California Institute of Technology Pasadena and B. Rand University of Newcastle-upon-Tyne England
II
A Student hoyclnty-bulb Apparatus
T h e measurement a t known pressure and temperature of the density of a pure gas is the most direct method of determining its approximate molecular weight. The most accurate gas densities are provided by the buoyancy method, which has therefore become the most widely used research technique in this field. Moreover, the buoyancy method is particularly well suited to provide data for determining exact molecular (and hence atomic) weights by the "limiting density" extrapolation. Despite this preeminence, the buoyancy method is usually overlooked in textbooks of undergraduate experimental physical chemistry in favor of the classical methods of Regnault, Dumas, and Victor Meyer.' This omission probably arises from the difficulties in making suitable buoyancy bulbs and in measuring the small buoyancy forces with apparatus that is sufficiently inexpensive and robust for student use. Here we describe an apparatus which uses a table tennis ball as buoyaucy bulb and in which the buoyancy force is measured by an adaptation of the McBain balance, widely used in adsorption studies. A novel leveling arrangement obviates parallax and enables the small displacements of the buoyancy bulb to be magnified considerably. Apparatus and Procedure
Fignre 1 shows the apparatus. The table tennis ball is suspended by a helical silica spring within a glass tube into which gases a t known pressure can be introduced. When gas is admitted, the buoyancy of the gas exerts an upward force on the ball, causing a small compression of the spring. The lower section of the gas enclosure is jacketed by an outer glass tube containing water, the level of which can be altered by means of the 50 ml buret. Flexible tubing allows the buret to be clamped in either a high or a low position so that water may be run from the jacket to the buret or vice versa. A few milliliters of petroleum ether, colored faintly violet by the addition of a small iodine crystal, float on top of the water. The function of this layer is to provide a flat, clearlyvisible meniscus a t the water surface. When viewed through the outer jacket, the central field of vision holds two sections of meniscus: one in front of the gas enclosure and one behind. If the eye is positioned so that the two menisci merge, the line of sight must be horizontal. Water is now released from (or into) the buret until the bott,om Tim of the ball appears exactly 1 See for instance, SEOEHAXER, D. P., AND GARLAND, C. W., "Experiments in Physical Chemistry," McGraw-Hill Book Go., Inc., New York, 1962, pp. 46-53.
664
/
lournol o f Chemical Education
coincident with the merged menisci: the buret reading now provides a measure of the spring length. The range of the buret can be extended beyond 0-50 ml by adding or removing known volumes of water. On changing the gas pressure the ball will be displaced slightly, and the extent of displacement may be assessed by realigning the menisci with the rim of the ball and subtracting the two buret readings. A better procedure is to take measurements a t a series of pressures and plot buret reading versus pressure: if gas imperfections are ignored, a straight line graph results with gradient proportional to the molecular weight of the gas. I t is not necessary for the graph to extend to zero pressure, and therefore an efficientvacuum pump is not required. An ordinary water-pump was used in many of our experiments but, of course, the more efficient the pump the fewer times is it necessary to flush out the apparatus on changing from one gas to another. If the rubber stoppers blanking off the ends of the gas enclosure are tightly inserted, it is possible to work at pressures somewhat greater than atmospheric. I n our experiments a pressure of 850 nun of Hg was not exceeded. Sensitivity
The change in spring length L on altering the pressure P of the gas is given by
where M and T are the molecular weight and absolute temperature of the gas, assumed to be ideal. V, g, and R are, respectively, the volume of the buoyancy bulb,
Figure 1.
Diagram of the apparatus.
gravitational acceleration, and the gas constant. The spring is taken to obey Hooke's law with a proportionality constant K. The mass of a table tennis ball2 is such that it is convenient to select a silica, spring3having a maximum load of 2.5 g and a maximum extension of about 65 cm. For such a spring, K approximates to 50 dyne cm-'. V can be calculated from the diameter of the ball,%and substituting the values of various constants into (1)
Therefore, carbon dioxide (M = 44.0 g. mole-') will lift the ball by about 1.0 cm if admitted into the enclosure to increase the pressure by one atmosphere. Without a cathetometer, direct measurement of height changes of the order of one centimeter would be very inaccurate. However, the leveling system enables the height change of the buoyancy bulb to be magnified about twentyfold. This magnification arises because the area of the annular water,'ether interface is about twenty times greater than the cross-sectional area of the buret. The change in the buret reading, B, is equal to the change in L multiplied by the annular area, i.e.,
The apparatus is not suitable for studies over a range of temperatures, for pressures much above atmospheric, or for investigations on materials which are not gases under normal laboratory conditions. Whatever application is being exploited, the same experimental data are required: graphs of B versus P for one or more gases. Usually two gases are usedone being investigated, the second as a reference to establish the exact magnitude of the constant Z in equation (4). With the abandonment of oxygen as the basis of the atomic weight scale, no particular virtue now attaches to the use of this gas as reference. The greater the density of the reference gas the steeper is the graph of B versus P and the more precisely can the gradient be determined; we have therefore sometimes used butane as reference. For accurate work, however, the linearity of the graph is more important than its steepness and under these conditions nitrogen, one of the most ideal of gases, is the preferred reference gas.
where Do and Di are respectively the internal diameter of the outer tube and the external diameter of the inner tube, having values of about 7.0 and 5.0 cm in our apparatus. Making use of these figures and of equations (0, (3):
(a,
'*
(??) = r RTK
@ bP
= Z,
a constant r 0.50 ml mole g-' atm-I
To realign the menisci with the ball after the introduction of one atmosphere of carbon dioxide thus requires the discharge of about 20 ml from the buret. And since we find that an experimenter can attain a reproducibility in B of 0.1 ml on repeated realignment a t constant pressure, the apparatus is clearly capable of considerable precision.
*
PO0 pr..rur.,mm
Figure 2.
Applications
The apparatus can be used variously to illustrate Boyle's law, to measure molecular weights, to determine chemical formulas, to illustrate Dalton's law of partial pressures, to find the composition of binary gas mixtures, to establish Hooke's law, to investigate gas imperfections, to measure the equilibrium constant for dissociable gases, and to determine the gas constant. a The n~lesof the International Table Tennis Federation specify that "The ball shall be spherical, , .made of celluloid. . . not less than 4'/1 in. nor more than 43/1 in. in circumference.. . not less than 37 grains nor more than 39 grains in weight.. Examining balls from different sources, we find that all lie withim the specified tolerance for siae (diameter = 3.74 & 0.10 cm) but that many are appreciably lighter than the weight specification (2.46 + 0.06 g). Suitable springs are obtainable from: Thermal Syndicate Limited. Post Office Box 6. WaUsend. Northumberland. Enelend: or worden Laboratories, ~ncorpor&ed,695 Rocky ~ k e kosd; r Houston 27, Texas.
. ."
400 of H.,
-
GOO
800
Data polnl* for flve gases.
Figure 2 illustrates the principle of comparing slopes by showing data obtained with nitrogen, oxygen, carbon dioxide, and two commercially-available4gaseous alkyl halides: dicNorodiuoromethane and 1 :2 dichlorotetrafluoroethane. The slopes of the statistically determined best straight lines for these five gases are in the ratios Nz:Oz:COz:CF~C12:C2F4CIs = 1.0000:1.1426:1.5823:4.460:6.557 which are to be compared with the molecular weight ratios
'As "Arcton 12" and "Arcton 114" respectively from Imperial Chemical Industries Limited. Also as "Freon-12" and "Freon-114" from the Matheson Company, Incorporated. These and similar gases are marketed in a high state of purity, primarily as refrigerants and aerosol propellants. Volume 42, Number 12, December 1965
/
665
However, when corrected for gas imperfections5as explained below, the slope ratios become
becomes modified to
Nz:O2:CO1:CRCln:C1F,Cl1 = 1.0000:1.1421:1.571:4.36:6.12
in excellent agreement with the molecular weights. Gas Imperfections
The points in Figure 2 for each of the two alkyl halides show a very slight but decided curvature. Its magnitude and direction are what would be expected from nonideality in these gases. At pressures less than or not greatly exceeding atmospheric, the density of even the most imperfect of gases is accurately given by M P (1 - BP)/RT where 6, a second virial coefficient, is a constant for any one gas a t constant temperature. This virial coefficient usually has a small negative value (e.g. - 1.9 X 10WS atm-1 for methane at 20°C), but takes larger negative values for gases near their boiling points. Taking imperfections into account, equation (4)
T h e following values of the second virial coefficients were used in these corrections: nitrogen, -0.0003 atm-1; oxygen, -0.0007 atm-I; carbon dioxide, -0.006 atm-I; dichlom difluoromethane, -0.02 atm-1; dichlorotetratluoroethane, -0.06 atm-'. The first three of these values are available from the literature, the last two were calculated by the principle of corresponding states [see Reu. Pure A p p l . Chem., 3, 1 (1953)l using published values (from "Arcton Refrigerants," Imperial Chemical Industries, London S.W. 1) of the critical coonstants for these gases.
666
/
Journal o f Chemiccrl Education
showing that for real gases a B versus P graph is a shallow parabola as in Figure 2. The gradient of the straight line giving the best least-square fit to the parabola is ZM[1 B(P1 Pz)],where PI and P, are respectively the smallest and largest pressure attained in the experiment. Thus with 181 < atm-', PI 0 and Pp = 1 atm, an M calculated from the best straight line will be in error by less than l%, though with a second virial coefficient of larger magnitude a more serious error in molecular weight will result. If B is known, a correction is readily made; otherwise, the limiting gradient should be measured as P approaches zero.
-
+
+
Effect of Adsorption
With condensible gases, adsorption upon the walls of the table tennis ball, thereby increasing its mass, could cause spurious effects interfering with buoyancy measurements. A simple calculation shows that the adsorbed layer would need to be of considerably more than monolayer thickness to be detectable in our apparatus. An experiment in which no change in spring length could be detected on prolonged exposure of a punctured baU to an atmospheric pressure of dichlorotetralluoroethane shows no evidence for adsorption of this readily condensible gas.
