting t h e pressure. The experimental setup is shown in Figure 5. A mark is made to indicate the position of the mercury slug in contact with the entrapped air. This gives the value of the volume a t the starting temperature. I t usually is around 20 "C, and i t is kept constant using the same procedure a s i n the preceding Charles' law experiment. The stopcock, C, i s placed so that the manometer, A, is con-
Figure 7. Apparatus for the determination of the number of moles of a gas: A. Mercury or water manometer. B. Themlometer, C. Plastic beach ball. D. Gas supply. Figure 6. An experimental plot of Pversus T. nected to the gas cell. The pressure inside should be atmospheric, and the manometer reading should be zero. The values of temperature, length of the column, and atmospheric pressure are recorded. The temperature is raised 4 or 5 "C. Once thermal equilibrium has been reached, a syringe is used to restore the volume of the entrapped air to its initial value. The new pressure value and temperature are recorded. This procedure is repeated until a t least six pairs of readings are obtained. Table 3 and Figure 6 are sample results. It should be noticed that when one works with mercury confined in capillary tubes the metal tends to stick. If both mercury and glass are clean enough, sticking can be avoided by tapping gently and shaking the capillary carefully. Keeping the tubes covered and isolated from atmospheric dirt when not in use, helps to prolong their useful lifetime for as long as a year or more.
Table 3. A Set of Data for the Determination of Pversus TBehavior
Temperature K
Manometer Reading mm Hg
286.0 288.2 304.6 310.4 316.6 322.4
0.0 6 11 22 32 47
Table 4. Determination of Number of Moles: Experimental Data for Two Gases
Gas Temperature K Manometric Pressure mm Hg Weight g Ball Circumference cm
COz 292 7 8.0 71.0
Lighter Fuel 291 42 11.0 69.7
Number of Moles nor Molecular Weight M
The determination of the number of moles, n, is accomplished often as an application of the ideal gas law. The experiments can be very simple ( 6 )or rather complicated (7).For this set of experiments we developed a method based on a n idea published in this Journal (8)some time ago. Basically, the volume occupied by a weighed amount of a gas is determined at a pressure that is near atmospheric. The apparatus shown in Figure 7 is very easy to assemble. The procedure is as follows: a plastic beach ball of about a six-liter capacity is filled with gas from a n appropriate source. This source can be a cigarette lighter s u v ~ l vcan or any othcr source of a gas whose compodn~onis known (see the next exveriment) The amount of ans is determined by weighing the container before and &er the filling dure. The pressure is read using the manometer. Only a small difference should result with respect to the atmospheric value. The temperature is recorded. Using a measuring tape, the circumference of the ball is determined. This completes the necessary data for the calculation of n. Table 4 shows the results of a typical run. The calculation
is very easy, and it can be emphasized that what is being determined is n = w / M , the quantity that appears in the gas equation. With the data of Table 4 we obtain M = 42.5 g mol-I for COz, and 58.0 g mol for lighter gas, which is mainly a mixture of butane isomers. The Gas Constant R This time a simple modification in the calculation is made to eet the eas constant from an exoeriment entirelv similar to the preceding one. The gas used is COz, and the source is dry ice. A small amount of dry ice is placed in a test tube whose weight has been determined previously. The tube is placed in a balance sensitive at least to 0.01 g. Gas is allowed to form and to escape until a predetermined weight is obtained for the remaining solid COz. Once this happens the tube is quickly connected to the ball to be used as the source of gas referred to in the preceding experiment. Students should be told not to have solid COz confined in a closed container. The test tube where dry ice is placed must be either open to the atmosphere during
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weighing or connected to the beach ball while gas is collected. With the data of Table 4, assuming 100% purity of the gas and known molecular weight 44.0 g mol-l, a value of 0.0849 l-atm mol-' B' was obtained. This is a single value taken randomlv from students' r e ~ o r t s . Programs i n ~ a s i cfor , use withA~acintosh and IBM microcomputers have been written and are made available to the students. The listings will be published elsewhere and are available from the authors. Acknowledgment We acknowledge the contributions of our students in the development of these experiments. We would like to ex-
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Journal of Chemical Education
press our appreciation to the reviewer for his comments and his suggestions for improving the manuscript. Literature Cited 1. Lehmann,J. K J. Chem Edue. 1992.69,943.944, 2. George,A.: Zidiek,C J. Chem. Edue. 1991.68. 1042.1043 3. Carney G. D.; Kern. C. W J Chem. Edue 1919.56 823.8%.
4. Peck, L.;lrgolic,K: O'Connor. R. J. Chem Educ 1980,57,517418. 5. Hermens, R.A.J Chem. Edue. 1983,60,764.
6. Harris, A. D. J. Cham. Edur 19M. 61.74-75. 7. Danle1s.F.:Wil1iams.J.W:Bender,P.;AlbertyR.A.:Cornwell.C.D.;Harriman,J. E. ExprimenalPhvsicoi Chzmlslry, 7thed.:McGrau-Hill:NewYork, 1970,pp9-16.
8. Murdoek,H.D.;Hawthorne, R. M.J. Cham. Edue. 1913.50,628.
