study. T h e n a v e lengths of t h e absorbance peaks of praseodymium fluoride are essentially identical t o t h e wave lengths of t h e absorbance peaks exhibited by aqueous praseodymium solutions-444, 467,479, and j88 mp in the molten fluoride salt as conipared a i t h 444, 468, 482, and 588 nip in aqueous solution (8). The intensities of the absorbance peaks are not the same, however; in aqueous solutions, the 444-mp peak is 2 1 / 2 times as intense as the one a t 468 mp, and that peak is only slightly more intense than the peak a t 482 nip. The molar absorbance index of the 444-mp peak of praseodymium fluoride is estimated to be on the order of 1 to 5. Because of the concentration effect achieTed with molten salts, as discussed earlier, a possible method for determining praseodymium in fluoride salts or in precipitated rare earth fluorides could be developed. Further work ~ o u l dbe necessary to determine the spectra of other rare earth fluorides to evaluate the applicability of such a procedure fully. Uranium Tetrafluoride. T h e spectrum of uranium tetrafluoride (shown in Figure 5 ) resembles a spectrum of uranium tetrachloride in molten lithium chloride-potassium chloride t h a t was reported by Gruen a n d hIcBeth (6). Uranium tetrafluoride exhibits strong peaks a t 1100 and 658, and a shoulder a t 615 nip, compared to uranium tetrachloride which exhibits peaks a t 1090 and 655, and a shoulder a t 605 mp. The fluoride salt also has peaks a t 530, 470, and 428 mp; in this
region uranium tetrachloride presents a broad absorbance band Kith several weak absorption peaks. Actually, in the 400- to BOO-mp region the spectrum of uranium tetrafluoride more closely resembles the shape of the spectra of quadrivalent uranium in 1 M perchloric acid ( 7 ) ; the ware length of the absorbance maxima in the two solvents is not identical, however. The spectra of both uranium tetrafluoride and uranium tetrachloride exhibit an absorption minimum a t 710 nip; assuming that the absorbance of uranium tetrafluoride a t 710 mp represents the absorbance of the solvent, and n-ith a knon ledge of the concentration of uranium tetrafluoride and the density and neight of the molten fluoride pendent drop, it was possible to calculate an approximate value for the molar absorbance index of the 1100-mp peak of uranium tetrafluoride to be 15. This value compares favorably n-ith the molar absorbance index of 13 reported for the 1090-mp peak of uranium tetrachloride (6). Uranyl Fluoride. During t h e preparation of a particular solution of uranium tetrafluoride in lithium fluoride-sodium fluoride-potassium fluoride, t h e evpected green melt gradually turned yellon-. The spectrum of this resultant solution is presented in Figure 6. 4 single peak can be noted a t 424 mp; the solute present in solution is probably uranyl fluoride. I n this spectral region, uranyl ion in aqueous solution exhibits a maximum absorbance a t approximately 415 mp (9). It is assumed uranium
tetrafluoride was oxidized to uranyl fluoride by atmospheric oxygen during the preparation of this solution. Qualitative tests of the salt sample indicated that uranyl fluoride n a s present, and the molten salt spectruni showed no uranium tetrafluoride. ACKNOWLEDGMENT
The authors acknoidcdge the assistance of B. J. Sturni, Oak Ridge Sational Laboratory, u ho prepared most of the pure compounds used in this study. LITERATURE CITED
(1) Bastian, R., XXAL. CHEII. 23, 581 (1961).
( 2 j Boston, C. R., Smith, G. P., J . Phz~s. Chem. 62,109 (1958). (3) Cooper, S. S., ANAL. CHEM. 19, 258 (1947). (4) Gruen. D. XI.. J . Inora. and A - d e a r ‘ Chem. 4.’74 11957). ( 5 ) Gruen, D. XI., McBeth, R. L., I b i d , 9,290 (1959). (6) Gruen, D. M.,MeBeth, R. L., J . Phys. Chem. 63,393 (1959). (7) Heidt, L. J., Moon, K. A., J . Am. Chem. SOC.75,5803 (1953). ( 8 ) 3loeller. T.. Brantlev. J. C.. ANAL. CHEII.22: 43611950). . (9) Sjohlom, R.’, Hindman, J. C., J. Am. Chem. SOC.73, 1747 (1951). (10) Sunclheim, B. R., Harringtim, G., “Absorption Spectra of Molt& Salts,” U. S. At,omic Energy Comm., NYO7742, 43 (March 9, 1959). (11) Young, J. P., Khite, J. C., ANAL. CHEM.31, 1892 (1959). \
I
RECEIVED for review December 7, 1959. Accepted XIarch 28, 1960. Work performed under contract with U. S. Atomic Energy Commission.
Application of Diffusion Cells to the Production of Known Concentrations of Gaseous Hydrocarbons AUBREY P. ALTSHULLER and ISRAEL R. COHEN Air Pollution Engineering Research, Robert A. Tuff Sanitary Engineering Center, Public Health Service, U. S. Department o f Health, Education, and Welfare, Cincinnati 26, Ohio
,Diffusion coefficients have been determined for a number of hydrocarbons, including 2-methyl- 1,3-butadiene, hexane, 1-hexene, heptane, 1 octene, decane, benzene, and toluene. Diffusion coefficients at a number of temperatures have been determined for hexane, 1-hexene, heptane, 1 octene, decane, and benzene. The effect of turbulence at the end of the diffusion tube, resulting from the rapid flow of carrier gas over the top of the tube, has been investigated as a function of gas flow rate, temperature,
-
802
0
ANALYTICAL CHEMISTRY
diffusion tube diameter, and tube length. These results, with related data in the literature, should aid in defining the experimental limits within which a diffusion tube apparatus may be operated so that calculated values of diffusion rate can be used, if one experimental value of the diffusion coefficient i s available for the liquid compound of interest.
M
of producing known and reproducible amounts of low
ETHODS
concentrations of gases and vapors are essential in studies in the fields of air pollution, industrial hygiene, and other related areas. Because most organic compounds of interest are liquid a t room temperature, the liquid material must be vaporized so as to produce very lon- concentrations of the resulting gaseous compounds. K h e n a large chamber is available, a small known quantity of liquid can be vaporized by heat and flushed into the chamber. If the chamber can be evacuated, a very small amount of liquid can be in-
jected into it. \Then a chamber is not available or when a dynamic source of vapor is desired, another method must be employed. A method xhich has wide application and involves rather simple apparatus is based on the diffusion of vapors up a tube of known cross section into a gas stream. The use of diffusion cells for producing low concentrations of vapors has been suggested recently (6, IS). For some time the authors used the type of cell proposed by McKelvey and Hoelscher ( I S ) , but found it impossible to obtain rates of diffusion in agreement with those calculated from the appropriate diffusion equation, or to obtain good reproducibility. Subsequently, cells of the type used originally by Stefan (15) (and more recently by others) to determine vapor into gas diffusion coefficients have been used lvith considerable success. GENERAL DISCUSSION OF DIFFUSIONAL PROCESS
Data were sought which would aid in defining the conditions of operation under which diffusion cells could be used in routine work without the necessity of elaborate calibrations by each user. The reasons for such a problem can be understood only by discussing the nature of the processes involved in vapor-gas diffusion measurements. The diffusional process involves essentially the passage of molecules evaporating from a liquid reservoir into a gas space containing the diluent gasair, nitrogen, helium, etc. The driving force is the concentration gradient of the vapor up the tube. The reservoir serves as a material s o u ~ c en.ith a rate of production governed by the temperature a t which the reservoir is maintained. This temperature also defines the partial pressure of the vapor above the liquid. The diffusion equation has the form: T ==
2.30 3DJIPA _____ RTL
P log p-P
(1)
The diffusion equation has been set up here in terms of a weight measurement to determine the rate of loss of material. It can be readily modified in terms of a measurement of change in height of liquid which is often used. Approach to Steady State. The approach t o the steady state in diffusion cells is not instantaneous. Lee and Wilke ( I d ) and Fortuin (6) have treated the problem mathematically. A steady-state condition will be approached within lyOwhen t > L2/ 2 0 , where t is the total time in seconds and D is the molecular diffusion coefficient in square centimeters per second. For a somenhat extreme example, if D = 0.0500 sq. em. per second and L = 20.00 em., t >4000 seconds. Homever, even for D = 0.100 sq. em. and L = 5.00 or 10.00 em., t >125 and
Table I. Effect of Total Pressure on Diffusion Rate a t Various Assumed Partial Pressures yo Variation of P, hlm.
5
25 100 200 400 600
p, Mm, 740 750 760 740 750 760 740 750 760 740 750 760 740
750 760 740 750 760
Log
Log P/(P-p) 0.00294 0,00290 0.00286 0.01492 0.01472 0.01452
PAP-P) with P 1.38
0.0631 0.0622 0.0613 0.1368 0.1347 0,1326 0.3377 0.3310 0.3245 0.7231 0.6990 0.6767
1.45
1.36
1.56 2.00 3.39
500 seconds, respectively. The errors involved in ignoring the initial departure from steady-state conditions, in determinations of diffusion coefficients which extend over hundreds of minutes, are unlikely to exceed a few per cent. The error tends to be minimized by the rapid initial approach towards the steady state. However, when diffusion cells are to be used for short-time runs, the cells should be operated for a t least 10 or 15 minutes preceding actual use to ensure a close approach to steady-state conditions. Total Pressure Variations. The total pressure-dependent quantities in the diffusion Equation 1 include D,P , and the log P / ( P - p ) . Experimentally, it has been shown that the diffusion coefficient, D, varies inversely with P, so that D = B/P, where B contains the total pressure-independent part of D. Therefore, the quantity B / P x P log P / ( P - p ) or just log P / ( P - p ) is the one of interest. The effects of =!= lo-nim. variations in total pressure on log P / ( P - p ) and consequently on the diffusion rate are shown in Table I. Vapor Pressure and Temperature Variations. Because the vapor pressure, p , of the diffusing substance appears in the term log P / ( P - p ) , the sensitivity of this term to temperature fluctuations and consequently to the corresponding variations in vapor pressure is important. Log P / ( P - p ) has been evaluated for n-decane a t different temperatures (Table 11). Similar calculations have been made for n-hexane and n-heptane. I n these instances also, the sensitivity of the log term to temperature variations is a t a minimum near 150 mm. A tendency for the sensitivity to temperature to increase with decreasing molecular n-eight can be seen if the errors for 1O variations are compared a t about the same vapor pressures for n-hexane, n-heptane, and n-decane. For example, when 2, is in the 140- to 160-mm. range and P'is 760 mm. the variations of log
~
where
r
rate of diffusion of vapor out of the diffusion tube, grams per second D = molecular diffusion coefficient of the vapor into the diluent gas, square centimeters per second M = molecular n eight of vapor P = total pressure in diffusion cell, atmospheres A = cross-sectional area of the diffusion tube, square centimeters p = partial pressure a t a temperature T of the vapor, atmospheres R = gas constant, liter-atmospheres per mole-' K. T = temperature, K. L = length of diffusional path, centimeters =
Table II. Effect of Temperature and Vapor Pressure on Diffusion Rate of n-Decane n-Decane, Log t c. P/(P-p) yo Variation DIT Log ( P - p ) yo Variation 39 0 001919 -6.2to +6.5 3 801 X 10-7 -6.3 to +6.6 40 0 002045 4.057 X lowi 41 0.002177 4.326 X 86 0,02350 -4.4 to +4.6 4.995 X l W G -4.5 t o + 4 . 7 87 0.02459 5.232 X 88 0.02571 5.476 X 119 0 09271 -3.8 t o +4.0 2 060 x 10-5 -3 9 to+ 4 1 120 0 09612 2 144 x 10-5 121 0 10026 2 232 x 149 0 3042 -4.2 to +4 4 6 990 X 10-5 -4 1 to +a 5 150 0 3174 7 299 X 151 0 3314 7.626 x 10-5 169 0.9072 - 9 . 0 t o +11.7 2.138 X -9.2 to $11.6 170 0.9972 2.352 X 171 1.1134 2.629 X
VOL. 32, NO. 7, JUNE 1960
803
P / ( P - p ) nith a i1' change in temperature are i 4 . 9 , 1 4 . 6 , and i 3 . 9 % for n-hexane, n-heptane, and n-decane. respectively. The entire temperature-dependent part of diffusion Equation 1 is D I T log P/(P-p). However, the variation in diffusion coefficient of decane per degree change in temperature is in the range from 0.3 to 0.5%. It seems unlikely that the variation in diffusion coefficient would be more than 1% per degree. Furthermore, the diffusion coefficient and the temperature vary in the same way, so that DIT is only slightly sensitive to small temperature changes. Consequently, the variation in the rate of diffusion with temperature is due largely t o the sensitivity of the vapor pressure of the diffusing substance to small temperature changes. A comparison for n-decane of the entire temperature-dependent part of Equation 1 with the variation in the log P / ( P - p ) with temperature a t various temperatures also is shown in Table 11. The above discussion and the computations in Table I1 show that teniperature control to about 1 0 . 1 " is highly desirable for precision determination of diffusion coefficient or the maintenance of diffusion rates within close bounds. Furthermore, n here the choice is available, it is wise to minimize this source of error by avoiding very low or very high vapor pressure ranges. Cooling Effects. GAS-LIQUID INTERFACE COOLING. This eff ect results from t h e cooling of t h e interface between liquid and gas phase on-ing t o vaporization a t t h e surface. Both Lee and JJ7ilke (19) and Cummings and Ubbelohde (4) have measured the magnitude of this cooling and have found it to be small except for liquids of high volatility at the temperatures used. Consequently, the magnitude of the temperature lowering is related to the rate of evaporation. Also, the use of temperatures a t which the diffusing substance will have a very high vapor pressure mill increase the magnitude of the error from this source. REVERSETHERMAL DIFFUSION EFFECT. Temperature cooling results nhen unlike molecules are spontaneously mixed together. This phenomenon is a reverse thermal diffusion effect. Lee and Wilke (22) found that temperature differences between the liquid surface and the gas volume directly above it were never more than 0.1' and usually were 0.05' or less. Both this effect and the gas-liquid interface cooling usually mould be responsible for errors which are small compared to other errors in this type of diffusion experiment. If extremely precise measurements of diffusion coefficients at high vaporization rates are to be made, these cooling effects must be considered. 804
ANALYTICAL CHEMISTRY
Temperature Dependence of Diffusion Coefficient, The temperature dependence of t h e diffusion coefficient is espressed in the equation D2/D1 = ( T 2 / T J "where D2 and D1 are the diffusion coefficients at temperatures 2'2 and T I . The exponent n lies between 1.50 and 2. However, there has been and still is considerable uncertainty about just where in this range n will be for a particular system. Application of classical kinetic theory to a model system of rigid spherical molecules leads t o a T30 dependence. The n = 1.50 exponent has been used in several semiempirical equations for diffusion coefficients including those of Arnold(1) and Gilliland (7). The data for the diffusion of water into air seem to fit a n n of 1.8 to 1.913. Application of kinetic theory using the Lennard-Jones potential for intermolecular forces by Hirschfelder, Curtiss, and Bird (9, 10) leads to a temperature dependence of the diffusion coefficient on the quantity Ts/z/QD where Q D is a weakly temperature-dependent collision integral. Fair and Lerner (6) state that this integral generally has a temperature dependence such that the net dependence of the molecular diffusion coefficient is in the range of 1.6 to 2.0. One practical reason for concern over the exact number to be used for n is the extrapolation of diffusion coefficients over a fairly extensive temperature range. For example, Cummings and Ubbelohde (4) experimentally determined that dodecane has a diffusion coefficient into nitrogen a t 399.4' K. of 0.0813 sq. em. per second. If dodecane a t 293.2' K. is used for diffusion rate measurements, extrapolation to 293.2" K. of the diffusion coefficient using T'.W gives 0 0511 sq. em. per second, whereas extrapolation to 293.2' K. using T 2 gives 0.0438 sq. cm. per second. I n this instance there exists a 15% uncertainty as to !!-hat is the true difhsion coefficient. I n cases in which a smaller temperature interval is involved in the extrapolation, the uncertainty in true diffusion coefficient still can be 5 or 10%. There is a definite need for more experimental diffusion coefficient data over a range of temperatures. Variation of Diffusion Coefficient with Nature of Carrier Gas. For a given diffusing vapor or gas a t a fixed temperature, t h e diffusion coefficient will usually increase with decreasing molecular weight of t h e carrier gas. For example, t h e diffusion constant of cyclohexane into argon, oxygen, nitrogen, and hydrogen increases in this same order (4). However, the effect of carrier gas is the result not only of a difference of molecular weight but of intermolecular forces. consequently, the diffusion coefficients obtained for the diffusion of the same gas into tn-o dif-
ferent carrier gases of the same molecular weight should not be identical. For the extreme example, the experimental data indicate a five- t o sevenfold greater diffusion coefficient for diffusion into hydrogen than for diffusion into carbon dioxide (14). Fortunately, the diffusion coefficients of various mpors into nitrogen, oxygen, or air are fairly close. Cummings and Ubbelohde (4) obtained data for the diffusion coefficients of six hydrocarbons into oxygen and nitrogen. The greatest difference was about 2.570 and the average about 1%. Similarly. the experimental data for the diffusion of benzene into oxygen (26) and air (12) are within about 1% after appropriate correction for the small difference in temperature. Therefore, it appears that the differences in diffusion coefficients of vapor into nitrogen, oxygen, and air are at most no greater than the uncertainties associated n-ith even carefully performed diffusion measurements. It would seem permissible a t the present time to use data for the diffusion coefficients of various hydrocarbons into nitrogen, oxygen, or air interchangeably. Honever, this procedure is not a satisfactory approximation if hydrogen, helium, or even argon or carbon dioxide is substituted as the carrier gas. K i t h these gases, each system must be tested separately. Cross-Sectional Area. The diff usion rate is proportional t o t h e crosssectional area of the diffusion tube. Accurate calibration of t h e crosssectional area a t several points along the diffusion tube length, preferably t o nithin a t least 1 or 2%, is most desirable. The cross-sectional aiea along t h e tube length also should be uniform. Tube diameters beloif 1 or 2 mm. present some filling problems =ilso, the strong capillary effects for yery small tube diameters increase difficulties in making accurate diffusion path length measurements. Tery large diameter tubes, 2 em. and above, also should be avoided because the turbulent effects discussed below may be aggravated by large tube diameters Diffusion Path. SURFACE TENSION EFFECT. T h e path over which diffusion of t h e vapor occurs ideally would be from a plane surface of t h e liquid in t h e t u b e t o t h e very top of t h e t u b e where t h e vapor encounters laminar flow of t h e carrier gas. I n practice, surface tension ail1 produce a meniscus in most liquids in t h e usual tube materials. Consequently, t h e diffusion path of molecules evaporating near the liquid-solid interface (for most of the liquid-solid combinations of interest) will be shorter and the diffusion path near the bottom of the meniscus somewhat longer than the diffusion path from a plane surface.
Lee and Wilke (1.2) concluded that the distance from the bottom to the top of the meniscus (which they term Ax, and subtract from the measured overall diffusion path length) is on the order oflto2mm. TURBULEXT EFFECT. As the flow rate of the carrier gas is increased, the opportunity increases for turbulent behavior in the upper chamber to extend eddies down into the diffusion tube. At sufficiently high flow rates, a very appreciable correction needs to be made for the decrease in the effective diffusion length. Lee and Wilke (1.2) estimated corrections of up to 1.3 cm. in the diffusion path length for the diffusion of nitrobenzene into air a t a carrier gas flow rate of 4.8 liters per minute. Trautz and Muller (17) discussed the fact that the various sources of error in diffusion measurements, such as turbulence, which are independent of the total diffusion path length, can be largely corrected by extrapolation of D us. 1/L to infinite path length. Lee and l17ilke ( l a ) derived the expression 1, D , = -Ax/LD, 1/D, where D , is the apparent diffusion coefficient based on the apparent path length L,, and D is the true diffusion coefficient based on the effective path length, L, and Ax = L , -L, where L , and L are the apparent and true diffusion path lengths. They suggest that for data obtained at long diffusion path lengths, their expression and the estrapolation procedure of Trautz and LIiiller (17') should give equivalent results .
+
EXPERIMENTAL DETAILS
Diffusion Cells. The diffusion cells originally used have been described (13) except that the upper and reservoir flasks nere of 100- rather than 50-ml. capacity. The diffusion tubes n ere 10.0 cm. in length to v-ithin a feiv hundreds of 1 cm. The cross-section areas 1%-ere determined by mercury calibration and the corresponding diameters were calculated to be 0.516, 2.03, 4.04, and 5.0 mm. The later cells, with one exception, are one-piece glass cells. The diffusion tube is closed a t the bottom to serve also as a reservoir and the diffusion tube is sealed to the upper chamber. The top of the diffusion tube protrudes about 2 cm. above the lower surface of the upper chamber. The design of the upper chambers varies. The 3.20- and 3.40mm. diameter cells have upper chambers of approximately spherical shape with 8-mm. tubing as inlets and outlets for the carrier gas. The tubes make arightangled bend outside of the cell and extend a few inches upn-ard. The cell with a 7.85-mn~diameter diffusion tube has a n upper chamber about the same shape as the cells described, but a coarse glass frit is sealed t o the inlet tube inside the chamber to give better mixing
analyses. confirmed by gas chromatographic
'
AlR Cdl
N
. R
I
cl
Figure 1.
1
Diffusion cell
of the carrier gas. TKO cells n i t h cliff usion tubes of 11.07- and 11.08-mm. diameters have cylindrical upper chambers which taper d o w n m r d t o the inlet and outlet tubes which have coarse glass frits sealed into them just inside the upper chamber. The over-all lengths of the diffusion tubes are between 12 and 14 cm. Ground-glass joints are sealed to the top of the chamber directly above the diffusion tube on all cells, so that the tubes can be filled from the top of the cell (Figure 1). One cell nas put together using a 8.20-mm. diameter diffusion tube, of about 30 cm. in length, attached by a rubber stopper to an upper spherical flask from the IIcKelvey and Hoelschertype cell. This cell was used to obtain data a t longer diffusion path lengths than was possible n ith the all-glass cells. Hydrocarbons. The hydrocarbons used \yere Phillips Petroleum chemicals of 99 mole 70purity, nhich m-as
Table Ill.
Tube
Compound
Z-lIethyl-2-butene 2-\lethyl-1,3-butadiene
eter, Mm. 2
4
0
Preliminary Measurements.
Liters; Calcd. Min. Temp., Diffusion F l o ~ O C. Rate, Rate Calcd. yihlin. 0 35 = 34 0.35
a
138
3.8 61
0.5 2
1. O 1 .o
4
1.0
a
244
a
1.0
a
383
0.5 0
1.0 1. 0 1. 0 1.0
-7
1. 0
4 4 2 4
1 .00 1.4 1 .44 1.4
-3 4
Toluene
EXPERIMENTAL RESULTS
The
Results Obtained with Separate Reservoir-Type Diffusion Cells
Diam-
n-Heptane
Temperature Control. A number of the earlier runs nere made using a n air oven. Temperature cycling in this air bath was ne11 over 1'. However, most of the later determinations were made in water or oil baths. depending on the temperature desired, and the baths usually were thermostated to = t 0 . l o C. or less. However, the 150" C. oil bath could be controlled only to about k0.2'. Weight or Volume Determinations. Almost all the diffusion rates were determined by weighing the cells on a n analytical balance before and after a run. I n a few instances both weight and volume changes were measured and checked within 5%. Honever, because no cathetometer was available for precision measurements of small changes in liquid level, neight measurements generally were used. The diffusion path lengths TTere measured either with a millimeter ruler or by engraved calibrations on the tube, estimating to the nearest 0.1 nim. Diffusion paths ranging from 2 to 3 up to 10 or 11 cm. were used in most of the series of measurements reported here. The carrier gas was laboratory air of lorn moisture content, and any gross particulates were removed by a glass wool filter. I t s temperature was adjusted to approximately the temperature of the diffusion cell by passing the air through a copper coil immersed in the same constant temperature bath as the diffusion cell. The vapor pressures of the hydrocarbons used were obtained from the National Bureau of Standards tables of selected values of properties of hydrocarbons, API Project 44.
L l rl
0
a a (i
0.22 3.50 14.0 22.0 2.25
0
30 45 45
9 .0 1 22.33 6 . 66 226.4 64
O b e r v e d Iliff~isionRate + Calcd. Diffusion Rate 1 *5, 2 0 14,12
16. 70, 24) 73, 58, 42, 5 2 , 66 2.0, 4.1, 3.3, 3.0, 6.0, 2.6, 2 . 5 , 3.0, 5 . 2 2.4, 1.7, 1.4, 1.4) 1.8, 1.6, 1 . 5 . 1 . 4 . 1 . 5 , 3 . 4 ,1 . 5 , 1 . 2 , 1 1 ,1 7 . 2 0 , 3 3 1 2 , 0 9 , 1 1 , 1 3 , 1 3, 1 . 3 , 0 9 18, 6 , 13, 1 2 , 10 3.5, 1 . 2 , 1.4, 1.5, 1 . 5 1.4, 1.3. 1.4, 1.4, 1 . 3 " 9 , 2 , 4 >1 . 7 2 . 2 , 0 . 8 , 5.6, 0 . 8 , 2 . 9 , 0.7, 3 . 1 ., 2 . 8 ., 1 . 8 ., 1 . 3 1 .99 , 11 . 5 ,, 22. 88 4 .66 , 22 . 6 3 .77 , 00. 9 : 3 .77 ,, 1 . 77 1 .33 ,, 11. 1 ,~1 .18 8, 1, . 10 ,01,. 01 0
Room temperature.
VOL. 32, NO. 7, JUNE 1960
0
805
Table IV.
Compound illethanol n-Hexane
Heptane Decane
Experimental Molecular Diffusion Coefficients Diffusion Flow Tube Rate, Diffusion Diameter, Liters/ K O . of Coefficient, Min. Detns. Nm, t , " C. D, Sq. Cm./Sec. 4 25. 3.20 4.0 0.156 1 0 . 0 0 8 * 25" 4 7.85 1.o 0.155 1 0 . 0 1 2 4 25. 7.85 4.0 0.151 &00.030 n n797c 3 25.0 11.07 0.4 7 8.20 0.0811 i 0 . 0 4 4 0.5 30.0 4 7.85 48.5 0.5 0.0889 10.0026 7 11.07 49.5 0.0903 1 0 . 0 0 2 8 2.0 3 50.25 0.4 11.07 0 . 0903c 12 7.85 16.8 0.1 0.0705i0.0024 7 64.6 3.20 0.0847 1 0 . 0 0 3 8 0.1 9 39.9 11.08 0.5 0.060610.0046 9 60.5 11.07 0.5 0.0686 5 0.0010 7 86.4 3.40 0 077110.0051 2.0 7 86.4 2.0 7.85 0.0790 i 0.0060 7 86.4 2.0 7.85 0.0810 5 0 , 0 0 3 3 7 86.4 11.07 0.1 0.0765 5 0 . 0 0 1 6 7m 86.4 11.08 0.0760 i 0 . 0 0 0 6 0.5 86.4 11.08 0.077110.0016 1.o 86.4 11.07 0.0758 1 0 . 0 0 1 4 2.0 4 0.0864i0.0007 118 7.85 0.5 149.1 6 11.07 0.1 0.0920&0.0013 149.1 10 11.07 0.093710.0012 1.o
iJ
2-Methyl-1,3-butadiene I-Hexene
7 5
7
1-Octene Benzene
10
10 7 8
11
Toluene
2 2 2
15 20.0 30.0 40.0 97.0 26.9 60.8 30.0 25 45 45
3.20 3.20 11.08 11.08 11.07 11.07 11.07 11.07 7.85 3.19
7.85
0.5 0.5 0.5 0.5 0.5
0.275 0.26 0.275 1.o 1.0 1.o
0,0905 1 0 . 0 0 0 7 0.0788 1 0 . 0 0 3 5
0.0829 5 0 . 0 0 1 5 0.0708500.0012 0.0933i0.012 0.0926 1 0 . 0 0 2 2 0.1148500.0010 0.0951 i 0 . 0 0 4 0 0 .0908c 0 .O96lc 0 . O97Oc
Room temperature, 25' 12". Precision measure, 1one standard deviation. c Insufficient measurements available to determine precision.
cells originally used were modeled a f t e r those suggested by McKelvey and Hoelscher (IS). Because no comment n-as made about any particular level of liquid in the spherical-type reservoir, no effort was made to maintain a given level. I n initial determinations the results for toluene diffusion in the same temperature range as t h a t used by hIcKelvey and Hoelscher checked fairly well. I n the work that followed, some thermally and photochemically reactive compounds such as alkyl nitrites were used and the poor results nere attributed to the instability of the compounds. Hoviever, later rrork using hydrocarbons led us to suspect the cell design. Consequently, the diffusion rates of toluene, 2-methyl-2-buteneJ P-methyl-lJ3-butadiene (isoprene) , and ??-heptane in these cells were re-csnmined. Data with 0 5 , 2-, 4, and 5mm. diffusion tube diameters for flow rates ranging from 0.36 to 1.4 liters per minute of air were obtained (Table 111). The discrepancies between observed values and those calculated from the presumably applicable diffusion equa-
806
ANALYTICAL CHEMISTRY
tion are large. The ratio of observed to calculated rates is especially large and unreproducible for the diffusion cells using the 0.5- and 2-mni. diameter tubes. Some of the results obtained for cells with 4- and 5-mm. diameter tubes begin to approach satisfactory agreement with the calculated values. Some of the same data could be obtained n i t h fair reproducibility. The only experimental work presented in the McKelvey and Hoelscher paper was for toluene between 35" and 60" n-ith a tube of 4.9-mm. diameter. Because a 100-ml. roundbottomed flask n-as used to hold the liquid, it is felt that the amount of vapor space above the liquid may hare been partially responsible for the difficulty. Fortuin ( 6 ) , Jj-ho used both diffusion cells with separate reservoirs and a diffusion tube with a closed bottom, pointed out that error can result from concentration gradients of the vapor in a liquid reserroir which is separate from the diffusion tube. He also indicated the necessity of filling such vessels so that the distance from the liquid surface to the lower end of
the diffusion tube is as small as possible. For pure liquids, Fortuin preferred the type of cell in which the diffusion tube also serves as a reservoir for the liquid. I n a limited number of experiments the reservoir flask was filled to within about I em. of the bottom of the diffusion tube. However, the results again were much too high and erratic. A midget impinger vessel, with fairly uniform cross section, was substituted for the spherical-bottomed flask. The results were somewhat closer to the calculated values, but even with this container and with the liquid filled to within 1 cni. of the diffusion tube, values of 4.4 and 7.6 y per minute a t 46" C. were obtained for toluene compared to the calculated value of 6.6 y per minute, Initial Results Obtained with Stefan-Type Diffusion Cells. All work was discontinued with cells using liquid reservoirs separate from the diffusion tube itself. All of t h e diffusion constant values reported in this paper were obtained with onepiece Stefan-type ($, 4, 13, 16, 17) diffusion cells with the diffusion tube closed at the bottom and serving as its own liquid reservoir. The data obtained on these new diffusion cells for toluene, methanol, and water agreed satisfactorily with the literature values. Consequently, the diffusion coefficients of a number of hydrocarbons into air were studied in more detail. Detailed Results. D a t a have been obtained on t h e diffusion rates into air of n-hexane, n-heptane, n-decane, 2methyl-lJ3-butadiene, 1-hexene, l-octene, and benzene. T h e apparent diffusion coefficients, D,, were calculated a t each diffusion path length used and the true diffusion coefficient D, was obtained by applying the least squares method to the relationship 1/D, = a b/L, where a = 1/D and b = -Az/D,. The experimental conditions, molecular diffusion coefficients in square centimeters per second a t 760 mm. of pressure, and their standard deviations are listed in Table IV. Where only a fev- measurementh were made, no attempt was made to estimate measurement precision. The highest precision obtained (Table IV) corresponds to a coefficient of variation of about i0.87, for a fexy series of experiments and 2 to 370 for a number of other series. The 9570 confidence ranges are about twice as large. Trautz (16-18) obtained values for the diffusion coefficient of benzene, acetone, and carbon tetrachloride into oxygen and hydrogen which had been assigned uncertainties in the range of i 0 . 5 to 1%. Cummings et al. (3, 4) reported precisions usually in the 1 to 3% range, although numerous measurement series
+
were reported to have precisions between 0.3 and 1%. It appears from Cumniings' measurements and those reported here, t h a t uncertainties of less than 1y0 are difficult t o obtain even with careful work and close attention t o sources of error. Many of the diffusion coefficients in the literature are probably in error by a t least several per cent. I n view of the small differences betvieen the diffusion coefficients into oxygen and nitrogen ( 4 ) , of n-hexane, 2 , 3 -dim e t h y lb 11t ane, c yc 1oh e xa n e, methj-lcyclohexane, n-octane, and 2,2,4-trimethylpentane aiid the values for tlie diffusion of benzene into oxygen (16) and air (I@, i t would seem useful t o conip:ire the present values n i t h those available for the diffusion of the same hydrocarbons into nitrogen. Data also are available for the diffusion coefficient of n-decane into nitrogen (4). The temperatures of the experiments and the values for the molecular diffusion coefficients of n-hexane, n-heptane, and n-decane into nitrogen are as follons: 288.6' IC., 0.0757 + 0.0004; 303.0" K., 0.743 =t 0.0012; 364.6'K., 0.0841 + 0.0017 sq. em. per second. At the same temperatures the interpolated or extrapolated values for the molecular diffusion coefficients of n-hexane, n-heptane, and n-decane into air are as follons: 0.0752, 0.0743, and 0.0777 sq. tin. per second. The agreement for n-hexane and n-heptane is very good considering the uncertainties involved, including the small variation resulting from tho use of different carrier gases. The difference of more than 0.006 sq. cin. per second in the n-decane results is larger than can be accounted for by the uncertainties in the measurements. Actually, if the Cummiiigs (3, 4) data on n-hexane through ndodecxne are extrapolated to a common temperature of 293.2' K., using either n = 1.5 or n = 2.0, the n-decane value is clearly too high. The values obtained for n-decane actually are equal to or higher than the n-nonane values depending on the n value used. Therefore, it is felt that the value for n-decane into nitrogen given by Cuniniings and Ubbelohde ( 4 ) probably is too high.
obtain the calculated diffusion coefficients. The data (Table V) show t h a t the experimental diffusion coefficients are from 5 t o 20% larger than thoqe calculated from theoretical considerations. Similar calculations (14) indicate smaller theoretically calculated diffusion coefficients than experimental diffusion coefficients for a variety of hydrocarbon-carrier gas combinations. These combinations include benzene-air, noctane-air, toluene-air, propane-carbon dioxide, ethylene-carbon monoxide, benzene-heliuni, ethj-lene-nitrogen, benzene-oxygen, and ethylene-oxygen. The average difference betn een the calculated values and the evperimental values is about 10% but can range bet n een 20 and 30%. The differences DhrZ- Do2 obtained experimentally are small. The theoretical calculated differences Dv, - Do2 range from two to almost ten times the experimental values. The rather appreciable discrepancies betn een tlie experimental and theoretical values for both the diffusion coefficients themselves and in the differences betn een diffusion coefficients for the Same hydrocarbon into dlfferent carrier gases suggest caution in the uqe of the calculated values. 0111y if a n approximately correct diffusion coefficient is usable should cdculated values be used. The diffusion coefficients tlccrease most in passing from tlie first nicmber of a class of compounds to the second meniber of the series. For example, the diffusion coefficients into various gases of ethane, ethyl alcohol, and acetic acid are 20 to 30% loner than those of methane, methanol, and formic acid. (11, 1 4 ) . The decreaqe in diffuqion coefficient continues slon-ly as olie ascends various series, even to the eight- t o ten-carbon range of hydrocarbons or esters (10) Another pronounced cffect iq the higher diffusion coefficients of aromatic hydrocarbons compared to those of
Table V. Comparison of Experimental with Theoretical Diffusion Coefficient of n-Hexane, Cyclohexane, and n-Octane into Nitrogen and Oxygen
DISCUSSION
The experimrntal diffusion coefficients (4)for n-hexane, cyclohexane, and n-octane into nitrogen and oxygen are compared with the theoretically calculated diffusion coefficients in Table IT. The theoretical calculation depends on the method used to compute the force constants between molecules (9, 10). These force constants can be computed from experimental gas viscosity data and also from critical temperature and volume data. Both sourees of data have been used to
aliphatic hydrocarbons. Benzene diffusing into air a t 25' C. has a diffusion coefficient of 0.096 sq. em. per second while n-hexane has a diffusion coefficient of only 0.080 sq. em. per second. Similarly, the diffusion coefficient a t 25" C. of toluene is about 0,091 sq. em. per second, nhile n-heptane has a diffusion coefficient of only 0.072 ~ q . cm. per second. Comparison of the data of Cummings et al. (3, 4) and the present data also reveals tentative trends in saturated and unsaturated conipouiids and straight-chain and branched-chain molecules all of the same molecular \I eight. Thus 1-hexene and l,5-hexndiene appear to have slightly higher diffusion coefficients than hexane by about 2%. This correlation is in line with the much larger increase noted in aromatic compounds. Branching of the hydrocarbon chain appears t o lead to somewhat lower diffusion coefficients. For example, the diffusion coefficients of 2,3-dimethyl-1,3-butadiene and 2,3dimethyl-2-butene are about 3 and 8% loner, respectivcly, than the diffusion coefficient of 1,5-hexadiene. SimilarlJ-, the diffusion cot4icients (3, $) of the branched-chain and cyclic alkanes for which data are available are somewhat loner than tliosc. of tlie correspondiag straight-chain compounds of the same carbon number. The data in Table IT' on the diffusion coefficients of n-hexane, l-hc,xeiie, nheptane, n-decane, and benzene a t various temperatures supplemented b y earlier data (3, 4 ) on n-hexane and nheptane can be used to calculate the temperature coefficient, n. Temperature coefficients also can be calculated from the theoretical equation of Hirschfelder rt al. (-9, 10) using both viscosity and critical state data nhcn available to obtain tlie molecular force parameters. The teniperature coefficients, n, obtained experimentally, with those obtained from the theoretical treatment of diffusional phenomena, are listed in Table VI. KO data are avail-
Carrier Gas Kitrogen Oxygen Nitrogen Oxygen Kitrogen Oxygen a
Diffusion Coefficients, Sq. Cm./Sec. n-Hexane Cyclohexane n-Octane 0.0757 0.0760 0.0710 0.0753 0,0744 0.0705 Diff. 0.0004 0 0016 0.0005 Theory, viscosity 0.0716 0.0726 0,0593 data usedb 0.0687 0.0697 0.0566 Diff. 0.0029 0,0029 0.0027 Theory, critical 0,0701 0.0744 0.0652 data usedb 0.0663 0.0699 0.0609 Diff. 0.0038 0.0045 0.0043 Method Experiment a1 data used"
(4).
Calculated using data from (9, 10).
VOL. 32, NO. 7, JUNE 1960
0
807
Table VI. Compound n-Hexane n-Hept ane n-Octane -N on ane n-Decane 1-Hexene 1-Octene Benzene TZ
Temperature Coefficient of Diffusion Coefficient Temperature Coefficient, n Temp. Range, Theory Theory O K. Exptl. (viscosity) (critical) 183.2-293.2 ... 1.96 1.96 183.2-323.2 1.95 1.95 1.90 1.90 293.2-323.2 1.56 2 ' 0 . 0 8 183.2-337.8 ... ... 1.91 290.0-337.8 1.2 ... 1.86 290.0-363.2 ... *.. 1.85 223.2-398,2 ... 1.96 2.01 223.2-423.2 1.85 ... 313.1-422.3 1.42 2 ' 0 . 2 1 ... ... 293.2-303.2 1.5 ... ... 313.2-370.2 1.6 ... ... 278.2-353.2 ... 1.91 1.91 300.1-334.0 2.00 1.93 1.91 303.2-334.0 1.95 1.93 1.91
able which will permit the calculation of the temperature coefficient from the theoretical equation, using viscosity data for 1-hexene, n-heptane, or ndecane, or using critical state data for 1-hexene, 1-octene, n-nonane, or ndecane. The standard deviations given for the experimental temperature coefficients of n-hexane and n-decane are based on calculation of the temperature coefficient throughout the temperature range and for pairs of temperatures within that range. The experimental temperature coefficients for the long-chain aliphatic hydrocarbons are consistently much smaller than those obtained from the theoretical equation for the diffusion coefficient. The extremely low temperature coefficient obtained experimentally for n-heptane is most curious. However, i t may be of consequence that the temperature dependence of the viscosity of n-heptane also is anomalous and that the anomaly is associated with the cigar-like shape of the n-heptane molecule (9). On the other hand, the agreement between esperiment and theory for the more compact hexagonally shaped planar benzene molecule is good. Very few data are available in the literature on the temperature dependence of the diffusion coefficient except for gas into gas diffusion of carbon dioxide into air and water vapor into air ( 1 4 ) . I n these cases, the agreement with the theoretical equation is good. However, Hirschfelder (9) has pointed out that the force constants for hydrocarbons obtained by the use of a relation n-hich involves two constants is unsatisfactory. Instead, a three-constant force model may be necessary. It also is generally true that the model used is not strictly applicable to nonspherically shaped molecules. The theoretical model tends to give low values for the diffusion coefficients for hydrocarbons and to overestimate 808
ANALYTICAL CHEMISTRY
the effect of varying carrier gas a t least for air, nitrogen, and oxygen. It also appears that a theoretical equation based on the interaction of spherical nonpolar molecules niay lead to overestimation of the magnitude of the temperature coefficients for long-chain hydrocarbons. Corrections for Turbulence a n d Surface Tension on Diffusion P a t h Length. T h e length of t h e diffusion tube, r+hich is not involved in t h e actual diffusional process u p the tube, can be calculated from the relationship Ax = - bD,, where Ax is the path length to be subtracted froni the measured path length to correct for shortening of the path due to penetration of the eddies to the uppermost portion of the tube, and for curvature of the liquid due to surface tension; where b is the slope of the line derived from the extrapolation equation l/D, = 1/D b/L; and where D is the actual diffusion coefficient given in Table 1V. Values of Ax for the hydrocarbons investigated are listed in Table VII, with the 95% confidence limits in these values. The confidence ranges in Ax are fairly wide because this parameter appears to be more sensitive to experimental uncertainties than is D . The values of Ax range from those which are essentially zero to a few values betnyeen 0.5 and 1.5 cm. No consistent relationship between Ax values and temperature or vapor pressure is evident. On the basis of two series of measurements a t different flow rates for benzene and nitrobenzene a t 25" C., Lee and Wilke (12) felt that the association of greater Ax values with substances of lon-er vapor pressure was indicated. Our data do not confirm such a relationship. When the flow rate of carrier gas is increased a t constant temperature and tube diameter, only a small effect of flow rate can be seen up to 2 liters per minute. For example, for n-decane a t 86.4' C. and with a tube diameter of 11 nini.,
+
a comparison of the values at 0.1, 0.5, 1.0, and 2.0 liters per minute s h o m only a small increase of Ax with flow rate. At 149.1' C. and a 11-mm. tube diameter, no appreciable difference exists between the values a t 0.1 and 1.0liter per minute. Similarlyat 50' C., n-hexane diffusing out of a n 11-mm tube s h o w no increase in Ax n i t h increasing f l o ~rate. Indeed, in this example, the Az values obtained cannot be distinguished from zero within the 95% confidence limits of these measurements. Consequently, flon- rates up t o 1 and possibly 2 liters per minute can be used without increasing Ax. K h e n Ax values a t constant temperature and flow rate are compared a t differing tube diameters no effect on Ax values from increasing the tube diameter is apparent in the range of diameters used. One might expect that turbulent effects would be aggravated at sufficiently large tube diameters. However, if so, the effect certainly must occiir a t tube diameters larger than those used in these experiments. As mentioned, the Ax values are composed of turbulent and surface tension effects. The surface tension effect is small. I n the present measurements a number of Ax values have most probable values of only 0.1 to 0.4 em. with the 95% uncertainty ranges including zero. Actual measurements of the distance from the bottom to the top of the meniscus of n-decane in 6- and 11-mm. tubes are 1.8 and 2.2 mm. Honever, the actual decrease in diffusion length, even if the total length is originally measured from the bottom of the meniscus, is less than 2 mm. This is because molecules evaporating from the portions of the curved surface between the bottom and top of the meniscus which touch the glass walls have less than 2-mm. shortening in diffusion distance to the top of the tube. The actual contribution from surface tension is often felt to be less than 0.1 mni., and surface tension generally will have a negligible effect on the diffusing path length of evaporating molecules. CONCLUSIONS
Diffusion cell measurements provide a method, experimentally simple and reproducible, for providing concentrations of vapors up to about 10,000 p.p.m. To achieve concentrations above the 10,000-p.p.m. range necessitates temperatures close to the boiling point or tubes of very large diameter. The objections to working under these experimental conditions in terms of vapor pressure errors and turbulent corrections may become too great t o justify use of the method in this range. The application of diffusion cells to
the production of concentrations below 10 p.p.m. and particularly below 1 p.p.m. may be more difficult. The limitation here is not in the diffusional method itself. Calibration in this concentration range in principle can be done by at least four alternative procedures. Unfortunately, the direct weight or liquid level determinations normally used involve inconveniently long calibration periods at diffusion rates below 10 y per minute. Diffusion rates in the vicinity of 10 y per minute necessitate several days of continuous running of the cell to obtain rreight losses large enough to permit accurate determinations of the rates. A diffusion cell can be used with a diffusion tube of appreciably larger cross-sectional area than the tube needed to obtain the trace concentration of interest but a t the same temperature, diffusional path length, and flow rate as the smaller tube. The diffusion rate is inrreased proportionately, thus reducing the calibration period. Because all variables except tube crosssectional area are held constant, the ratio of the diffusion rates equals the ratio of tube areas, and the diffusion rate in the smaller tube can be obtained simply and directly. It is assumed that the flow rate is maintained a t such a value that the correction for turbulence in the larger diffusion tube is small or negligible. If this is done, it is possible to vary the flow rate in the range below the maximum permissible rate when using the cell mith the smaller diffusion tube. Also, because the diffusion constant should be only slightly dependent on the diffusional path length under these conditions, in practice there is a t least a limited range of diffusion lengths over which it is safe to operate the cell mith the smaller tube. Another procedure is to use the literature value for the diffusion constant uitli the values for the other variables in the diffusion equation discussed earlier. However, one of these variables is the partial pressure of the liquid being diffused. Very low diffusion rates result in a considerable measure from small vapor pre,,swres. It is possible that the necessary vapor pressure data in the range of interest n-ill not be available. If this is the case, either lengthy extrapolations or enipirical approximations must be made t o obtain a vapor pressure value. Such espedients can only result in uncertainties and loner accuracies in the calculation of the diffusion rate. It also is possible to calibrate the cells by determining the amount of materials passing out of the cell, if a n appropriate chemical or physical analytiral method is available and applicable. Caution is necessary n-hen applying such methods. For example, i t
must be established independently t h a t the vapors are being collected n i t h high or a t least constant efficiency. It is felt t h a t these cells can be used a t flow rates from about 100 to 1000 to 2000 ml. per minute without appreciable turbulent effects. Higher flow rates niay be permissible under some circumstances. On the other hand, determinations near the boiling point may involve considerable turbulent behavior. Tube diameters from a fell- millimeters to a t least l cm. can be used n-ith equal facility. Tube diameters up to 2' em. may be justified under many circumstances. Filling problems and liquid films or droplets on the walls may make tube diameters under 1 or 2 mni. somen h a t objectionable. Surface tension effects, although ordinarily of slight importance, may be aggravated to an appreciable degree in very narroTT tubes. Although air vias used as a carrier gas in the present n-ork, the experimental data available indicate that the results can often be used interchangeably n i t h air, nitrogen, or oxygen. If helium, hydrogen, or argon is used as carripr gas, no simple correction permits t h e use of data obtained n i t h air, nitrogen, or oxygen. The theoretical diffusion equation of Hirschfelder et 02. (IO) can be used to obtain approximate
Table
VII.
values for hydrocarbons diffusing into these gases. Honever, the vide deviation of most hydrocarbons from the spherical shape used in the theoretical model limits the applicability of the theoretical relations. The diffusional method can be extended to any volatile organic materials such as aldehydes, ketones, esters, alcohols, acids, and halogenated hydrocarbons. Metal cells can be operated a t elevated temperatures in furnaces with materials n hich are essentlally nonvolatile a t loner temperatures. The limitations on the use of elevated temperatures are those imposed by thc accelerated rate of oxidation, decomposition, or rearrangement reactions n hich may occur n-ith many classes of molecules. Similarly, substances ~thicb are gases a t room temperature may be diluted by gas diffusion or by operatiiig a t reduced temperatures or by dissolving the gas in a medium in ahich i t is stable. Gordon, TT'ong-Woo, and Helnig (8) recently have discussed the application of diffusion to produce low concentrations of ozone, sulfur dioxide, and nitrogen dioxide by such methods. I n our laboratories me have used diffusion cells for a variety of purposes. The collection efficiencies of bubblers and impingers containing concentrated sulfuric acid have been determined for 1-hexcne using a diffusion crll to gen-
Nondiffusional Lengths, A x , Resulting from Turbulent and Surface Tension Effects
Compound n-Hexane
n-Heptane n-Decane
t,
a
c.
Diffusion Tube Diameter, Mm.
30.0 48 .5
8.20
16.8 64.6 39.9 60.5 86.4 86.4 86.4 86.4 86.4 86.4 86.4
7.85 3.20 11.08 11.07 3.40 7.85 7.85 11.07
118
149.1 149.1
Flow
Rate, Liters/ hlin.
7 8.5
11.08
11.08 11.07 7.85 11.07 11.07
0.1 0.1
0.5
0.5 2.0 2.0 2.0 0.1
0.5
1.0 2.0
0.5 0.1
1.0
3r i 95yo C.L.[I 0.40 2~ 0 . 6 0
0.44 i 0.29 0.04 i 0.30 0.38 i 0 . 4 3 0 . 0 8 =k 0.39 0.51 =t0.53 0.17 i 0.22 0.31 i 0.10 (-0.09) i 0.75 1.20 i 0.66 0.87 i 0.52 0.07 i 0.14 0.17 i 0 05 0.12 i 0.15 0.32 i 0.14 0.40 i 0 10 0.83 i 0.16 0.71 i 0 . 1 3
2--bIethyl-1,3-
butadiene 1-Hexene 1-Octene Benzene
15 20.0
30.0
40.0 97.0 26.9 30.0 60.8
a
3.20
3.20 11.08 11.08
11.07 11.07 11.07 11.07
0.5 0.5
0.5 0.5 0.5 0,276 0.275 0.26
0.55 i 0.08 0.26 i 0 . 6 1 0.11 i 0 . 2 3
0.10 i 0.13 0.34 f 0.12 0.04 i 0.21 0.05 =k 0.16 0.09 i 0.08
95% confidence limits.
VOL. 32, NO. 7, JUNE 1960
809
erate the olefin. The interference of benzene in the analytical method for the determination of olefin? in concentrated sulfuric acid has been determined by generating benzene and 1-hexene in two parallel diffusion cells, The sensitivity of a gas chromatographic detector to benzene a as measured by using a diffusion cell to prepare a benzene in helium gas mixture. The response of a mass spectrometer to several hydrocarbons in the 10- to 100p.p.m. range was ascertained by passing the hydrocarbon in air or nitrogen gas stream past the capillary inlet system of the mass spectrometer. Diffusion cells have also been used in a preliminary may to calibrate continuously monitoring instruments. Elsewhere (8) more extensive use of diffusion cells for the calibration of continuous monitoring colorimeters has been made. Diffusion cells have also been used in our laboratories and elsewhere (f9) to obtain approximate concentrations of odorants in very low concentration ranges. The use of diffusion cells has many advantages in terms of simplicity, reproducibility, and flexibility. The inacroscopic diffuqion eqnations should
be fairly exact. Equations based on simplified molecular models can be very useful in providing approximate diffusion rates when applied to molecules which do not fit the model used. Satisfactory diffusion rates can be calculated for systems which do fit the molecular model employed. Consequently, diffusion rates and diffusion coefficients can be determined using either completely empirical calibration or a theoretical calculation, n i t h a good degree of confidence in the method, if the limitations of each approach are understood. LITERATURE CITED
(1) Arnold, J. H., Znd. Eng. Chem. 22,
1091 11930’1.
(2, Chambeis, F. S., Sherwood, T. K., Zbid., 29, 1415 (1937). (3) Cumminas. G. A . h4.. RlcLauehlin. E.. Ubbelohdc A. R.. J . ’Chem. SYc. 1955:
1141. (4) Cummings, G. -4. M., Ubbelohde, A. R.,Zbid., 1953,3751. (5) Fair, J. R., Lerner, B. J., A . Z. Ch. E . Journal 2, 13 (1956). (6) Fortuin, J. M. H., Anal. Chim. Acta 15, 521 (1956). ( 7 ) Gilliland, E. R., Znd. Eng. Chem. 26, 681 11934). (8) Gordon,’ C. Ii;, Rong-Woo, H., HelLvvig, H. I,., Techniques for the
Calibration of Atmospheric Analysers. Production of Dilute Gas Streams by ’Diffusion,”Air Pollution Control Association Meeting, Los Angeles, Calif., June 1959. (9) Hirschfelder, J. O., Bird, R. B., Spots, E. L., Chem. Reus. 44, 205 (1949). ( l o ) , Hirschfelder,lrJ. O., Curtiss, C. F., Bird, R. B., Molecular Theory of Gases and Liquids,’’ Wiley, New Torlr, 1954. (11) International Critical Tables, Vol. V, pp 62-3, AIcGraw-Hill, XeTv York, 1928. (12) Lee, C. Y., Wilke, C. R., Znd. Eng. Chem. 46, 2381 (1954). (13) McKelvey, J. PIT., Hoelscher, H. E., - ~ N A L .CHEM.29, 123 (1957). (14) Reid, R. C., Sherwood, T. K., “Properties of Gases and Liquids,]’ hIcGraw-Hill, Xem York, 1958, pp, 274-*5 ~~.
(15) Stefan, J., Fien. Ber. ( 2 ) 63, 63 (1871); 65, 323 (1872); 68,385 (1873); 98, 1418 (1889). (16) Trautz, hl., Ludwig, O., Ann. Physik. [ 5 ] 7,887 (1930). (17) Trautz, ll., Rluller, IT., Zbzd., [5] 22,329, 333 i1935). (18) Trautz, &I., Res, W.,Zbid., [ 5 ] 8 , 163 (1931). (19) Turk, A,, J . Agr. Food Chem. 1, 306 (1953). RECEIVED for review November 9, 1959. Accepted March 10, 1960. Division of Water, Sewage and Sanitation Chemistry, 136th Aleeting, ACS, Atlantic City, K.J., September 1959.
Separation and Characterization of Polynuclear Aromatic Hydrocarbons in Urban Air-Borne Particulates EUGENE SAWICKI, WALTER ELBERT, T. W. STANLEY, T. R. HAUSER, and F. T. FOX Air Pollution Engineering Research, Robert A. Tuft Sanitary Fngineering Center, Public Healfh Service, U. S. Departmenf of Healfh, Education, and Welfare, Cincinnafi 26, Ohio
b A simplfiied procedure is described for the characterization of polynuclear hydrocarbons in air-borne particulates. The method involves one pass through a chromatographic column and subsequent ultraviolet, visible, and fluorescence studies on the fractions thus obtained. The final step then involves a destructive method of analysis -e.g., spectral analysis in sulfuric acid-or a color test. The ultravioletvisible absorption spectra of analogous fractions obtained from different communities are closely similar. In the air-borne particulates of some 100 communities pyrene, fluoranthene, benzo[a]fluorene and/or benzo[b]fluorene, chrysene, benz[ a ]anthracene, benzo[ alpyrene, benzo[ e] pyrene, benzo[ klfluoranthene, perylene, benzo[ g,h,i]perylene, anthanthrene, and coronene are found consistently. 810
ANALYTICAL CHEMISTRY
A
SIMPLE standardized
analytical procedure is badly needed for the separation and identification of polynuclear aromatic hydrocarbons in the air-borne particulates of urban communities. A method was developed which involves one pass of the benzenesoluble fraction through a chromatographic column and then appropriate fluorometric studies and color tests dependent on the ultraviolet spectrum of each fraction. The pioneering work of Falk in column chromatographic and ultraviolet spectral studies of polynuclear hydrocarbons ( 1 ) and the fluorometric work of Van Duuren in cigarette tobacco tar (10 ) have been invaluable in application to air pollution studies. Extensive use has been made of the recently described activation and fluor t w t m p spectral techniques to identify a
fluorescent hydrocarbon in a mixture (e), This new analytical methodology is derived from the fact that in many instances it is possible to obtain the pure fluorescence spectrum of an aromatic compound in a mixture by determining the fluorescence spectrum of the mixture at an appropriate activating v-ave length maximum of the aromatic compound. The methods herein presented have been applied to samples from over 100 communities, with excellent reproducibility of analytical results. COLUMN CHROMATOGRAPHY
Procedure. The methods for t h e collection of air-borne particulates and the extraction of the benzenesoluble material from these particulates, as ne11 as t h e equipment and materials for column chromatography, have been described ( 7 ) .
