In the Laboratory
Using Dalton’s Law of Partial Pressures To Determine the Vapor Pressure of a Volatile Liquid
W
Fred R. Hilgeman* Department of Chemistry, Southwestern University, Georgetown, TX 78626; *
[email protected] Gary Bertrand Department of Chemistry, University of Missouri–Rolla, Rolla, MO 65409-0010 Brent Wilson Department of Chemistry, Southwestern University, Georgetown, TX 78626
All liquids have a characteristic vapor pressure, which is the pressure exerted by a vapor in equilibrium with its liquid at a given temperature. Vapor pressures of volatile liquids are typically measured in chemistry laboratory experiments. In general chemistry, the techniques involve measurement of a trapped quantity of gas at different temperatures (1). Often in an undergraduate physical chemistry laboratory class, students use a more sophisticated closed system to observe a pressure–temperature relationship for the liquid (2). Presented here is a simple experiment appropriate for a general chemistry laboratory that uses Dalton’s law of partial pressures to measure the vapor pressure of a volatile liquid. A predetermined volume of air is injected into a closed-end tube filled with the liquid to be measured. The volume of liquid displaced will be greater than the volume of air injected because of the vapor pressure of the liquid. Using Dalton’s law of partial pressures, the sum of the partial pressure of the liquid and of the air is directly related to the final volume, allowing the calculation of the vapor pressure of the liquid in the tube. Procedure An inexpensive 10-mL plastic syringe is attached to one end of a Tygon tube. The other end of the Tygon tube is attached to a copper or glass tube bent in a U shape, the end of which will fit easily into the end of a modified buret.1 The syringe is then calibrated by filling it with water at a known temperature and determining the mass of the water delivered by the syringe. The modified buret is also calibrated with water. A small glass container (a 75-mL crystallizing dish works well) is half filled with acetone, or other liquid to be measured. The calibrated buret is filled completely with acetone and, using a latex glove, the filled tube is inverted and immersed into the dish of acetone such that no air bubbles are allowed to enter the tube. The dry syringe and associated tubing are filled with dry air, and a 10-mL volume of air (Vinjected) is injected into the inverted buret. This is accomplished by placing the U tube into the dish of acetone and into the buret. As the air is slowly injected into the buret, it will displace the acetone. The syringe tubing is then removed and once equilibrium is achieved, in about 15 minutes, the volume of the trapped air (Vobserved) is measured. Because the height of the liquid in the buret is different from the height of the liquid in the dish, a correction for that difference in height must be made by
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carefully measuring this height difference (h) in millimeters. The temperature of the liquid in the dish must also be measured because the vapor pressure of liquid varies significantly with temperature. Calculations According to Dalton’s law of partial pressures, the pressure in the tube is the sum of the partial pressures of air and the vapor of the liquid: Pinside = Pliquid + Pair
(1)
The difference in levels of the acetone inside and outside the buret results in a pressure inside the tube other than atmospheric pressure. To account for this, the pressure inside the tube must be corrected for the difference in levels (h) of the acetone inside and outside of the tube. Using the observed barometric pressure in mm Hg, Patmospheric, the difference in acetone heights, h, and the appropriate densities, the pressure of the gas inside the tube Pinside can be calculated using eq 2: Pinside = Patmospheric − h
density liquid densitymercury
(2)
Under these conditions, the gases involved can be assumed to behave ideally and the partial pressure of the air in the buret, Pair, can be described by:
Pair = Pinside
Vinjected
(3)
V observed
Substituting eq 3 into eq 1 and solving for Pliquid,
(
Pliquid = Pinside 1 −
Vinjected V observed
)
(4)
This is the reported vapor pressure of acetone in mm Hg. Data Treatment and Results The following data were collected from a typical student measuring the vapor pressure of acetone: For a lab temperature of 19 ⬚C, density of acetone is 0.79 g兾cm3, density of mercury is 13.59 g兾cm3 (all relevant data are taken from ref 3 ), Patm is 743 mm Hg, h is 50.0 mm, Vinjected is 10.0 cm3, and Vobserved is 12.7 cm3.
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Journal of Chemical Education
469
In the Laboratory
The calculations show Pinside = 743.0 mm Hg − 50.0 mm acetone
0.79
mm Hg
13.6 mm acetone
= 740 mm Hg
Pacetone = 740 mm Hg 1 −
10.0 cm 3 12.7 cm 3
= 157 mm Hg
At this temperature, acetone has a vapor pressure of 166 mm Hg for a 5.4% error. Because the change in vapor pressure with temperature for acetone is significant, a class average for vapor pressure is not a reasonable test of the reproducibility of the experiment. However, on average the percent error of our classes is between 3 and 8 percent, with most values being below the accepted value. Discussion and Conclusions The error in the vapor pressure, Pacetone, is directly related to the error in Vobserved.2 An error of approximately 0.5 mL will result in an error of approximately 20 mm Hg. This crucial final volume must be taken with care and sufficient time must be allowed for equilibrium to be achieved. The error in measurement of the height (h) is insignificant. An error in h of as large as ± 5 mm causes an error of only ± 0.2 mm Hg in Pinside. Some students noted that evaporative cooling resulted in the container of acetone sweating significantly, lowering the temperature of the acetone. This can also cause condensation of water into the acetone, lowering the final vapor pressure of the solution. There was also a concern that the solubility of air in the acetone might introduce an error. Results showed no difference between acetone that had dry air bubbled through it for 30 minutes and acetone used without the air bubble treatment. The vapor pressures for other liquids were measured, but for several reasons, acetone seems to be the best liquid for a general chemistry lab. Acetone is an inexpensive solvent, is reasonably safe and non toxic, and has a high vapor pressure. The vapor pressure for the liquids pentane, hexane, heptane, benzene, ethyl acetate, methanol, ethanol, and propanol are all measurable with this technique. However, these liq-
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uids all have either safety issues (they must be measured in a hood because they may be flammable or toxic), are more expensive, or are much less volatile so errors are significant. For students who are in an accelerated chemistry class, binary liquids can be studied measuring their vapor pressure versus mole fraction. The results for the acetone兾hexane system illustrate the nonideality of this binary liquid mixture showing clearly the change in vapor pressure with mole fraction. Hazards There are no chemical hazards associated with this experiment as long as the laboratory is well vented. Acetone is, however, flammable and caution must be taken to be sure there are no flames in the area. It is also harmful if swallowed or inhaled and causes irritation to skin, eyes, and respiratory tract. Gloves should be worn when inverting the tube in the dish of acetone. Acknowledgments We are indebted to the Robert A. Welch Foundation (grant no. AF 0005) for their support of this project and to the Southwestern University students who were involved in developing this experiment. W
Supplemental Material
Detailed instructions for the students are available in this issue of JCE Online. Notes 1. A broken buret that has been sealed off with a volume of between 12 and 15 mL works well for this purpose. Sealing the broken buret will cause the volume of the sealed portion be unmeasurable, thus requiring calibration. 2. The method of propagation of errors was used.
Literature Cited 1. Hunt, H. R.; Block, T. F.; McKelvy, G. M. Laboratory Experiments for General Chemistry, 4th ed.; Brooks/Cole-Thomson Learning: Pacific Grove, CA, 2002. 2. Garland, C. W.; Nibler, J. W.; Shoemaker, D. P. Experiments in Physical Chemistry, 7th Ed.; McGraw-Hill: New York, 2003 3. Handbook of Chemistry and Physics; Weast, R. C., Ed.; The Chemical Rubber Publishing Company: Cleveland, OH, 2001.
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