ñiques may result in significantly different trace element concentrations. However, the trace element concentrations observed in this work provide a basis for estimating the contamination problems arising from the use of a wide variety of materials and reagents.
ACKNOWLEDGMENT The author wishes to acknowledge the capable assistance of Mrs. Ermel F. Briggs in performing much of the data processing and calculations.
Received tor review February 26, 1968. Accepted April 1, 1968. This paper is based on work performed under United States Atomic Energy Commission Contract AT(45-1)-1830. Many of the items compared in this report were commercial items that were not developed or manufactured to meet Government specifications, to withstand the tests to which they were subjected, or to operate as applied during this study. They are representative of typical items not necessarily inclusive of all those commercially available. Any failure to meet objectives of this study is no reflection on any of the commercial items discussed herein or on any manufacturer.
Diffusion Coefficients of Some Organic and Other Vapors in Air Downloaded via UNIV OF WINNIPEG on January 23, 2019 at 09:05:53 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
G. A. Lugg Defence Standards Laboratories, Maribyrnong, Victoria, Australia
Diffusion coefficients of 147 organic and other vapors diffusing into air have been determined at 25 °C and 760 mm. These values have been compared with the calculated figures from nine prediction methods. Approximately 75% and 70% of the diffusion coefficients calculated by the Chen and Othmer, and Wilke and Lee equations, respectively, were within ±5% of the mean observed values. The Hirschfelder, Bird, and Spotz equation is satisfactory for application to high molecular weight acids, alcohols, and esters. The other six equations have limited value for the estimation of diffusivity of the vapors of liquids into air.
served diffusion coefficients. However Scott (72, 13) has pointed out many of the values used in these comparisons were not in fact measured and some of the early experimental results need reevaluation. In this paper, diffusion coefficients determined experimentally at 25 °C and 760 mm are reported for a number of vapors of liquids diffusing into air, and these are compared with the values obtained from the available prediction methods.
EXPERIMENTAL
Many
require a dynamic system whereby known low concentrations of vapors can be maintained in an air stream. Methods commonly employed have been reviewed by Fortuin (7) who used for liquids diffusion cells either sealed at one end or connected to a reservoir (2, 3). In such gas kinetic systems, the rate at which one component will diffuse into another can be determined from the Stefan (4) equation provided the diffusion coefficient is known or calculable. Because the accurate experimental measurement of the diffusion coefficient is time consuming, relatively few values for organic vapors diffusing into air are available from the literature (3, 5-9). A number of equations have been proposed for the calculation of diffusion coefficients and several authors (8-77) have published reviews of predicted and obtoxicological
studies
(1) J. . H. Fortuin, Anal. Chim. Acta, 15, 521 (1956). (2) J. M. McKelvey and . E. Hoelscher, Anal. Chem., 29, 123 (1957). (3) A. P. Altshuller and I. R. Cohen, ibid, 32, 802 (1960). (4) J. Stefan, Ann. Physik, 41, 723 (1890). (5) W. P. Boynton and W. H. Brattain, “Interfusion of Gases and Vapors,” International Critical Tables, 1st ed., Vol 5, McGrawHill, New York, 1929, pp 62-3. (6) W. E. Forsythe, Ed., “Smithsonian Physical Tables,” 9th ed., Smithsonian Institution, Washington, D. C, 1954, pp 355-6. (7) F. Call, J. Sci. Food Agr., 8, 86 (1957). (8) R. E. Emmert and R. L. Pigford, “Perry’s Chemical Engineers’ Handbook,” 4th ed., McGraw-Hill, New York, 1963, Section 14, pp 19-23. (9) R. C. Reid and T. K. Sherwood, “The Properties of Gases and Liquids. Their Estimation and Correlation,” 2nd ed., McGrawHill, New York, 1966. (10) E. N. Fuller and J. C. Giddings, J. Gas Chromatog., 3, 222 (1965). (11) E. N. Fuller, P. D. Schettler, and J. C. Giddings, Ind. Eng. Chem., 58, 19 (1966).
1072
e
ANALYTICAL CHEMISTRY
Chemicals of the highest purity available were obtained and redistilled prior to use. Refractive index measurements were used as a confirmatory test for purity. Diffusion coefficient measurements were based on the method originally used by Stefan and subsequently modified by a number of workers (J, 14-16). Basically, the method involves passing a stream of carrier gas over the open end of a vertical, cylindrical, uniform-bore tube which contains the liquid. After a stationary state has been reached, the loss of liquid may be measured in a number of ways. The method adopted for this work was to note the rate of fall of the meniscus level by means of a cathetometer which could be read to
within 0.02 mm. Air containing less than
0.1 mg of water per cubic meter the carrier gas. The experiments were carried out at 25 ± 0.05 °C at normal atmospheric pressure and using an air flow of 100 ml minute-1 and a tube diameter of 0.517 cm. Some measurements with liquids of low diffusion rates were made using the method of Narsimhan (77) employing a wide diameter cell with a calibrated side arm inclined at 5° to the horizontal to reduce the time involved for measurements. Six determinations were made on each compound. For each determination, the liquid level was noted at various time intervals. The square of the diffusion path was plotted against the time in seconds and from the slope of the straight
was used as
(12) D. S. Scott, Ind. Eng. Chem. Fundamentals, 3, 278 (1964). (13) D. S. Scott and K. E. Cox, Can. J. Chem. Eng., 38, 201 (1960). (14) G. H. Hudson, J. C. McCoubrey, and A. R. Ubbelohde, Trans. Faraday Soc., 56, 1144 (1960). (15) C. Y. Lee and C. R. Wilke, Ind. Eng. Chem., 46, 2381 (1954). (16) J. F. Richardson, Chem. Eng. Sci., 10, 234 (1959). (17) G. Narsimhan, Trans. Indian Inst. Chem. Engrs., 8, 73 (1955-56).
line obtained, the diffusion coefficient was calculated according to the method of Desty (18) and corrected to 760 mm.
required data were available. The value of 28.967 (19, 20) for the molecular weight of air was used in each equation. In the equations of Arnold (21), Gilliland (22), Wilke and Lee (23), Hirschfelder, Bird, and Spotz (24), and Andrussow (25) a value of 29.9 cc/gram mole (26) for the molecular volume of air at its boiling point was employed. The molal volume of each compound at its boiling point (Vm), for use in the above five equations, was calculated according to the method of Le Bas (27) as summarized by Partington (28) and, wherever possible, using the molecular weight and density as well as the parachor and surface tension (29). Parachor values were obtained from Quayle (30) and most of the densities and surface tensions were obtained from Timmermans (31) and extrapolated when necessary to the boiling point. The equation of Fuller, Schettler, and Giddings (11) employs atomic diffusion volumes and was used for those compounds for which this data was listed by the authors. The atomic diffusion volume used for air was 20.1 (11). So as to simplify calculations by a computer an empirical expression for the Sutherland constant, as required by Arnold’s equation, was derived from the table given by the author as
0.0007468FmVll9(1.47Dfl
(1)
where 119 is the Sutherland constant for air and TB is the 0 boiling point, K, of the other component. The equations of Hirschfelder, Bird, and Spotz and Wilke and Lee use the force constants, collision diameter, (rAB) and collision integral, (Id). The collision diameter rAB
rA
+ 2
rB
(2)
(18) D. H. Desty, C. J. Geach, and A. Goldup in “Gas Chromatography, 1960,” R. P. W. Scott, Ed., Butterworths, London, 1960.
(19) F. Din, Ed., “Thermodynamic Functions of Gases,” Vol. 2,
Butterworths, London, 1956, p 39.
kT
where k is the Boltzmann COn-
—
ÍAB
Fuller and Giddings (10) have discussed nine methods for the calculation of diffusion coefficients of gaseous binary systems. Each formula was used for calculating the coefficients of as many of the compounds in Table I for which the
-
ID is a function of
(26).
PARAMETERS USED FOR THE PREDICTION OF DIFFUSION COEFFICIENTS
7.0168
where rA and rB are the collision diameters of air and the compound respectively; rA for this work was taken as 3.617
(20) P. N. Tverskoi, “Physics of the Atmosphere,” Israel Program for Scientific Translations, Jerusalem, 1965, p 16. (21) J. H. Arnold, Ind. Eng. Chem., 22, 1091 (1930). (22) E. R. Gilliland, Ibid., 26, 681 (1934). (23) C. R. Wilke and C. Y. Lee, ibid., 47,1253 (1955). (24) J. O. Hirschfelder, R. B. Bird, and E. L. Spotz, Trans. Am. Soc. Mech. Engrs., 71, 921 (1949). (25) L. Andrussow, Z. Elektrochem., 54, 566 (1950). (26) R. E. Treybal, “Mass Transfer Operations,” McGraw-Hill, New York, 1955, p 27. (27) G. Le Bas, “The Molecular Volumes of Liquid Chemical Compounds,” Longmans, Green, New York, 1915. (28) J. R. Partington, “An Advanced Treatise on Physical Chemistry,” Vol. II, Longmans, Green, New York, 1951, p 22. (29) S. Sugden, “The Parachor & Valency,” Routledge, London, 1930, pp 30-32. (30) O. R. Quayle, Chem. Rev., 53, 439 (1953). (31) J. Timmermans, “Physico Chemical Constants of Pure Organic Compounds," Elsevier, New York, 1950.
slant, T is 298.16 °K in this work and molecular interaction eAB
k
For air,
was
taken
_
^/(ía)
tAB is
the energy of
(Cfl)
(3)
(k) (k)
as 97.0
(26).
Although recent rules for deriving rB and
—
k
have been
given (32), these were not used as the data on which they were based were obtained from a restricted group of nonpolar, nonassociated substances. For this work rB was taken as 1.18 Vm (23) and
—
as 1.15 TB
(23) because these parameters
k were available for all compounds. In order to simplify computer calculations an empirical expression for ID was calculated from the tables given by Hirschfelder, Bird, and Spotz as 9.490
-
-
•^90.136
for
TB
4
(f)’
-
4.38
+
9.6398
(4)
in the range 273 to 673 °K.
The equations of Chen and Othmer (33), Othmer and Chen (34), and Slattery and Bird (35) employ critical parameters and the number of diffusion coefficients which were calculated was limited by the data available (9, 36). The critical values used for air were 132.45 °K, 37.2 atm and 89.4 cc (9). Othmer and Chen also use as a factor the viscosity of air at the diffusion temperature; the value employed was 0.01843 centipoise which was calculated from National Bureau of Standards Circular 564 (37). RESULTS AND DISCUSSION
The values of the diffusion coefficients determined experimentally are listed in Table I. The results show that the diffusion coefficients for position isomers are in the order o- > p- > m- and for chain isomers in the order iso- > n- for most groupings. Of 21 sets of structural isomers, 6 have diffusion coefficients differing by more than 5 %. Values for three compounds in Table I have been determined recently at 298 °K by Altshuller and Cohen (3). The diffusion coefficient they obtained for methyl alcohol was within 1 % of the value shown in Table I, but their values for hexane and toluene were more than 5% higher. However, their gravimetric procedure was less precise than the method described above. Diffusivities for the above three com-
(32) L. S. Tee, S. Gotoh, and W. E. Stewart, Ind. Eng. Chem. Fundamentals, 5, 356 (1966). (33) N. H. Chen and D. F. Othmer, J. Chem. Eng. Data, 7, 37 (1962). (34) D. F. Othmer andH. T. Chen, Ind. Eng. Chem. Process Design Develop., 1, 249 (1962). (35) J. C. Slattery and R. B. Bird, A. I. Ch.E. Journal, 4, 137 (1958). (36) K. A. Kobe and R. E. Lynn, Jr., Chem. Rev., 52, 117 (1953). (37) “Tables of Thermal Properties of Gases,” National Bureau of Standards Circular 564, U. S. Government Printing Office, Washington, D. C, 1955, pp 10—11, 69.
VOL 40, NO. 7, JUNE 1968
·
1073
Table I,
Observed and Calculated Diffusion Coefficients 25 °C and 760 mm
10=
X Diffusion coefficient cm2sec_1
102
X Diffusion coefficient cm2sec -I
Calculated
Compound
Observed StanMean dard of deviasix tion
Calculated
Wilke
felder,
and
Chen and
Bird, &
Lee
Othmer
Spotz
8.44 7.53 6.31
8.26 7.33 6.04
8.42 7.32 6.16
Pentane Hexane Octane
0.182 0.066 0.169
Diacetone alcohol 2-Ethyl-1butanol Hexyl alcohol Methyl-2pentanol
Aromatics Benzene
9.32 8.49
0.149 0.114
8.83 7.83
8.70 7.68
Toluene Phenylethylene Ethylbenzene o-Xylene m-Xylene p-Xylene Mesitylene
7.01 7.55 7.27 6.88 6.70 6.63
0.076 0.076 0.036 0.101 0.040 0.064
7.23 7.09 7.06 7.10 7.38 6.49
6.90 6.93 6.88 6.86
zz-Propylbenzene
6.69
0.098
6.51
6.23
benzene Pseudo-
6.77
0.056
6.53
6.24
cumene
6.42 6.30
0.029 0.028
6.48 6.06
and Lee
Chen and
Othmer
&
Spotz
5.71
0.031
5.68
p-Cymene
toluene
benzene
Nitrobenzene
Aniline
0.071 0.201
6.93 6.91
6.33 6.30
6.18
0.063
7.00
6.39
5.54
0.041
6.37
6.23
5.81
5.06
0.057
5.93
5.77
5.41
6.94 9.22 9.18
0.107 0.057 0.080
6.72 8.67 8.79
8.88 8.76
6.83 5.36
0.051 0.049
7.17 6.03
7.06
10.49
0.057
10.32
10.18
9.03
0.027
8.92
8.75
7.93 7.60 6.02
0.061 0.015 0.019
7.92 7.33 6.06
15.30 12.35
0.154 0.150
12.86 10.46
10.91
9.52 7.75
0.083 0.070
8.96 7.92
9.18 7.99
7.85
0.065
7.96
8.00
zz-Caproic acid
6.53 6.02
0.279 0.106
7.18 6.56
6.56 5.98
Iso-caproic acid
5.96
0.038
6.55
5.97
10.90
0.088 0.086
11.02
11.19
9.76
9.42
9.44
9.78
0.152
9.41
9.46
8.61
0.140
8.31
8.25
8.62
0.132
8.30
8.30
8.31
0.081
8.29
8.24
7.10
0.025
6.91
7.84
0.179
7.49
7.66
0.376
7.49
7.45
0.092
7.47
ethylether
p-Dioxan Diethylether Iso-propylether zz-Butylether
5.89
Ketones Acetone ketone
Methylpropyl7.12
0.063
ketone
7.18
Mesityl oxide Iso-phorone
7.47 7.21 7.35
0.186 0.021 0.089
7.69 7.07 7.73
7.13
0.059
6.91
6.88
0.025
6.98
acid zz-Butyric acid
6.45
0.094
6.97
Iso-butyric
6.21
0.027
6.97
acid Iso-valeric acid
7.54
.
Avida
8.04
Formic acid Acetic acid Propionic
5.83
0.038
5.72
Aliphatic Esters 15.20 11.81 10.21
0.155 0.128 0.035
14.85 11.57 10.12
14.85 11.79 10.27
9.93
0.074
9.71
9.89
Methyl formate Ethyl formate Methyl
zz-Propyl
alcohol Iso-propyl alcohol
6.21
Dichloro-
Alcohols
Methyl alcohol Ethyl alcohol Allyl alcohol
6.56
Methylethyl-
p-Chlorotoluene Toluene-2,4diisocyanate
6.18
Ethers
zzz-Chloro-
toluene
6.78
alcohol
Benzyl
chloride o-Chlorotoluene
0.038
alcohol
Substituted aromatics Benzyl alcohol Chloro-
6.47
zz-Octyl
p-fm-Butyl-
acetate
Ethyl 10.13
0.392
zz-Butyl
9.79
9.92
8.61
0.092
8.47
8.53
8.80
0.165
8.52
8.60
8.91
0.070
8.56
8.67
see-Butyl
tert- Butyl
alcohol Amyl alcohol sec-Amyl alcohol
Wilke
Hirschfelder, Bird,
zz-Heptyl
Iso-propyl-
alcohol
Observed StanMean dard of deviasix tion
Alcohols
Aliphatics
alcohol Iso-butyl alcohol
Compound
Hirsch-
acetate
Methyl propionate Propyl formate Ethyl cyanoacetate
8.73
0.008
8.65
7.16
0.233
7.58
6.93
7.28
0.064
7.66
7.00
zz-
Iso-butyl formate Ethyl propionate Methyl-zibutyrate
7.23
7.38 (Continued)
1074
·
ANALYTICAL CHEMISTRY
Table I.
(Continued)
25 °C and 760 mm 10*
X Diffusion coefficient cm*sec-1
10*
X Diffusion coefficient cm*sec-1
Calculated
Compound
Observed StanMean dard of deviasix tion
Wilke and Lee
Chen and
Othmer
Calculated
Hirschfelder, Bird,
Compound
Mean
of
dard devia-
Spotz
six
tion
and Lee
8.28 7.67 8.88
0.063 0.115 0.187
8.09 7.59 9.00
9.53
0.063
9.46
10.37
0.490
10.36
7.97
0.023
7.44
8.75
0.023
8.25
6.73
0.036
6.63
7.22
0.041
7.15
7.94
0.077
7.94
7.92
0.071
7.88
8.26
0.064
7.82
9.19
0.081
9.02
8.79
9.07 9.89
0.027 0.106
8.88 9.58
9.05 9.29
6.86 9.75
0.037 0.052
6.52 9.50
9.29
7.94
0.147
7.87
8.75
0.044
8.40
9.14
0.077
8.46
8.68
0.082
7.73
8.78
0.119
7.79
10.05
0.381
9.95
8.79
0.025
8.69
7.30
0.071
7.17
5.90
0.059
5.85
8.84
0.058
8.87
7.88
0.046
7.89
6.10
0.053
6.21
7.48
0.078
7.52
7.42
acetate
7.68
0.098
7.48
7.34
7.70
0.103
7.53
6.63
0.129
6.81
6.84
Dichloro-
6.75 6.72
0.048 0.072
6.84 6.82
6.78 6.71
Tetrachloro-
n-Amyl formate Iso-amyl formate «-Butyl acetate Iso-butyl acetate
Ethyl-nbutyrate Ethyl-isobutyrate Methyl valerate Ethyleneglycolmonoethyl-
Carbon tetrachloride Bromoform
Chloroform Bromochloromethane methane
«-Amyl acetate
«-Butyl propionate Iso-butyl propionate Ethyl valerate Methyl-«-
ethylene
6.90
0.176
6.86
6.58
6.69
0.041
6.84
6.52
6.75
0.074
6.88
6.54
6.65
0.026
6.82
6.54
ethylene Pentachlorethane 1,1,2,2-Tetrachlorethane 1.1.1- Trichlorethane 1.1.2- Trichlorethane Ethylenedibromide 1,1-Dichloroethane 1,2-Dichloro-
6.10
0.026
6.45
6.10
0.037
6.32
6.08
0.029
6.32
6.11 6.03
0.022 0.144
6.35 6.31
ethane
Ethyl bromide 1,2-Dibromo3-chloro-
6.21
propane
Allyl chloride
6.10
0.018
6.30
6.10
0.048
6.32
6.17
6.22
0.130
6.35
6.21
6.38
0.100
6.40
5.59
0.070
5.89
5.59
0.069
5.92
5.76
5.39
5.51
0.179
5.94
5.80
5.41
5.56
0.065
5.89
5.36
4.86
0.112
5.53
5.04
4.96
0.078
5.62
5.12
4.94
0.097
5.58
5.08
6.00
0.016
6.03
4.97
0.033
4.84
phthalate
4.21
0.042
4.13
Diisooctyl phthalate
3.37
0.060
3.29
caproate n-Propyl-n-
butyrate n-Propyl-isobutyrate Iso-propyliso-butyrate n-Amyl propionate Iso-butyl-nbutyrate Iso-butyl-isobutyrate n-Propyl-nvalerate n-Amyl-«butyrate «-Amyl-isobutyrate Iso-butyl valerate
Aromatic Esters Benzyl acetate
Diethyl phthalate
Dibutyl
Chen and
&
Othmer
Spotz
7.87
Trichlor-
ether acetate
Hirschfelder, Bird,
Halogen hydrocarbons
Methyl-isobutyrate «-Propyl acetate
Wilke
&
Aliphatic Esters
Iso-propyl
Observed Stan-
Propylene
5.37
dichloride «-Propyl bromide Iso-propyl bromide «-Propyl iodide Iso-propyl iodide Glycols Ethyleneglycol Propyleneglycol Diethyleneglycol Triethyleneglycol Ethyleneglycolmono-
methylether Ethyleneglycolmono-
ethylether Diethyleneglycolmono-
ethylether
(Continued)
VOL 40, NO. 7, JUNE 1968
·
1075
Table I.
(Continued)
Table II.
25 °C and 760 mm
X Diffusion coefficient cm!see_1
102
L, D.
Calculated Observed Stan-
Compound
of
dard devia-
six
tion
Mean
Wilke and Lee
Chen and
Othmer
Hirschfelder, Bird,
P.
Deviation of the Calculated Results from the Observed
Molar volume calculated from additive volumes of Le Bas Molar volume calculated from molecular weight and density Molar volume calculated from parachor and surface tension
&
% Deviations
Spotz
—
Amines and
No. of
amides
10.09 8.72
0.201 0.231
9.61 8.44
9.00 9.93 7.54
0.114 0.050 0.045
8.49 8.51 6.93
9.73
0.079
8.78
10.59
0.032 0.020
10.47 7.31
Iso-butylamine
Diethylamine Triethylamine Dimethylformamide
Equation
7.10
Benzonitrile
Triethyl
0.016
5.52
phosphate
Tributyl
0.044
4.32
phosphate Tetraethylpyrophosphate Bis-2-ethylhexyl phosphate
observed
Mean
tion
mean
4.35 4.38 4.10
55.8 53.8 45.5
22
L P
147 91 22
9.41 10.39 8.13
5.21 5.37 4.88
27.2 18.7 36.4
L D
147 91
9.37
and Spotz
P
22
4.43 4.77 3.62
16.3
10.20 7.76
22.7
Wilke and Lee
L D P
147 91 22
4.25 4.30 5.00
4.31 4.09 4.60
70.1 71.4 68.2
L D
147 91
P
22
7.28 8.07 6.19
4.64 4.72 3.17
33.8 29.7 31.8
134 68 66 66
7.55 7.36 3.90 8.33
6.29 6.35 3.49 4.62
42.5 47.1 75.8 25.8
Hirschfelder, Bird,
5.52
4.75
0.030
4.74
3.94
0.046
3.81
4.38
0.116
3.64
of
devia-
P
Gilliland
Andrussow
4.23
±5%
5.45 5.72 5.84
8.31
Inorganic esters
within
147 91
6.90
7.13
pounds
results
L D
Arnold
Nitriles
Acrylonitrile
dard
com-
Ethylenediamine n-Butylamine
%of
from calculated
observed means (n 6) Stan-
Fuller, Schettler, and Giddings Slattery and Bird Chen and Othmer Othmer and Chen
D
9.9
Tri-orthocresol phosphate
Miscellaneous
Bromine Carbon disulfide
Chlorpicrin
10.64
0.072
10.33
10.54
10.45 8.11
0.121 0.096
10.46 7.58
10.71
9.64
0.036 0.031
12.49
Ethylene-
chlorhydrin Mercury
14.23
8.66
9.35
were also available at temperatures other than 298 °K Diffusion coefficients calculated for 298 °K, using the kinetic theory expression
pounds (5).
to
II
to
'(f)'Y—) (760)
(5)
n is 2 (38) for these compounds, gave agreement within 5% of the observed results. The entropy equation of Usmanov and Berezhnoi (39), claimed to have an accuracy of ±1.2%, could not be used because of lack of data. Table II lists for each of the nine equations the number of compounds for which calculations were made, the mean per mean observed)/ cent deviation expressed as [(calculated
where
—
(38) R. C. Roberts, “American Institute of Physics Handbook,”
McGraw-Hill, New York,
1957.
(39) A. G. Usmanov and A. N. Berezhnoi, Russ. J. Phys. Chem. English Transí. 37, 85 (1963).
1076
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ANALYTICAL CHEMISTRY
mean observed] X 100, the standard deviation of the per cent deviations, and the per cent of calculated results within ±5% of the observed mean values. The table also shows these figures for the five equations from which the diffusion coefficients were also calculated using molar volumes derived from the densities and parachors. In all three methods of deriving the molar volumes, the mean deviations of the calculated diffusion coefficients from the observed values were not significantly different (probability 0.05). The Le Bas method of obtaining the molar volume is therefore preferred as it allows the diffusion coefficient of any compound to be calculated. Table II shows that all equations except those of Chen and Othmer, and Wilke and Lee gave deviations from the means of the observed values greater than ±5% and therefore have limited value for calculating the diffusion coefficients of vapors of liquids diffusing into air. The Chen and Othmer equation gave the lowest deviations from the means of the observed values with 75.8% of the calculated results within ±5% of these means. There is, however, poor agreement with the determined values for aromatics, amines, and C7, C8 acids (Table I). The Wilke and Lee equation gave approximately 70% of the calculated results within ±5% of the observed values. It has the advantage that it can be used for the calculation of the diffusion coefficients of all compounds. When calculations using this equation were confined to the smaller number of compounds used for the Chen and Othmer equation, the number of calculated results within ±5% of the determined values was increased to 79%.
Classes of compounds giving poor agreement with the determined values using the Wilke and Lee equation were C8-C9 aliphatic esters, C5-C6 acids, and C5-Cs alcohols (Table I). For these relatively higher molecular weight compounds, the Hirschfelder, Bird, and Spotz figures were in closer agreement with the determined values.
ACKNOWLEDGMENT The author is indebted to G. L. White for advice and M. W. Jarvis for aid with computer programs.
Received for review November 9, 1967.
Accepted February
2, 1968.
Spectral Distribution of X-Ray Tubes for Quantitative X-Ray Fluorescence Analysis J. V. Gilfrich and L. S. Birks U. S. Naval Research Laboratory, Washington, D. C. 20390
Spectral distributions were measured for W, Mo, Cu, and Cr target X-ray spectrographic tubes, for use with a direct mathematical method of quantitative X-ray fluorescence analysis. Operating voltages ranged from 15 to 50 keV but not for all targets. There are three important features of the spectra common to all target materials: there is a jump in the continuous spectrum at the characteristic absorption wavelength of the target material; there is an unexplained secondary peaking of the continuum which varies in wavelength with target material but is always present; the characteristic radiation contributes an appreciable part of the total intensity, the extremes being 24% for L lines of W and 75% for K lines of Cr. A Cu target the X-ray diffraction tube was examined to measure effect of the X-ray emergence angle on spectral distribution. The most noticeable effect was a two- to three-fold decrease in continuum intensity just on the short wavelength side of the CuK absorption edge. There is a trend in quantitative X-ray spectrochemical analysis to substitute mathematical analysis for comparison standards in correcting for interelement effects {1-3). The most general mathematical approach (4) requires knowledge of the spectral distribution of the primary radiation for the X-ray tube used to excite the specimens. Existing theory (5, 6) and experiment (1) H. J. Beattie and R. M. Brissey, Anal. Chem., 26, 980 (1954). (2) L. S. Birks, “X-Ray Spectrochemical Analysis,” Interscience, New York, 1959, pp 58-62. (3) R. J. Traill and G. R. Lachance, Geological Survey of Canada, Ottawa, Canada, Report No. 64-57 (1965). (4) J. W. Criss and L. S. Birks, Anal. Chem., 40, 1080 (1968). (5) D. L. Webster, Phys. Rev., 9, 220 (1917). (6) . A. Kramers, Phil. Mag., 46, 836 (1923).
Table I.
Operating Conditions for Measurements X-ray take-off
Target W
Cr Mo Cu Cu
Tube type OEG-50
OEG-50 OEG-50 OEG-50
Diffraction
Window
angle
20°
1
20° 20° 20° 3°
0.25 mm Be 1.0 mm Be 1.0 mm Be Mica-Be
mm Be
Voltage 50 35 25
kVp kVp kVp 15 kVp 45 kV(c.p.) 45 kV(c.p.) 45 kV(c.p.) 45 kV(c.p.) 45 kV(c.p.)
Figure 1.
Schematic of experimental arrangement
(7, 8) are not sufficiently accurate for predicting either the exact slope of the continuous spectrum or the relative contribution from the characteristic lines of the X-ray tube target element. Therefore, it is necessary to measure the required spectral distributions experimentally for the conditions which prevail in analysis. Particularly it is necessary to measure various standard X-ray target elements for standard operating conditions of voltage, etc.
EXPERIMENTAL The measurements were made on a modified single-crystal X-ray spectrometer shown schematically in Figure 1. Radiation from the X-ray tube passes through the slit system, is diffracted by a LiF crystal and measured with a gas-flow proportional counter using P-10 gas. The slit limits the beam width so that the crystal will intercept the entire beam even at the smallest diffraction angle of 4.5° . The tubular collimator merely serves to limit the fanning divergence on the crystal. A knife edge shields the detector from radiation scattered by the slit edges. Spectral intensity was measured from the short wavelength limit, which varies from 0.25 to 1.0 A depending on tube voltage, up to 2.5 or 2.8 A. Counting circuitry consisted of a multichannel analyzer for visual examination of the com(7) C. T. Ulrey, Phys. Rev., 11, 401 (1918). (8) H. Kuhlenkampff, Ann. Physik, 69, 548 (1922). VOL. 40, NO. 7, JUNE 1968
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