Simple Determination of Henry's Law Constant for-carbon Dioxide Jack 6. Levy, Fred M. Homack, and Matthew A. Levy University of North Carolina at Wilmington, Wilmington, NC 28403 With the aid of inexpensive pressure gauges available from automotive supply stores, the solubility of carbon dioxide in carbonated beverages or other solutions can be studied. The procedure provides a new opportunity for "hands on" experience with the concept of gas solubility and can be used as a demonstration or laboratory experiment to enrich formal lecture presentations. For the determination of the Henry's Law constant, a pressure gauge with a full scale reading of 60 psi was outfitted and installed as shown in Figure 1.The gauge has subdivisions of 1 I b h . 2 and can be read to about 0.25 psi. In the range of 10-40 psi, our gauge showed deviations of less than 0.5 psi when checked against a reducing-valve gauge on a gas tank. A critical element is a spout that can be screwed onto a standard beverage bottle. We used a plastic wash bottle top (molded in one piece) with the correct thread size. The curved portion of the spout was removed and a rubber washer, cut from the inner tube of a tire, was installed inside the cap. In lieu of a wash bottle cap of the proper size, the
original beverage-bottle cap can be adapted by means of tubeless-tire valve-stem kit. A center hole must be drilled, and a washer should be placed inside the cap, as indicated in the exploded assembly shown on the left in Figure 2. The heavv rubber tubine must fit tiehtlv. " " .and hose clamos are recommended. Henrv's Law.. the ~rooortionalitv of the equilibrium ores. . sure of a gas to its concentration in solution, is expressed in the form P = KM, where M is the molarity of the dissolved gas. Starting from an initial equilibrium pressure, the basic idea is to vent the carbon dioxide to the atmosphere and then to measure a new equilibrium pressure. By repeating the process, a series of equilibrium pressures is obtained, each one corresponding to a new, lower concentration of Cop in the liquid phase. Conveniently, the gauge is equipped with a pressure release button. Each release of gas momentarily drops the gas pressure to atmospheric pressure. The top of the gauge should be tapped gently with a pencil before each reading. From these data and other parameters, the change in gas solubility a t each stage can be calculated, and the Henry's Law constant becomes accessible as indicated below. T o create the desired gas phase volume, the bottle is inverted over a large graduated beaker, and the cap is opened slightly to remove some of the liquid without admitting air. From a bottle originally containing 946 mL (32 fl oz), an approximate volume of 100 mL is removed. A stirring magnet is added, the gauge assembly is installed, and the bottle is centered on a magnetic stirrer. The pressure release button may be pushed briefly to flush air out of the gauge.
Figure 1. Apparatus for the determination of Henry's Law constant. The push bunon for pressure release is visible an the left side of the gauga.
Figure 2. Left Explodsd valve-stem kit and bottle cap assembly. Right: Alternate appwatus fw the d e t m n a t i m of Henry's Law constam.
260
Journal of Chemical Education
The tendency of carbon dioxide to supersaturate dictates a viaorous aaitation of the solution to achieve eauilihrium. \ve'"sed a s h n g magnetic stirrer and stirring I&. and we chose a soda water l~ottlewith a relativelv tlat hottom. After three or four 10-s agitations over a period of several minutes, a constant pressure was observed. In the absence of equipment that will "churn" the solution, good results can be obtained by vigorously shaking the bottle in a vertical direction for a few seconds. During the course of the experiment, no significant heating effect was noted; the liquid remained near room temperature, as indicated by a thermometer inserted for a final check. At each stage, before venting the system t o the atmosphere, the system should be allowed to stand quietly for a few minutes. Then, the push button is pressed until the gauge reads zero; several seconds are required for complete release and, with supersaturation working now in our favor, only a relatively small amount of solute gas is lost from the solution. Agitation then takes the system from atmospheric pressure to a new equilibrium pressure. The change in pressure reflects the amount of carbon dioxide transferred out of the liquid, and this change happens to be equal to the gauge pressure PD (a differential pressure). Therefore, the number of moles of carbon dioxide lost from the solution at each stage is simply PDVGIRT,where VGis the gas phase volume and R and T have their usual meanings. At the end of the experiment, the temperature T inside the hottle can he verified, and the corrected barometric pressure P g noted. The volume of the gas phase can he measured by carefully filling the bottle to the brim with a 50mL graduated cylinder and keeping track of the amounts added. The valve and cap assembly contributed an additional 2 mL in our case. By emptying the bottle into a 500-mL graduated cylinder, the total capacity and subsequently the volume VL of the liquid phase can be measured to f3 mL. Typical data from an experiment were as follows: T = 295.7 K; Pe = 765 torr or 14.8 psi; VG = 135 mL; VL = 860 mL. Successive gauge readings in psi were 29.0, 24.0, 21.0, 17.0, and 14.5. The analysis proceeds by casting Henry's Law into a form suitable for a least-squares treatment. From P = KM we can write P = K(M - M,) + KM,
where Po is the initial equilibrium pressure. Hence, by plottina messure against the cumulative chanee in molaritv AM. a line of slope K is obtained. A Henry's Law constant of 29.2 is obtained from a leastsquares analysis of the ahove darn, as compared to a literature valueof !X.6at 21.5 "C.' In general, thr vlotsshow good linear correlation with the standard deviation of the slope being about 1 atm/molarity unit. The linearity of the plot may he considered to be a verification of Henry's Law. Recent data on the solubility of carhon dioxide in water and sea water has been reviewed by Weiss? On the basis of this work, the slope of the pressure-molarity curve (or "apparent" Henry's Law constant) a t 5 atm is calculated to he only about 3% higher than the limiting value a t low pressure. Henrv's Law is thus applicable in eood annroximation over .. .. the prensure ranges used in the experiment. Literature values for the constants in molaritv units at 20°C and 25 "Care 25.7 and 29.5, respectively. ~ k c only e about 0.2% of the dissolved COz is hydrated to form carbonic acid, these values closely reflect the solubility of the COZmolecular species. A convenient "one shot" determination of K is possible using thegaugeassembly shoanon the right in pigurL 2. The xaupe has a full scale reading of 15 psi and ran be read to0.1 psi;-a small zero-point correction to the reading may he required. About 400 mL is removed from the bottle of carhonated water as desrrihed ahove to hriny the pressure down to a suitahle level, and \.cry effective shaking he come^ posaible. T o obtain the initial static nressure. a few eood shakes over a 5-min period should he'sufficient. ~ f t l ar smooth pressure release and further aeitatiou. a new eauilihrium pressure is established and the ~ e n r y ' s~ a constant w can he determined from A P = KAM. This one-step method is particularly suited to measurements a t different temperatures where effective magnetic stirring may not be available. The system can he removed from a water bath from time to time and shaken until equilibrium is attained.
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Acknowledgment -
The authors wish to thank Charles R. Ward and James H. Reeves for helpful discussions and technical assistance.
.... '-- 9. F. Mar. Chem. 1974. 2 20%
Volume 64
Number 3
March 1987
261
