0.13 Physical properties of gases  (Page 2/8)

Pressure is measured in a variety of ways using a variety of units. One simple unit is the “atmosphere” (atm), where 1 atm is approximately the pressure exerted by the gases in the atmosphere at sea level. Another unit is “torr,” which is equal to 1/760 of 1atm. The torr was defined by the height of a column of mercury in millimeters. Since 1 atm pressure can support a column of mercury 760 mm high, then 1 torr supports a column of mercury 1 mm high. Consequently, pressure is often measured in “mm Hg.” The standard unit of pressure is the “Pascal” (Pa), technically defined as 1 Newton per square meter. For our purposes, we only need to know that 1 atm = 760 torr = 101,325 Pa.

To observe the pressure-volume relationship for gases, we trap a small quantity of air in a syringe (a piston inside a cylinder) connected to a pressure gauge, and we measure both the volume of air trapped inside the syringe and the pressure reading on the gauge.

In one such sample measurement, we might find that the volume of gas trapped inside the syringe is 29.0 mL at atmospheric pressure (760 torr). If we then compress the syringe slightly, the volume becomes smaller, now 23.0 mL. We feel the increased spring of the air resisting this compression, and this is registered on the gauge as an increase in pressure to 960 torr. It is simple to make many measurements in this manner. A sample set of data appears in Table 1. We note that, in agreement with our experience with gases, the pressure increases as the volume decreases. These data are plotted in Figure 1, and the graph shows that as volume increases, pressure decreases. Notice also that the graph is not a straight line. A change of 6 mL of volume produces a 200 torr change in the pressure from 760 torr to 960 torr. However, a change of only 4 mL of volume is needed to produce another 200 torr change in the pressure from 960 torr to 1160 torr. Equal changes in pressure do not arise from equal changes in volume, and equal changes in volume do not produce equal changes in pressure.

Since the relationship between pressure changes and volume changes does not appear to be simple, we should ask whether there is a quantitative relationship between the pressure and volume measurements. One way that we can try to explore this possibility is to try to plot the data in such a way that the quantity on the x-axis increases so does the quantity on the y-axis. Since pressure decreases when the volume increases, the inverse of the pressure (1/P) will increase when the volume increases. In Table 2 and Figure 2, we calculate and plot 1/P for each of the volumes in Table 1.

Notice also that, with elegant simplicity, the data points form a straight line. Furthermore, the straight line seems to connect to the origin (0,0). If we were to write the equation for this straight line with its y-intercept as zero and its slope as k, the equation relating pressure and volume is: