Chemistry Everyday for Everyone
A Simple Boyle’s Law Experiment Don L. Lewis Bee County College, 3800 Charco Road, Beeville, TX 78102
The volume of a fixed mass of a confined gas maintained at a fixed temperature is inversely proportional to the pressure of gas. This relationship is usually called Boyle’s law after Robert Boyle (1627–1691), a contemporary of Isaac Newton (1642–1727). There are commercially available devices that can be used to demonstrate Boyle’s Law. However, the relatively expensive commercial apparatus thoroughly obscures the notion of pressure as a force per unit area by using a direct-reading pressure gauge. The experiment described in this article provides pressure measurements in a familiar unit (lb/in2) and makes no assumptions concerning atmospheric pressure. Indeed, one outcome of the experiment is an estimate of initial pressure of the gas sample arrived at by a means analogous to the method of standard additions as used in analytical chemistry.
because one does not want measurements of rubber compressibility. Apply sufficient force to reduce the gas volume to 50 mL and maintain the force for about 30 s before recording the force indicated by the scale. Repeat the process, recording the applied force at 5-mL intervals to a minimum compressed volume of 15 mL. Discussion The cross sectional area of the syringe plunger (Ax) can be calculated either by measuring the diameter of the syringe piston or by measuring the distance between the 0- and 60-mL calibration marks on the syringe barrel and dividing the volume by the measured distance. ∆P, the increase in pressure accomplished by the force applied to the plunger, is given by eq 1. ∆P = F/Ax
Experimental Procedure One item of special equipment used in the experiment (bathroom scales) can usually be borrowed from students or colleagues, and the other item (60-mL syringe) can be purchased at agricultural supply stores for less than two dollars. A small amount of castor oil, a high viscosity oil, should be applied to the piston portion of the syringe. Adjust the piston in the 60-mL syringe to its maximum volume position (about 65 mL). To close the delivery orifice of the 60-mL syringe, purchase a disposable 3-mL 23G1 syringe and needle, clip the needle to a length of about 3 mm, and unscrew the needle from the syringe. Apply enough modeling clay to almost fill the needle socket and reattach the syringe needle to the 60-mL syringe. Reshield the shortened needle and use pliers to insure the needle is securely locked. Move the syringe piston, alternately compressing and expanding the gas, until a good seal has been achieved. Of course, one could epoxy seal the 60-mL syringe orifice but the modeling clay procedure has the advantage that one can easily unseal the syringe either to change the gas or to readjust the piston position. Position the syringe on the bathroom scale as shown in Figure 1. The wooden block shown in the diagram has a 7/8-in. diameter hole in which the shielded needle is protected. One should Figure 1. Syringe and not use a laboratory rubber stopscale configuration. per in place of the wood block
(1)
P, the total pressure of the gas in the syringe, is the sum of the added pressure, ∆P, and the initial pressure of the gas in the syringe when no force is applied to the plunger, P0. P = P0 + ∆P
(2)
The graph of ∆P as a function of V{1 is a straight line. The spreadsheet program (Lotus 123R5) contains a linear regression option that can be used to calculate the empirical constants a and b of eq 3. The constant b is the value of P0. For the data displayed in Figure 2, P0 = 14.2 lb/in2. ∆P = aV{1 – b
(3)
As a consequence of eq 2 and since P0 has been evalu-
Figure 2. Volume as a function of pressure.
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Chemistry Everyday for Everyone
ated, the pressure–volume relationship can be stated in the form given by eq 4. PV = a
(4)
The spreadsheet program constructs a graph that displays the volume as a function of pressure (Fig. 2). The program automatically produces an average for the PiVi values and calculates an uncertainty in the constant a, expressed as a population standard deviation and as a percent. One might anticipate that the crude means of measuring the applied force and the frictional forces operating on the piston would render the measurements meaningless. Surprisingly, the vast majority of studentconducted experiments show an uncertainty in the con-
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stant a of less than 8%. The relatively small error can be explained by considering two factors: an economy of scale and the means whereby a value for P0 was assigned. Frictional forces are usually related to forces normal to the contact surfaces and are only weak functions of contact area. The experiment as described can be thought to keep the normal force on the contact surfaces relatively constant and the applied forces are large—a robust student may be able to apply an 80-lb force! Not only are frictional forces small compared to the applied compression force but also the value for P0 is chosen in a manner that includes the frictional force initially operative. Thus, the frictional forces that contribute to the applied force in maintaining a reduced volume are included in the expression for P (eq 2).
Journal of Chemical Education • Vol. 74 No. 2 February 1997
