A LABORATORY EXPERIMENT TO ILLUSTRATE DEVIATION FROM IDEAL GAS LAWS HERMAN B. WAGNER Loyola College, Baltimore, Maryland
IT
HAS been noted that, while deviations from the ideal gas laws receive quite adequate lecture attention in the usual undergraduate course in physical chemistry, experimental difficulties usually prohibit their laboratory demonstration. A simple and easily managed method is described here which serves as a demonstration of nonideal gaseous behavior and supplies reasonably accurate data for the calculation of the equation of state. In the procedure which is given below the only apparatus required is: (a) a small commercially available steel gas cylinder of the type shorn in Figure 1 (about 14 in. high, 2 in. in diameter, and supplied as shown with the brass fitting, A , for connection to the regular laboratory gas cylinders); (b) a Bourdon gage with high-pressure range to fit into part a of A as shown; (c) a heavy-duty beam balance of sufficient sturdiness to handle weighings of the order of 1000 to 1500 g., which need be sensitive at this load only to differences of f0.2 g.; (d) a constant-temperature (f0.5"C.) w?tt.er bath about 12 in. deep t o accommodate the above cylinder. The procedure in determining a particular gaseous isotherm is as follows. (1) The small steel cylinder is filled to some relatively high pressure (700 to 1500 p.s.i.) with the gas to be used. (2) The cylinder is then weighed to the nearest 0.2 g. and then immersed to its neck in the constant-temperature bath. (3) After five to ten minutes, which will usually sufficeto bring temperature equilibrium in experiments conducted near room temperature, the gage is fitted to the cylinder while the latter is still immersed in the bath, and a readmg of pressure (&lo p.s.i.) is made. (4) The cylinder is then removed from the bath, dried thoroughly with a towel, the gage removed, and a weighing made to check the original weighing. (5) While the cylinder is still resting on the balance pan the valve is opened slightly and gas allowed to escape until the weight of the cylinder is observed to diminish by some predetermined value, perhaps 5 to 10 g. The valve is then closed and an accurate weighing made. (6) The cylinder is once more immersed in the bath and the cycle repeated until in this way a series of weighings with corresponding pressures dourn to atmospheric is obtained. Typical data, obtained with carbon dioxide a t 23 & 0.5"C., are given below.
fits largo cylinder
i
1
Om containing Cylinder
The volume occupied by the carbon dioxide in the cylinder was most conveniently determined by noting the rise in water level in a large glass graduated cylinder when the steel cylinder was entirely immersed, this giving the outside volume of the cylinder. From this was subtracted the volume of the steel cylinder walls, as evaluated from the weight of the empty cylinder and the density of steel. It is'to be noted that the pressure, in atmospheres,
278
MAY, 1949 TABLE 1 Weight of Gage pressu?e, Gage pressure, Weight of eylindev g. p.s.z. atm. gage eylinde~ -Wt. (10). 0.
(valve open) Inner Volume of Cylinder: 400
+
3 ml.
%
to be substituted in the expression PV/nRT in evaluating this quantity must be the Bourdon gage pressure plus 1 . Further, in determining the total weight of carbon dioxide in the tank in any instance there must be added to the quantity tabulated in the last column of Table 1 the weight of carbon dioxide gas contained in the cylinder at zero gage pressure (ie., a t 1 atmosphere responding to the lower pressures are somewhat off the absolute pressure). At this pressure the ideal gas laws broken line curve. These erron seem to be quite ranmay be employed in calculating this weight as follows: dom, however, and the mean curve through these falls near to that of Michels. PVM ( 1 atm.) (400 ml.) (44) = g, 1" = -= By estimating the slope of the curve in the low presRT (82 atm. ml. (296 OK.) sure region it is possible to evaluate the constant in the g. mol. "K. ~ linear linear equation of state for this i s ~ t h e r m . The When these two corrections were applied to the data equation of state, which is applicable only to the left of Table 1 the values tabulated below were obtained. hand portion of the curve, is:
)
TABLE 2 Total weight of Total g. mol. of Absolute pwsCOXin cylinder, CO? in cylinder sure atm.
p y
As a test of the general correctness of these values the isotherm PV/nRT versus P was plotted as shown below (Figure 2, heavy line). This was compared with the same isotherm plotted from calculations based on the work of Michels, Michels, and Woutersl (Figure 2, broken line). I t is seen that the values obtained corresponding t o the relatively high pressures in the demonstration method fall very nearly on the curve of Michels. At lower pressures the errors in weighing, and in particular in readings of the pressure gage, represent a greater percentage of the total weight or pressure read, and for this reason the demonstration points cor-
The value of the constant fl thus graphically evaluated is -0.0052. The accepted value is -0.0051. I t was found that in conducting this experiment the five- or ten-minute intervals allowed for temperature equilibrium t o be attained provided an excellent opportunity for the instructor to discuss with the students the underlying theory of the experiment, corrections to be applied, sources of error and their magnitude, etc. During the course of the experiment it is of course impossible to draw the full curve of Figure 2. It is possible, however, with the first data obtained in the demonstration, to show that the gas is not behaving ideally. This may be done as follows, using the data from items 2 and 3, Table 2, for illustration: If the ideal gas laws were being obeyed, then P = n R T / V . Since in this experiment T and V are constant, we may rewrite this equation as P = Kn, where the constant K = R T / V . From this it would follow that we should have p = Kn. From item (2), Table 2, K = P / n = 59.5/1.74 = 34.2. From item (3) it is found that K = P / n = 53.7/1.42 = 37.8. The fact that K is not constant shows that the gas laws are not being obeyed in this pressure range.
1 M I C H E L SMICHELS, , A N D WOUTERS, PTOC. Ray. Soc. (Ladon) A153, 201 (1935).
a E ~ ~ AmN Dn ROLLEFSON, ~ ~ "Physical Chemistry," Graw-Hill Book Co., New York, 1947, p. 70.
n
nRT
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