In the Laboratory
Determining Atmospheric Pressure with a Eudiometer and Glycerol Jed Brody* and Kate Rohald Department of Physics, Emory University, Atlanta, Georgia 30322, United States *
[email protected] Atasha Sutton Department of Chemistry, Emory University, Atlanta, Georgia 30322, United States
A eudiometer is commonly used to measure gas volumes over a liquid. It is well-known that the height of the liquid column is proportional to the difference between atmospheric pressure and the pressure of the trapped gas. It is therefore also well-known that changes in atmospheric pressure can be detected through changes in the height of the liquid column (1, 2). We demonstrate, perhaps for the first time, that absolute atmospheric pressure can be determined simply by moving the eudiometer up and down to vary the height of the liquid column. The analysis is simplest when the vapor pressure of the liquid is negligible. For this reason, we choose to use glycerol as our liquid. Suppose that a volume of air, V, is trapped in a eudiometer containing glycerol, as shown in Figure 1. The pressure of the trapped air, P, and the height of the glycerol column, h, are related to atmospheric pressure, Patm, according to P ¼ Patm - Fgh where F is the density of the glycerol and g is the gravitational acceleration (2). Assuming constant temperature, we can use Boyle's law. The product of P and V is constant, so that PV ¼ Patm V0
Figure 1. Air trapped above the glycerol column in a eudiometer.
where V0 is the volume of the trapped air when P = Patm and h = 0. We can combine the equations to eliminate P and solve for V: V ¼ V0
Patm V0 ¼ Fgh Patm - Fgh 1Patm
Procedure
The term Fgh/Patm is roughly h/(800 cm), which is very small. We can thus use the Taylor series expansion 1/(1 - x) ≈ 1 þ x, for x , 1. The Taylor series expansion in this case is also a binomial expansion (3). Alternatively, we can remind students of the geometric series 1 þ x þ x2 þ x3 þ ... = 1/(1 - x); we can neglect all but the first two terms when x , 1. Applying this approximation, we find V ¼ V0 þ V 0
series. The objective of the experiment is for students to gain confidence in their ability to combine familiar facts in an unfamiliar way.
Fgh Patm
We filled a 1 L graduated cylinder with glycerol. We next filled a 50 mL eudiometer about halfway with glycerol and inverted it into the graduated cylinder. We waited for the glycerol to settle before taking the first measurement. We recorded h and V for four different elevations of the eudiometer relative to the graduated cylinder. We repeated the entire procedure for two other initial volumes of trapped air. For comparison with our results, we recorded the pressure indicated by a commercial barometer. Room temperature was 21.8 °C. Hazards
If we vary h by moving the eudiometer up and down, we can plot V as a function of h. The V intercept gives V0, and Patm is found by multiplying the reciprocal of the slope by V0Fg. It is worth emphasizing to students that they can derive this result from three simple formulas: the basic description of a hydrostatic balance, Boyle's law, and an approximation to the geometric
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Glycerol is nontoxic, even edible. However, it is extremely slippery. Care should be taken to immediately wipe up spills. Results and Analysis Results are shown in Figure 2. All three data sets are remarkably linear. Using Patm = V0Fg/slope, derived above, we find
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r 2010 American Chemical Society and Division of Chemical Education, Inc. pubs.acs.org/jchemeduc Vol. 87 No. 12 December 2010 10.1021/ed900006m Published on Web 09/27/2010
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In the Laboratory
settle before taking each measurement. Also, the assumption of isothermal conditions may be only approximately valid. Conclusions We have shown how to determine atmospheric pressure using a eudiometer and glycerol. This is a quick and fun exercise that allows introductory students to use a familiar instrument in a novel way. Students may be asked to speculate as to how other familiar instruments could find new and surprising applications. Literature Cited
Figure 2. Measured results and linear fits. Negative h occurs when the top of the glycerol column in the eudiometer is below the glycerol level in the graduated cylinder.
Patm = 101 kPa from the top data set, Patm = 88.4 kPa from the middle data set, and Patm = 92.6 kPa from the bottom data set. The average of these three results is 94.0 kPa, which is within 6% of the barometric reading of 99.1 kPa. Some of the error may result from failure to wait sufficiently long for the glycerol to
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1. Barometer, Wikipedia, the free encyclopedia Web Page. http://en. wikipedia.org/wiki/Barometer#Water-based_barometers (accessed Aug 2010). 2. Serway, R. Physics for Scientists & Engineers, 3rd ed.; Saunders College Publishing: Philadelphia, PA, 1990; p 399. 3. CRC Handbook of Chemistry and Physics, 75th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FA, 1995; pp A-84, A-85.
Supporting Information Available Student handout; instructor notes. This material is available via the Internet at http://pubs.acs.org.
pubs.acs.org/jchemeduc
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r 2010 American Chemical Society and Division of Chemical Education, Inc.
