An Apparatus for the Study of the Gas Laws OlTO F. STEINBACH and GEORGE F. CONERY
City College of New York, New York City above the stopper of the flask. The assembled apparatus is shown in Figure 1. To obtain the data for Boyle's law, it is first necessary to know the volume of the Erlenmeyer flask. This may be determined with an ordinary graduated cylinder. Fifty cc. of dibutyl phthalate are first poured into the flask; the apparatus is then assembled and placed in the constant temperature bath a t room temperature with the buret stopcock open. Wben the system has come to temperature equilibrium, the stopcock is closed and the buret is filled with dibutyl phthalate. The reading of the manometer is recorded and also the barometric pressure. For simplification of the calculations, tbe barometric pressure may be changed from cm. of mercury to cm. of dibutyl phthalate by multiplying the barometric height by 12.96, since that is the ratio of the densities of the two liquids, 13.546 and 1.045. Then sulicient dibutyl phthalate is added from the buret to give increments in pressure of 5 cm. The buret and manometer readings should be recorded each time. Table 1 is a sample of the data obtained from one experiment. Since the volume of the empty flask was 275 cc. and 50 cc. of manometer liquid were added, the actual volume available to the air a t the beginning was only 225 cc.
Bum.
cc.
'1'
HE following apparatus, which can be assembled from ordinary stock, can be used in the laboratory for the study of the gas laws.
-
T 20°C. Volvmc,
cc.
TABLE 1 Barometric pressure = 76.7 eh. Monomdrr.
Prcsrurc.
cm.
cm.
P X V
cc. X cm.
Since the level of the liquid in the Erlenmeyer flask changes only about 0.1 cm. due to the liquid added from the buret, i t is not necessary to read the lower end of the manometer each time in order to establish L A W S OR BOYLE AND CHARLES the height of the manometer, as the error introduced is The apparatus consists of a 250-cc. Erlenmeyer flask, small. It will be observed that there is a continuous a 50cc. buret, a 1-liter beaker or a large tin can to drift in the value of the P IT product. This is probably serve as a thermostat, a thermometer, and 60 to 80 cm. due to the increased solubility of air in the manometer of 2.5-3-mm. capillary tubing, which functions as a liquid a t the higher pressure. This also produces a manometer. The manometer tubing is graduated drifting manometer. When mercury was used as the every 0.2 cm. on the lower end for a length of 2 cm., manometer liquid, this drift was not observed. It is and thereafter is graduated every centimeter. This possible to obtain similar results by using a number can be done e i t h crucible marking ink which should be 10 or 0 motor oil in place of the dibutyl phthalate. When the apparatus is used for the study of Charles' fired on if permanency is desired. Alternately, a paper metric scale may be pasted on the manometer law the accuracy is only around 10 per cent. The 216
apparatus is set up as previously described. After it has reached temperature equilibrium, the stopcock is closed and the temperature of the water bath is raised. The temperature of the water should be carefully controlled and sufficient time allowed for temperature equilibrium to be attained. The temperature and manometer readings are then recorded. Table 2 is a sample of the results obtained from an experiment. A thermometer divided in whole degrees was used. The barometric pressure was 75.3 cm. of mercury. Mononrdrr. lnifid Final
reading of the manometers, and then the average of the two readings is taken as the observed h a 1 pres-
1
IF
Prcmrrr,
T,-K. 292.8
Cm.
Cm.
0.8
975
311.6
56.8
1031
T,colc. 'K.
...
309
In order to obtain reasonable experimental results, considerable care must be used in adjusting the temperature of the water bath. Likewise, a t least 10 minutes should elapse before the final manometer reading is taken. DALTON'S LAW OF PARTIAL PRESSURES
The apparatus consists of suction flasks of 250- and 500-cc. size, two graduated manometer tubes made from 2.5-mm. capillary tubing about 60 cm. long, three screw clamps or glass stopcocks, and two large tin cans to serve as constant temperature -baths. The assembled aawaratus is shown in F i m e 2. The voi;me of the flasks shoild be predetermined with a graduated cylinder. Then 50 to 75 cc. of dibutyl pbthalate are placed in each flask and the apparatk assembled as shown in the accompanying diagram. The barometric pressure is then recorded. Dry air is then passed into the large flask B, and 0%obtained from a steel cylinder into flask A through the tops of the manometers while the stopcocks are open. Since the pressures required are small, the source of the compressed air may be a foot or hand bellows or a bicycle pump. If carbon dioxide is substituted for oxygen, it can be obtained from a large Kipp generator which has been stoppered on the top. After the flasks have been flushed out thoroughly with dry air and oxygen the connection is removed, the stopcock closed, and the gases allowed to come to room temperature. To adjust the pressure in the flasks to atmospheric pressure, the stopcocks are opened momentarily and then shut again. The zero readings of the manometers are then recorded. As long as the room temperature is fairly steady and there are no drafts, it is not necessary to place the flasks in the tin pails which serve as constant temperature baths. The air is now forced in through stopcock E and the oxygen through stopcock C. After the desired pressures have been attained the stopcocks are closed, and when the liquid in the manometer tubes has ceased to rise the readings are taken. The stopcock D is then opened and the gases are allowed to mix. The manometers are read when the liquid in them ceases to change. The readings are corrected for the initial
F I G ~2 E
sure. This is necessary because the amounts of manometer fluid may be different in the flasks, and also because the manometers are not necessarily located a t the same depth in the liquid. The procedure can be repeated as often as desired; each time, however, it is necessary to flush each flask out with the respective gas to be used in that flask. The following data were taken from one experiment employing oxygen in the small flask and air in the large flask. The atmospheric pressure was 76.0 cm. of mercury, which is equivalent to 985 cm. of dibutyl phthalate. The volume of flask A was 300 cc. and that of flask B was 560 cc. Then 50 cc. of dibutyl phthalate were added to flask A and 60 cc. added to B, so that the actual volume of A was 300 - 50 or 250 cc., and that of B was 560 - 60 or 500 cc. The initial reading of the manometer in flask A was 1.20 cm., and in flask B it was 1.0 cm. Oxygen was allowed to enter flask A until the manometer stood a t the height of 20.0 cm. Thus the corrected height is 20.0 - 1.2 or 18.8 cm. Air was forced into flask B until the manometer stood a t the 56.6-cm. mark, and when corrected for the initial reading, the value is 55.6 cm. Thus the pressure in flask A is 985 18.8 or 1003.8 cm., while the pressure in flask B is 985 55.6 or 1040.6 cm. The calculated pressure can be obtained by applying Boyle's law to each gas, assuming that it is expanding into a vacuum.
+
+
Thus, if the oxygen in flask A was allowed to expand into flask B which had been evacuated, i t would have a pressure of 1003.8 X 220/7so or 334.6 cm. For the air in flask B the pressure would be 1040.6 X "o/rso or 693.6 cm. Since the total pressure is the sum of the partial pressures, namely, 334.6 and 693.6, it should be equal to 1028.2.
After stopcock D was opened and the manometers stood steady i t was observed that the manometer in A read 44.6 cm., while that in B read 44.2 cm. When corrected for the initial reading, the manometer A is 44.6 - 1.2 or 43.4 cm. and the reading of B is 44.2 1.0 or 43.2 cm., and the average of the readings is 43.3 cm. Thus the total observed pressure is 985 43.3 or 1028.3 cm. This agrees very nicely with the calculated pressure of 1028.2 cm. In concluding, it may be mentioned that other liquids such as light motor oil or mercury can be used in place of the dibutyl phthalate.
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GRAHAM'S LAW OF EFFUSIOX AND THE RELATIVE n s COSITY OF GASES
The assembled apparatus, which is a modified Bunsen effusiometer, is shown in Figure 3. The apparatus consists of a 250-ml. pyrex suction flask, a pipet of either lo-, 25-, or 50-ml. size, two glass stopcocks, aluminum foil, a length of glass tubing, capillary tubing from broken thermometers, and a large tin can to serve as a constant temperature bath. The orifice is constructed by perforating the aluminum foil with a sharp, slender needle. Another method which was found to be very satisfactory is to fold.the foil in two right-angle folds. This generally produces a hole in the foil which is smaller than that made with a needle. The foil is rolled flat again with some glass tubing. The foil is theu fastened to a short piece (1") of glass tubing with sealing wax or de Khotinsky cement, and this in turu is held to the stopcock D by a shod length of rubber tubing. The apparatus is first calibrated with dry air. This is accomplished by adding 50 to 75 cc. of dibutyl phthalate or a very light motor oil to the flask. The apparatus is then assembled and dry air is forced in through E to bring the liquid to the mark A on the pipet. Since the pressure required is small, the air may be obtained from a foot or hand bellows or a bicycle pump if a source of compressed air is not available. The flask is next placed in the constant temperature water bath, and when it has attained temperature equilibrium, stopcock D is opened. The time for the level of the liquid to fall from marks B to Cis determined. To determine the molecular weight of carbon dioxide. for example, the air is flushed out of the flask by counecting the source of the gas to the open end of the pipet and allowing the gas to pass into the flask for 5 to 10 minutes, with the stopcock E open. This also saturates the liquid in the flask with carbon dioxide. The procedure for filling the flask with carbon dioxide is then repeated, as previously. described for air, and the time of efflux between marks B and C is determined. Several trial runs should be made in order to displace completely the air in the tube leading to the orifice. The molecular weightis then calculated by the equation.
Since the pressure required to force the liquid from the flask into the pipet is not large, the carbon dioxide may be obtained from a large Kipp generator which is stoppered on the top. Gas obtained from steel cylinders is much more convenient, however. Using a 25-cc. pipet and a time of efflux of 300 seconds for air in the above apparatus, an accuracy of 1 per cent can be easily obtained for the molecular weight of either O2or COI. The glass tube upon which the foil is mounted may be removed and replaced without appreciably changing the time of efflux, providing i t is pushed down to make contact with the glass stopcock (Continued on page 227)
AN APPARATUS FOR THE STUD* OF THE GAS LAWS (Catinued from $age 218)
each time. An extra length of glass tubing may be the time for the liquid to pass between the marks is joined to the pipet by a small piece of rubber tubing to halved. It can also be shown that to measure effusion prevent loss of liquid in the flask through overllow while a small orifice is needed in a very thin foil, for even upon cutting the capillary tube down to a length of filling the pipet. i t can be determined that viscosity is being measThe relative viscosity of gases may be determined by replacing the orifice tube with the aluminum foil by a ured and not effusion. Carbon dioxide can be used to piece of thermometer tubing and the 25-cc. pipet by a illustrate this very nicely, since its molecular weight 10-cc. pipet. The flask is filled with dry air, as pre- is greater than air, while its viscosity is less than that of viously described, and the time for the liquid to pass air. The effect of temperature upon the viscosity of between established marks is determined. The viscos- air can also be easily shown by simply changing the ity of other gases, such as COz, relative to air may be temperature of the water bath. In this way i t can be obtained by replacing the air in the flask by the COz demonstrated that the apparatus measures Poiseuille by the procedure described above. The relative flow and not molecular flow, for the time of efflux deviscosity compared to air is calculated from the for- creases with increasing temperature instead of increasing as it should when the mean free path of the molemula cules is large compared to the diameter of the capiltime (air) = relative viscosity of air and Con lary. time (Cog) The authors wish to thank Professor R. A. Baker The results obtained are accurate to 5 per cent. for his suggestions and Mr. Harold Wilson for supplyIt can be shown that the time is dependent upon the length of the capillary, for if the capillary is cut in half ing the diagrams.
