Article pubs.acs.org/jchemeduc
A Simple Mercury-Free Laboratory Apparatus To Study the Relationship between Pressure, Volume, and Temperature in a Gas Donna McGregor,* William V. Sweeney, and Pamela Mills Department of Chemistry, Hunter College of the City University of New York, New York, New York 10065, United States ABSTRACT: A simple and inexpensive mercury-free apparatus to measure the change in volume of a gas as a function of pressure at different temperatures is described. The apparatus is simpler than many found in the literature and can be used to study variations in pressure, volume, and temperature.
KEYWORDS: First-Year Undergraduate/General, High School/Introductory Chemistry, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Gases, Laboratory Equipment/Apparatus
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laboratories is generally considered a safety hazard; as of September 2004 (according to the Environmental Conservation law, Article 27, Title 21), the use of elemental mercury is no longer allowed in New York City schools.5,6 Thus it became necessary to seek an alternate experimental apparatus. The Gas Module unit places particular demands on the apparatus. An apparatus was required that can collect Boyle’s law (PV) data at a series of different fixed temperatures. The resultant PV plots must be sufficiently accurate to observe the curvature in a plot of pressure versus volume. The device must be amenable to student-designed protocols used to collect PV data at temperatures above and below room temperature. An appropriate mercury-free experimental approach from the literature was not found that satisfied the criteria. However, numerous experimental methods for the measurement of changes in volumes as a function of pressure (to determine Boyle's law at a fixed temperature) were found; data were collected using cylinders with moving pistons7,8 and syringe pump type devices.9−12 A range of approaches were found for measuring pressure (fixed volume) or volume (fixed pressure) as a function of temperature, including a U-tube apparatus,12 an experimental design consisting of a graduated cylinder inverted in a beaker of water,13 and a commercial device from Vernier.14 None of these designs could be readily adapted to this experiment.
reviously we described an integrated, inquiry-based, classroom and laboratory unit that focused on the physical behavior of gases and the “discovery” of the ideal gas law.1 The unit (called the “Gas Module”) was designed for first-year students and requires an apparatus that can collect both Boyle’s law data and the temperature dependence of the PV data. The original apparatus used a capillary tube that is sealed at one end and contains a fixed volume of air that is trapped beneath a small plug of mercury (Figure 1).1,2
Figure 1. Schematic diagram of the experimental apparatus used in the original model to measure the volume of a gas as a function of pressure. A thick-walled capillary tube, sealed at one end, contained a small volume of mercury over a trapped volume of air. The capillary tube is attached to a half-meter stick with millimeter markings.
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DISCUSSION The redesigned apparatus is composed of two standard 50 mL glass burets whose tips are connected using a 7 foot length of 3/8 in. diameter clear plastic vacuum tubing (Figure 2).
The force that the mercury plug applies on the trapped air column can be changed as the angle of tilt of the capillary tube is varied.1−4 Now, however, the use of mercury in student © 2012 American Chemical Society and Division of Chemical Education, Inc.
Published: January 27, 2012 509
dx.doi.org/10.1021/ed200605v | J. Chem. Educ. 2012, 89, 509−512
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Figure 2. Schematic representation of the experimental apparatus used to measure the volume of a gas as a function of pressure: two standard 50 mL glass burets connected by a fixed length of clear vacuum tubing. A predetermined volume of water is poured into one of the burets and the system allowed to come to equilibrium. The buret on the left is then sealed with a stopper and the buret on the right is allowed to remain open. In this representation the water in the system is at equilibrium and the applied pressure on the air column is due only to the force exerted by the atmospheric pressure.
Figure 3. Schematic representation of the apparatus when there is a positive pressure being applied to the gas in the trapped air column; V represents the volume of the air column, h represents the vertical height difference between the water levels in each buret and Y1 and Y2 represent the vertical heights of each water level relative to a predetermined zero point.
where ρHg and ρH2O are the densities of mercury and water, respectively. The pressure on the trapped air is altered by raising or lowering one of the burets in relation to the other. This causes a change in h and thus the hydrostatic pressure. In the laboratory students record the volume of the trapped air column (V), as well as the vertical heights (Y1 and Y2) of the water levels in each buret relative to a predetermined (and arbitrary) zero point such as the floor or the top of the lab bench (Figure 3). The values for V are read directly from the buret and added to the already measured fixed volume of the buret that is above its graduations. The vertical height difference (h, where h = Y1 − Y2) between the water levels in each buret reflects the hydrostatic force on the trapped air column due to the water column. This force is related to the total pressure of the trapped gas column by eq 3. To obtain a large enough range of data a maximum h value of approximately 130 cm must be reached in both the positive and negative pressure directions. To achieve this, the vacuum tubing must be at least 7 feet long.15 A representative set of data, collected at room temperature, can be seen in Table 1.
To create the trapped air column the burets are attached to a ring stand and placed at equal heights on the laboratory bench. Water, 200 mL, is poured into the top of one of the burets, is allowed to flow through the tubing into the second buret, and is permitted to reach a state of equilibrium between the two vessels. Once the water in the apparatus has stopped moving, a rubber stopper is secured in the top of one of the burets thereby trapping a fixed volume of air in its headspace, while leaving the water in the other buret exposed to the atmosphere (Figure 2). At this point the pressure of the trapped air column is equal to the atmospheric pressure. The pressure of the trapped volume of air can be varied by creating a height differential between the two water levels. With a confined incompressible liquid with unequal levels (Figure 3), Pascal’s principle states that the resulting hydrostatic pressure is given by
PH = ρg Δh
(1)
where PH is the hydrostatic pressure, ρ is the density of the liquid, g the acceleration of gravity, and Δh the difference in height of the two liquid surfaces. When the water is not moving, the pressure exerted on the trapped air, Ptrappedair, by the water must be equal to the sum of the atmospheric pressure, Patm, and the hydrostatic pressure, PH:
Ptrappedair = Patm + PH
Table 1. Representative Set of Height and Volume Data and the Calculated Pressure
(2)
An important consideration is the units of pressure. When PH is expressed in cm of water, its magnitude is then equal simply to h. To convert atmospheric pressure in cm mercury to units of cm water, the relative densities of mercury and water can easily be used,
a
Y2/cma
h/cma
V/mLa
172.2 136.9 0.1 2.1 44.3
43.6 71.1 0.0 63.1 169.4
128.6 65.8 0.1 −61.0 −125.1
28.1 29.6 31.7 33.9 36.5
Ptrappedgas /(cmH2O)b 1168.3 1105.5 1039.8 978.7 914.6
Data collected at room temperature. bData calculated using eq 3.
The plot of pressure versus volume using the data from Table 1 produces a slight, but observable, downward curve (Figure 4). One useful learning objective for students is to understand the functional relationship between variables in a
Ptrappedair(cmH2O) = Patm(cmHg)(ρHg /ρH2O) + h(cmH2O)
Y1/cma
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The PH2O values at a various temperatures can be obtained from tabulated values found in a range of sources, such as the CRC Handbook of Chemistry and Physics.16 It became clear after the first implementation of the apparatus in the laboratory that students with weak laboratory skills are not always careful enough in their technique (with variable temperature data collection) to ensure that the water near the water−gas interface and the trapped gas are both at the same temperature.17 For groups of students of this type, a separate estimation of the water temperature near the interface is required. This is successfully accomplished by providing the students with an inexpensive digital infrared thermometer (Thermapen IR-Mini), with the understanding that students need to take care to hold the device near the desired point of measurement. A diverse number of student-designed protocols have been used to collect PV data at various temperatures, among them the use of cold or hot packs attached to the portion of the buret that houses the trapped air column, ice baths for low temperature data, and hair dryers for high temperature data. In the representative data shown here (Figure 6), a plastic zipper
Figure 4. Representative data correlating the volume (V) of the gas in the air column with the total applied pressure (Ptrappedgas) at room temperature.
linearized plot of data, including the ability to discern the difference between a graph with a slight curvature and one that is linear. Using the above apparatus students are able to observe both the curvature in the PV data and the linearity in the P versus 1/V plot (Figure 5).
Figure 6. Representative data demonstrating the linearity of 1/volume (1/V) of the gas in the air column versus the total applied pressure (Pdryair) at 3 temperature values (5, 26, and 57 °C). The solid lines represent the best linear fits.
Figure 5. Representative data demonstrating the linearity of 1/volume (1/V) of the gas in the air column versus the total applied pressure (Ptrappedgas) at room temperature. The solid line represents the best linear fit.
storage bag filled with ice and water (attached to the portion of the buret that contained the air column) was used to collect cold temperature data (5 °C) and a hairdryer (set on medium heat), positioned to blow hot air into a large plastic bag that covered the entire sealed buret, was used to collect hot temperature data. Because the apparatus is “self-assembled” and pressure is dependent on the number of moles of gas in the air column, any variations in the assembly of the experimental apparatus will result in inconsistent pressure values for the temperature trials. The apparatus thus needs to be reconstructed by the students at the beginning of each lab period to re-collect the room temperature data.18 This is important to ensure that all the temperature dependent data can be accurately compared when combined on a single plot. To determine the functional relationship between pressure, volume, and temperature in kelvins (constant number of moles of trapped gas), students must collapse all their data into a single line by plotting pressure versus temperature/volume.
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TEMPERATURE DEPENDENT MEASUREMENTS From the above data it is clear that the new apparatus satisfies the Boyle’s law criterion, but the apparatus must also be able to acquire useful PV data at a range of temperatures. It is important to realize that the trapped air contains both dry air and water vapor, Ptrappedair = Pdryair + PH20 (4) where PH2O is the vapor pressure of water and Pdryair is the pressure of the dry air in the trapped air column. Because the pressure of the water vapor is temperature dependent, it is important that the pressure of only the dry air be used when comparing PV plots over a range of temperatures. Combining eq 4 with eq 2 gives
Pdryair = Patm + h − PH2O
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A representative graph of the “hybrid variable” (T/V) using the Kelvin temperature scale is shown in Figure 7. Clearly, the
(7) Practical Physics. http://www.practicalphysics.org/go/ Experiment_380.html (8) University of Maryland Lab Experiments. http://www.physics. umd.edu/lecdem/services/demos/demosi3/i3-41.htm (accessed Dec 2011). (9) Science Kit. http://sciencekit.com/low-cost-boyleandrsquo%3Bslaw-apparatus/p/IG0023590/ (accessed Dec 2011). (10) Lewis, D. L. J. Chem. Educ. 1997, 74, 209. (11) Deal, W. J. J. Chem. Educ. 1975, 52, 405. (12) Ivanov, D. T. Phys. Educ. 2007, 42 (2), 193. (13) Kim, M.-H.; Kim, M. S.; Ly, S.-Y. J. Chem. Educ. 2001, 78, 238. (14) Bopegedera, A. M. R. P. J. Chem. Educ. 2007, 84, 465. (15) In order to collect a broad enough range of pressure values and to ensure that students can clearly see the curvature in a pressure versus volume plot, 7 feet of clear plastic vacuum tubing is recommended. The same effect can be achieved with as little as 5 feet of tubing, but the curvature in the pressure versus volume plot becomes difficult to discern when the range of pressure values is limited in this way. (16) CRC Handbook of Chemistry and Physics, 81st ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 2000. (17) In this module students determine their own experimental methods to collect variable temperature data. One of the most common weaknesses observed among students is a failure to obtain a uniform temperature over the entire length of the air column. In addition, it is important that the temperature remains constant while students are collecting their V, Y1 and Y2 measurements. These problems are obviously not observed for room temperature data. (18) Two of the more frequent errors observed are (i) students trap an air column that it too large to accurately collect temperature dependent data (with a column that is larger than about 15 cm it becomes difficult to maintain a fixed and uniform temperature, above or below room temperature, over the entire length of the column) and (ii) students tend to uncork the trapped gas between temperature dependent data sets.
Figure 7. Representative linear data correlating the volume of the gas in the air column with the total applied pressure at 3 temperature values and plotted using the “hybrid variable” temperature/volume. The solid line represents the best linear fit. The values for slope and R2 are those reported by Microsoft Excell.
temperature-dependent data coalesce. A single slope value can be obtained with a coefficient of determination (R2) value close to one. This compares very nicely with data collected using the original apparatus.1
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CONCLUSION As can be seen from the representative data here, this new experimental apparatus allows the successful collection of pressure and volume data (at various temperatures) using a simple and safe (mercury free) experimental setup that yields remarkably good results. The apparatus is of general utility and can be used for many types of gas law experiments. The need for a single, mercury-free apparatus that can be used to collect high quality P, V, and T data places an extra demand on the quality of the apparatusone that was met by this device.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected].
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ACKNOWLEDGMENTS Thank you to Benjamin P. Burton-Pye for his assistance in the first round of data collection and preparation of figures and to the Hunter College head CLT, Nicole Popa, for being so accommodating in the lab.
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REFERENCES
(1) Mills, P. A.; Sweeney, W. V.; Marino, R.; Clarkson, S. J. Chem. Educ. 2000, 77, 1161. (2) Domin, D. J. Chem. Educ. 1999, 76, 543−547. (3) Breck, W. G.; Holmes, F. W. J. Chem. Educ. 1967, 44, 293. (4) Hermens, R. A. J. Chem. Educ. 1983, 60, 764. (5) NYS Dept. of Environmental Conservation. http://www.dec.ny. gov/chemical/285.html (accessed Dec 2011). (6) Justia US Law Mercury. http://law.justia.com/newyork/codes/ environmental-conservation/env027-2107_27-2107.html (accessed Dec 2011). 512
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