1595
Anal. Chem. 1986, 58, 1595-1596
in tandem with significant figure code. Significant figure code has the potential to improve the written and electronic communication of tables of measurement data among scientists and engineers-especially across disciplinary boundaries.
APPENDIX Thus far we have considered only those uncertainties which stem from random errors of measurement. Rounding error also contributes to the uncertainty. An example of a pure rounding error is that which arises when a is rounded to 3.14159. If we restrict ourselves to a very liberal rounding convention (like f 2 to f20), then this oversight will not cause serious problems. However with the more popular f0.5 to f 5 convention, the rounding error can inflate the uncertainty appreciably. The estimated total uncertainty UTof a reported measurement is calculated as (5)
UT = (Urn2+ R2/3)lI2 where Urnis the estimated measurement uncertainty (which is the standard error of the mean for a large number of measurements) and R is the maximum possible rounding error (f0.5 on the last significant digit). The percent inflation (of uncertainty) is defined as % inflation = 1OO(UT - Urn)/Urn (2) Suppose that the measurement uncertainty on the last reported digit of the mean value is k0.5. By eq 1and 2, the inflation would be approximately 15%; i.e., the total estimated uncertainty would be 15% more than the estimated measurement uncertainty. Therein lies the ambiguity of the popular k0.5 to k 5 rounding convention. Is the reported uncertainty just a measurement uncertainty, or is it the total uncertainty? With
the f0.5 to f 5 convention, there can be an appreciable discrepancy between the two. With the f 2 to f20 rounding convention, the maximum inflation is just over 1%; the measurement uncertainty is essentially the same as the total uncertainty. Tables IV and V illustrate the ambiguities of the f0.5 to f 5 rounding convention vis-a-vis significant figure code. Table IV shows the relationship between the estimated measurement uncertainty and uncertainty code for the f0.5 to f 5 rounding convention. Table V is for the estimated total uncertainty. In Tables IV and V, note the large discrepancies between the estimated measurement uncertainty and the estimated total uncertainty in the lower uncertainty codes. If one formats data, using significant figure code in conjunction with the f0.5 to f 5 rounding convention, then one must also be explicit about what kind of uncertaintymeasurement uncertainty or total uncertainty-is contained within the SFC numbers. (We recommend using measurement uncertainty, since the absolute limits (6) for the uncertainty codes can be expressed compactly, as in Tables I and IV.) This distinction is not crucial for the f 2 to *20 rounding convention.
LITERATURE CITED (1) Skoog, Douglas A,; West, Donald M. Fundamentals of Analytical (2) (3) (4) (5) (6)
Chemistry, 3rd ed.; Holt, Rlnehart, and Winston: New York, 1976; pp 78-80. Flelds, Lawrence D.; Hawkes, Stephen J. J . Coil. Sci. Teach., in press. Natrella, Mary G. Experimental Statistics: National Bureau of Standards Handbook 91; US. Government Printing Office: Washington, DC, 1966; pp 2-12. Fields, Lawrence D. M.S. Thesis, Oregon State University, 1985. Sheppard, W. F. Proc. LondonMathematicalSoc. 1898, 29, 11, 369. ASTM E29-67, 1980.
RECEIVED for review December 19,1985. Accepted February 18, 1986.
Vortex Cooling for Subambient Temperature Gas Chromatography Thomas J. Bruno Thermophysics Division, National Bureau of Standards, Boulder, Colorado 80303 Subambient temperature gas chromatography, which has been used since the mid 1950s, is receiving renewed attention because of the advantages it provides in the analysis of very volatile species. Much of this interest stems from the need to determine trace quantities of priority pollutants in air samples. Subambient temperature gas chromatography generally refers to column operation at temperatures between -100 and 0 O C ; however, many separations are greatly enhanced at temperatures no lower than -40 O C (I). In this short ,note, an extremely simple yet very effective approach to subambient column temperature operation is described. Most of the studies done with subambient column temperatures involve the use of liquefied gases (cryogens), such as liquid nitrogen, as the cooling medium (2). Other approaches, such as the use of the Peltier effect or the JouleThompson effect, have received far less attention. In practice, the cryogenic fluid is introduced into the column oven through a microprocessor-controlled solenoid valve. This valve regulates the flow of cryogen into the oven and thus provides some degree of temperature control. There are many disadvantages associated with the use of liquefied gases to produce low temperatures in chromatographic equipment. The large
volumes of coolant typically required necessitate the use of large Dewar containers that are bulky, heavy, and expensive. The low temperature and high vapor pressure of most of the liquid gas cryogens pose potential explosion and burn hazards (3)*
DISCUSSION In the author's laboratory, chromatographic column temperatures as low as -40 O C are obtained routinely using an arrangement based upon the Ranque-Hilsch vortex tube. A detailed discussion of the operation of the vortex tube is provided elsewhere (4); thus only a brief description will be given here. The vortex tube (a commercial unit) is shown schematically in Figure 1. A source of compressed air (at 0.007 MPa, 100 psi pressure, with a flow rate of 0.34-0.42 m3/min, 12-15 standard ft3/min) is applied to the inlet nozzle of the tube, whereupon it is discharged tangentially through the tube by the vortex generator (see inset in Figure 1). This discharge will produce a high-frequency air vortex along the inside circumference of the tube, leaving the center of the tube virtually empty. At the end of the tube (left-hand side in Figure l), a needle control valve allows some of the air to
Thls article not subject to U.S.Copyright. Published 1986 by the American Chemlcal Society
1596
Anal. Chem. 1906, 58,1596-1597 VORTEX GENERATOR I
NOZZLE
'
HOT OUTLET
COLD WTLET
VORTEX GENERATION CHAMBER
Figure 1. Schematic drawing of a Ranque-Hlisch vortex tube.
escape (approximately 40430% of the total volume), while the remainder of the air returns through the (previously empty) center of the tube in a counterflowing stream. This counterflowing stream in the center of the tube forms a second vortex having the same angular velocity as the first vortex, traveling in the opposite linear direction. The principle of conservation of angular momentum requires that a particle in a vortex increase its speed as it moves toward the center of the vortex. Since both vortices are locked together at the same angular velocity, the inner stream must lose energy upon its formation. This energy leaves the stream as heat, carried by the fraction of air escaping from the needle control valve. The inner stream must therefore be cooled to compensate for this energy loss. This cooled air will emerge from the cold air outlet on the right-hand side of Figure 1. The air escaping from the hot end of the tube can have a temperature as high as 90 "C, while that escaping from the cold end may be as cool as -40 "C. The actual temperature obtained may be regulated by adjusting the needle control valve at the hot end of the tube. Thus, with most of the air flow escaping from the hot end, minimum temperature is obtained at the cold end. To utilize vortex cooling for subambient chromatographic column operation, the cold end of the vortex tube was fitted with a machined titanium adapter that was then attached to the column oven through an auxiliary port. This allows the
cold air stream to be directed inside the column oven. The low thermal conductivity of titanium ensures that the fitting will cause minimal heat leakage into or out of the oven. The hot air stream, which is set (using the needle control value) to comprise about 40-50% of the total air flow, was allowed to escape into the room. It is not possible to direct the cold stream of the vortex tube into the solenoid valve, which typically accepts the cryogen transfer line on commercial instruments. This is because any interference to the flow of the cold stream of the vortex tube will disrupt the operation of the tube. The equilibration time, which depends on insulation of the oven, is approximately 15 min. The only disadvantage experienced with this approach to cooling was the continuous noise of escaping compressed air (at a leJel of 78 dB). To remedy this problem, the acoustic spectrum was measured with a frequency analyzer. The noise spectrum was found to have two major peaks between 2 and 8 kHz and between 12 and 16 kHz. Subsequent installation of an appropriate baffle muffler to the hot air outlet of the tube and the use of sound-absorbing foam around the tube reduced the noise to an acceptable level of 25 dB. The compressed air supplied to the vortex tube can be taken from the house air supplied in most laboratories. It is important, however, that the air supply be free of moisture and oil vapor. Thus, it is necessary that the vortex tube be preceded with both a particulate filter and a coalescence filter. With these precautions, a vortex tube and ordinary compressed air can be a convenient substitute for many liters of cryogenic fluids.
LITERATURE CITED (1) Bruno, T. J.; Hume, G. L. Int. J . Thermophys., In press. (2) Brettell, T. A.; Grob, R. L. Am. Lab. (Fairfield, Conn.) 1985, 17(10), 19. (3) Zabetakis, M. 0. Safety with Cryogenic Fluids; Plenum: New York, 1987. (4) Aronson, R. B. Mach. D e s . 1978, 4 7 , 6.
RECEIVED for review January 13, 1986. Accepted February 14, 1986. This work was supported by the Gas Research Institute.
Radlometrlc Method for Determining Solubllity of Organic Solvents in Water J. M. Lo,* C. L. Tseng,and J. Y. Yang Institute of Nuclear Science and Nuclear Science & Technology Development Center, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China Cobalt-60 labeled cobalt(II1) pyrrolidinecarbodithioate (eoCo(PDC)3)has a peculiar stability during storage in organic solvent and when its organic solution is shaken with an aqueous solution containing different acids or ions (1-3). Using these characteristics, we have attempted to use 6oCo(PDC)3as a radioagent for determining solubilities of various organic solvents in water. The radioagent was first dissolved in the organic solvent under investigation before pure water was added. The solution mixture was shaken vigorously in order to let the organic phase contact with water sufficiently. Some of the organic solvent would dissolve in water after shaking, resulting in volume reduction of the organic phase. However, the radioagent was found not to accompany the organic solvent molecules going into water; i.e., all the radioactivity of 6oCo(PDC)3would be retained in the organic phase. Solubility of the organic solvent in water therefore can be calculated from the value of the volume change of the organic phase divided by the water volume. Direct mea0003-2700/88/0358-1596$01.50/0
surement of a small change in volume of organic phase with high accuracy is generally very difficult; alternatively, we have measured the specific activities of 6oCo(PDC)3(cpm/mL) in the original and the final organic solutions, and the counting results were used to estimate the decrease in volume of the organic phase. Several commonly used organic solvents were selected to test the applicability of the proposed radiometric method. The solubilities of the organic solvents selected for this study range from very small values (lo4) to relatively large values ( EXPERIMENTAL SECTION The volume of water in our experiments was much greater (at least 100-fold)than that of the organic solvent investigated. Both of the liquids were placed in a 1000-mL separation funnel. 6oCo(PDC)3 was concentrated in the organic solvent at about 1 X IO" M with a specific activity of 10 fiCi/mL. The radioagent was prepared by adding a suprastoichiometric amount of ammonium pyrrolidinecarbodithioate into 6oCo2+(New England 0 1988 American Chemical Society
