When arbitrary ethylene glycol line separations at the low, middle, and high temperature ranges were substituted in the four equations, the results in Table I were obtained. It is evident that at higher temperatures major differences occur and variations as large as 4 ‘C were observed among the different methods. These differences are rather significant since in the literature Equations 2, 3, and 4 have all been used to a certain extent in the calculation of kinetic parameters, and these differences may show up as systematic errors in the rate parameters. A sample calculation based on the literature values for the internal rotation of N,N-dimethylformamide is given in Table 11. The deviations, though not grotesque, are large enough to be annoying, In view of the painstaking experimental and computational work needed to derive accurate rate data, such obvious systematic errors are certainly unwarranted, and should be minimized, especially in regard to accurate temperature measurements. This, no doubt, may be accom-
plished if NMR kinetic measurements are performed in coaxial tubes with a calibrated temperature standard in the outer jacket. LITERATURE CITED (1) A. Allerhand. H. S. Gutowsky, J. Jonas, and R. A. Meinzer, J. Am. Chern. SOC., 88, 3185 (1966). (2) R. Duerst and A. Merbach, Rev. Sa‘.lnstrum., 38, 1896 (1965). (3) A. L. Van Geet, Anal. Chem., 40, 2227 (1966): Professor Van Geet has informed us that he has further refined his published equation, giving a result with which our data agree even more closely. His most recent results ( T OC = -1.705 Au 193.2) were presented at the Tenth Experimental NMR Conference, Mellon Institute, Pittsburgh, Pa., February 1969. (4) A. L. Van Geet, Rev. Sci. lnstrum., 40, 1914 (1968). (5) A. L. Van Geet, Anal. Chem., 42, 679 (1970). (6) 0. Yamamoto and M. Yanagisawa, Anal. Chem., 42, 1483 (1970). (7) Varian Associates, Palo Alto, Calif. 94303, Publication No. 87-202-006. (8) R. C . Neuman and V. Jonas, J. Am. Chem. Soc.,90, 1970 (1968). (9) M. Rabinovitz and A. Pines, J. Am. Chern. SOC.,91, 1588 (1969).
+
RECEIVEDfor review March 26, 1975. Accepted May 15, 1975.
Diffusion Cell for the Preparation of Dilute Vapor Concentrations Antonio H. Miguel and David F. S. Natusch School of Chemical Sciences, University of Illinois, Urbana, Ill. 6 180 1
One of the more difficult problems associated with analytical investigations of air pollutants involves the generation of known constant concentrations of gases and vapors. Most commonly such standard concentrations are required for calibrating instruments which operate in the parts-permillion (pprn) range, for use in diagnostic studies of analytical methodology, or for providing a constant source for experimental investigations of control processes ( I , 2). In all cases, it is desirable to have a continuously flowing gas stream in order to minimize errors due to adsorption on glassware and to provide large quantities of the gas mixture (3,4 ) . Permeation devices offer a simple method of preparing low concentrations of gaseous materials in the range of 0.001 to 100 ppm, depending on the thickness of the walls, the length and temperature of the tube, and the flow rate of the diluent gas ( 5 ) .A variety of gases, liquids, and solids have been permeated through Teflon, PTFE, and F E P to produce low concentrations of these materials in air or other gases (6-11). A dynamic dilution device which can be used for the production of gases in the 10- to 1000-ppm range has been described by Axelrod et al. (12). The simplest procedure for generating standard vapor concentrations is based on achieving either saturation conditions or a known rate of vapor diffusion into a diluent gas stream. Several devices based on these principles have been described in the literature (13-16) and their operating characteristics have been presented in a comprehensive article by Altshuller and Cohen ( 17). In this paper, we describe the construction, operation, and evaluation of a simple diffusion cell which can be used to obtain large amounts of a standard vapor ranging in concentration from a few ppm to several thousand ppm. Its main advantages over comparable devices are improved flow geometry which allows very precise calculations of experimental diffusion rates from theoretical diffusion coefficients, ease of operation over a wide range of concentrations, and the ability to maintain constant vapor concentrations over prolonged operating periods.
EXPERIMENTAL Apparatus. The diffusion cell (Figure 1) was constructed from Pyrex tubing, 8.0 cm long and 3-cm 0.d. The diffusion tube, D, which contains the liquid sample, was made from Kimax tubing, 8.0 cm long and 1.1-cm i.d. The diffusion tube holder, E, is an internally threaded glass connector (Ace Glass Catalog No. 7644-15) with a Teflon bushing and “0” ring (Ace Glass Catalog No. 750627). The diluent gas enters the cell via tube A . Its flow through the diffusion cell is controlled by a 4-mm Teflon valve, E , and is delivered t o the cell chamber, C, through a capillary, F , which is 2 cm long and 1.0-mm i.d. The diluent gas flow rate is monitored by a calibrated flow meter (Brooks Instrument Division No. R-2-15-B) situated between the Teflon valve, B, and the diluent gas supply. The standard vapor mixture leaves the cell through tube H, and can be sampled for analysis through a septum sealing tube, G. Where very low vapor concentrations are required, secondary dilution can be employed by introducing the gas mixture from tube H, into a second diluent gas stream. The whole device is enclosed in an insulated box equipped with an air circulating fan and a 100-watt lamp which is operated by a proportional heater controller (Texas Instruments, Inc. Bulletin No. DL-S 7211595, May 1974). This controller is capable of maintaining the cell temperature constant within f0.5 “C (long term). The temperature can be maintained to within fO.10 “C (short
Figure 1. T h e diffusion cell ( A ) Diluent gas inlet, ( B ) diluent flow rate control valve, ( C ) mixing chamber, (D)diffusion tube, ( E ) diffusion tube holder, (4diluent delivery tube, (G)sampling port, (.cl) vapor mixture outlet ANALYTICAL CHEMISTRY, VOL. 4 7 , NO. 9 , AUGUST 1975
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Table I. Experimental and Calculated Diffusion Rates of Benzene into Nitrogen Gas. Effect of Flow Rate on Experimental Rates Flow rate, rnl rnin-'
Temp, 'C
125 25.10 125 25.10 125 25.10 125 25.10 125 25.10 1,000 25.10 1,000 25.00 1,000 25.10 1,000 25.10 1,000 25.10 1,300 25.10 1,300 25.10 1,300 25.10 1,500 25.10 1,500 25.10 1,500 25.10 a Each experiment ran for 120 minutes.
P, m m H g
I f ! =m
i c a l c d , mg rnin-l
755.9 755.9 754.9 757.4 757.4 757.4 761.5 767.3 767.3 767.3 766.6 755.7 755.7 766.6 766.6 755.7
2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.70 2.71 2.70 2.71 2.73 2.71 2.72
0.7868 0.7868 0.7869 0.7867 0.7867 0.7867 0.7828 0.7860 0.7860 0.7860 0.7831 0.7868 0.7839 0.7774 0.7831 0.7810
term) by periodic adjustment of the heater controller. Prior to entering the diffusion cell, the diluent gas passes through 3 ft of 0.25-inch diameter coiled copper tubing contained in the constant temperature enclosure. This was sufficient to equalize the diluent gas temperature with that of the diffusion cell at all flow rates employed in the studies described herein. Operating Procedure. The temperatures of both the diffusion cell and the liquid reagent bottle are equilibrated at the chosen experimental temperature. About 5 ml of liquid are transferred to the diffusion tube, D, (Figure 1) which is then sealed with a cork stopper. The stoppered diffusion tube is weighed to the nearest hundredth of a milligram and the initial length, lo, of the liquid column below the tube opening measured with a precision ruler or a travelling microscope. (Nylon gloves are recommended for handling the diffusion tube to minimize contamination.) The diffusion tube is immediately inserted into the cell and positioned 1 cm below the diluent delivery capillary, F. After the generation time interval, which was 120 minutes for these studies, the diffusion tube is removed, stoppered and weighed and the final diffusion path length, lf, measured.
RESULTS The vapor concentration delivered by the diffusion cell is determined from the diluent gas flow rate, V l./sec, and the rate of diffusion of vapor from the diffusion tube, r mg/sec. The diffusion rate r, can either be measured experimentally from the change in weight of the diffusion tube or calculated from the diffusion equation ( 1 7 ) . DAMP P r=-lnRTl P-p where D = molecular diffusion coefficient of the vapor into the diluent gas stream, cm2/sec. A = cross sectional area of the diffusion tube, cm2. M = molecular weight of the vaporizing species, g/mole. P = total gas pressure in the diffusion cell, atm. p = partial pressure of vapor a t temperature T, atm. R = gas constant, 1. atm/mole, K. T = cell temperature, K. 1 = average length of the diffusion path, cm. If quasi-steady state conditions are assumed, 1 can be taken as the arithmetic mean of the lengths a t the beginning, l o , and end, l f , of the diffusion period to calculate an average diffusion rate (14, 15). For most purposes very little error is introduced by this assumption, however, if desired 1 can be measured and r calculated a t any time during the period of diffusion or it can be continuously adjusted to a constant value. Evaluation. Altshuller and Cohen (17 ) have performed an extensive evaluation of the influence on diffusion rate, r, of each of the parameters in Equation 1. Their results show 1706
ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
r,ptl,a
n g rnin-'
0.7870 0.7839 0.7833 0.7842 0.7810 0.7925 0.7925 0.7871 0.7846 0.7806 0.8564 0.8558 0.8630 1.3037 0.9883 1.1732
% difference
0.02, 0.37 0.46 0.32 0.73 0 -74 1.24 0.14 0.18 0.66 9.36 8.77 10.1 67.7 26.2 50.2
that considerable deviations from Equation 1 occur when diluent gas flow conditions produce turbulence a t the end of the diffusion tube. Otherwise, parametric dependences of r are well described by Equation 1 with the greatest dependence being on temperature via p and D. The temperature dependence thus resides in the ratio DIT In P / ( P PI. In view of these considerations, the diffusion cell depicted in Figure 1 was designed specifically to minimize turbulence and to operate a t closely controlled temperatures near the ambient value. Within these constraints, diffusion rates were determined gravimetrically for the diffusion of benzene into nitrogen gas. Representative results summarizing a large number of experiments are presented in Table I. The results show that for nitrogen flow rates of 1000 mllmin and below, experimentally determined diffusion rates are within 1.3% of those calculated from Equation 1 using D values for benzene reported in the literature ( 1 8 ) . Similar results were obtained using n- butanethiol and nbutylamine. As expected, r is most sensitively dependent upon temperature and diffusion path length making these parameters the most appropriate for controlling vapor concentration. The vapor concentration is also highly dependent on the diluent gas flow rate. Significant deviations from diffusion rates predicted by Equation 1 were, however, observed for diluent flow rates of 1300 ml/min and greater (Table I). The effects of diluent flow rate on benzene concentration a t various assumed diffusion path lengths are shown in Table 11. These concentrations are higher than required for most analytical purposes and a secondary dilution scheme was utilized effectively to produce vapor concentrations of a few ppm. The rate of attainment of a steady state is an important factor in the generation of standard vapor concentrations using a diffusion cell. In the case of the diffusion cell itself, Lee and Wilke ( 1 4 ) and Fortuin ( 1 5 ) have shown that a steady state will be approached within 1%in a time t , when t > 12/2D. For benzene in the present system, this relation predicts t > 40 sec and experimental observations indicate that a steady state is certainly attained within 60 sec. The approach of the diffusion cell to steady state, therefore, represents a negligible error when short diffusion path lengths and generation times of several hours are involved. Where a secondary dilution system is utilized, however, or where gas delivery lines are of considerable length, sig-
Table 11. Effect of Diluent Flow Rate on Benzene Concentrations at Various Assumed Diffusion Path Lengths Flow rate, 1 , cm
100 500 1000 4 100 500 1000 6 100 500 1000 8 100 500 1000 T = 25.0'Cc, P = 760 m m Hg, r 2
a
nil min-'
Steady state,
> I'/ZD) 3029 22 609 303 1514 88 303 151 1010 198 202 101 757 352 151 76 = 0.0910 mg min-I. ppma
sec(t
nificant amounts of vapor are lost because of wall adsorption. This can be a major problem in the case of low vapor concentrations ( 3 ) . In such circumstances, the time taken to attain a steady state may be several hours or even days depending on the nature and concentration of the vapor. Adsorption can be minimized by using short, all-glass lines of low surface area, or, in some cases, by presaturating delivery lines. For example, generation of 3 ppm of n-butanethiol utilizing a secondary dilution step, required approximately 6 hours to achieve an initial steady state although subsequent runs required only 30-45 minutes.
DISCUSSION In addition to its use as a generator for constant vapor concentrations, the high precision with which diffusion rates are attainable with this cell makes it useful as a calibration device. While for most purposes it is appropriate to determine the diffusion rate, and thus the exit vapor concentration, experimentally, the close obedience to Equation 1 means that diffusion rates can, if desired, be calculated provided that the appropriate diffusion coefficients and vapor pressure are available. Alternatively, the cell can be used to determine precise values for molecular diffusion coefficients. Ipdeed, the results represented in Table I show that agreement between the experimental and theoretical diffusion rates of benzene compares favorably with the precision (2.38 percent relative standard deviation) with which the diffusion coefficient of benzene is known ( 1 7 ) . The stability of the diffusion rate after steady state was f0.3896. This was evaluated by UV absorption of the benzene-nitrogen gas mixture passing through a 10-cm quartz flow cell. The range of vapor concentrations available depends, of course, on the molecular diffusion coefficient and on the operating parameters. For liquid samples, however, high flow rates and/or secondary dilution are recommended to achieve low concentrations rather than extensive temperature depression with its attendant difficulties of precise control. Where vapor concentrations of solid species are required, the solid should be melted in the diffusion tube to achieve a uniform surface and vaporized below the melting point. Alternatively a solid can be dissolved in a suitable solvent if associated solvent vapor can be tolerated. In all
cases, care should be taken to ensure that the vapor pressure does not approach saturation a t any point in the delivery system; otherwise condensation may occur. Operating experience with this diffusion cell has indicated the significant advantage of having a detachable diffusion tube both for maximizing precision in weighing and for ease of liquid replenishment. If very long diffusion periods are required (e.g., to approach steady state in an extended delivery system), the diffusion tube can be attached to an external reservoir and the diffusion path length maintained constant by utilizing an optical sensing device such as that proposed by Lugg (19). As indicated in Table I, significant deviations from Equation 1 were observed for diluent gas flow rates of 1300 ml/min and higher. This is ascribed to the onset of turbulent flow conditions occurring near the mouth of the diffusion tube. Turbulence is reduced by utilizing a capillary tube (Figure 1,F ) rather than a frit (17) as the diluent inlet to the mixing chamber provided that flow rates are lower than critical values. Thus, an elongated inlet has the advantage of ensuring nearly laminar flow but the possible disadvantage of being limited to low flow rates. Turbulence is also promoted by having a large diffusion surface area A , and a short diffusion path length, 1. Here one is faced with achieving a compromise between the advantages of reducing turbulence and of having large A and short 1 t o maintain 1 relatively constant and to minimize the time required to reach the steady state. In the present system, this compromise has been achieved since its requirement of low diluent flow rate is not considered to be a significant disadvantage for most analytical applications.
ACKNOWLEDGMENT The authors are indebted to Melton Bryant, School of Chemical Sciences, University of Illinois, for constructing the constant temperature box. LITERATURE CITED (1)J. P. Lodge in "Air Pollution", A. C. Stern, Ed., Vol. 11, Academic Press, London, 1968,p 465. (2)J. L. Hudson, E. H. Johnson, D. F. S. Natusch, and R. L. Solomon, Environ. Sci. Techno/., 8, 238 (1974). (3)R. K. Stevens, A. E. O'Keeffe, and A. C. Ortman, Environ. Sci. Techno/., 3, 652 (1969). (4)R. Koppe and D. Adams. Environ. Sci. Techno/., I,479 (1967). (5) F. P. Scaringelli, A. E. O'Keeffe. Ethan Rosenberg, and J. P. Bell, Anal. Chem., 42, 871 (1970). (6)M. D. Thomas and R. E. Amtower. J. Air Pollut. Contr. Assoc., 16, 632
(1966). (7)J. R. Jacobson, Am. Chem. Soc., Div. Water, Air, Waste Chem., Abstr., 7(1),232 (1967). (8)L. A. Elfers and C. E. Decker, Anal. Chem., 40, 1658 (1968). (9)W. L. Bamesberger and D. F. Adams, Environ. Sci. Techno/., 3, 258 (1969). (IO)A. E. O'Keeffe and G. C. Ortman, Anal. Chem., 38, 760 (1966). (1 1) F. Lindqvist and R . W. Lanting, Atmos. Environ., 6, 943 (1972). (12)H. A. Axelrod, R. J. Teck, J. P. Lodge, Jr., and R. H. Allen, Anal. Chem., 43, 496 (1971). (13)J. M. McKelvey and H. E. Hoelscher, Anal. Chem., 29, 123 (1957). (14)C. Y. Lee and C. R. Wilke, lnd. Eng. Chem., 46, 2381 (1954). (15)J. M. H. Fortuin, Anal. Chim. Acta, 15, 521 (1956). (16)R. S.Braman and D. L. Johnson, Environ. Sci. Techno/., 8, 996 (1974). (17)A. P. Altshuller and I. R. Cohen, Anal. Chem., 32, 802 (1960). (18) "Handbook of Chemistry and Physics", The Chemical Rubber Co.. Cleveland, Ohio, 46th ed., 1965-66. (19)G. A. Lugg, Anal. Chem., 41, 1911 (1969).
RECEIVEDfor review December 23, 1974. Accepted May 12, 1975. This work was supported by the National Science Foundation under grant No. GI-31605.
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