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PRO-TEKTM ORGANIC VAPOR G-AA AIR MONITORING BADGE NO. 2
TECHNICAL BULLETIN CALCULATED DIFFUSION COEFFICIENTS
If sampling rates for your particular compound are not available in the PRO-TEKTM Calculation Guide, they can be determined by using a calculated value for the diffusion coefficient from the Gilliland equation*11*2' or other equations*3' and the value of 14.8 cm for the badge (See Page 2, PRO-TEKTM Calculation Guide). It should be recognized, however, that sampling rates determined from calculated rather than experimental diffusion coefficients can be in error by as much as 20% (see sample calculations). The use of calculated diffusion coefficients is recommended where no good experimental data exist, but, where possible, reliable experimental data should be determined.
The Gilliland equation is expressed as follows:
/ \2 1 1 1/2
D, -- = 0.0043 xTMx --+-- sec \Ma Mb / (VA1/3 + VB1/3)2 xP
where MAand MB are the molecular weights of the air and the contaminant gas, and VA and VB are the molar volumes at the boiling point. Assuming the molar volume for air is 29.9 cm3/gmole*2' and T = 298K, P = 1 atmosphere and MA = 29.0 the equation can be reduced to the following:
D = 22.120 x /-j- +0.0345 V Mb
(3.103+ VB1/3 )2
Molar volumes can be estimated for organic compounds through the use of Kopp's law of additive columns with the rules and values for each element given by Le Bas*4'*5'. These values and rules are summarized in Table 1.
^'Gilliland, E. R., Ind. Eng. Chem., 26, 681 (1934). *2'Nelson, G. O., Controlled Test Atmospheres, Ann Arbor Science Publications, 1971, p. 133. *3'Reid, R. C. et al.. The Properties of Gases and Liquids, McGraw-Hill, 1977, pp. 544-601. *4'Arnold, Ind. Eng. Chem.,22, 1091 (1930).
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1 'Reid, R. C., et al., The Properties of Gases and Liquids, McGraw-Hill, 1977, p. 58.
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P
52
E-28616
January, 1980
A
Element Carbon Oxygen Chlorine Iodine Hydrogen Bromine Sulfur Fluorine
TABLE 1 LE BAS ADDITl viTY VALUES AND RULES
MOLAR VALUES = S ATOMIC VOLUMES
Atomic Volume 14.8 7.4 24.6 37.0 3.7 27.0 25.6 8.7
Oxygen in Aldehydes and Ketones
Methyl esters Methyl ethers
High esters and ethers
Acids
00 II II R--C--H, C-C-C
0| | CH3-O-C-R
CH3-0-C-R
0 (Cn-Hn)-C-0-(CnHn). (Cn--Hn)--C--0--(CnHn)
0| | R-C-OH
Nitrogen in Double and triple bonded In primary amines In secondary amines
R--N"N--CR, C=N R~NH2 R-NH-R
Special Rules: (1) Deduct 6 for three-membered ring. (2) Deduct 8 for four-membered ring. (3) Deduct 11.5 for five-membered ring. (4) Deduct 15 for six-membered ring. (5) Deduct 30 for naphthalene ring.
Definition: R -- CnHn+2 or CnHn or CnHn--j
7.4
9.1 9.9
11.0
12.0
15.6 10.5 12.0
R&St 66306
Table 1 (CONTINUED)
Examples (Molar Volume): Benzene, C6 H6; MW = 78 Molar Volume = 6 x 14.8 + 6 x 3.7 -- 15 = 96.0 Acrylonitrile, CH2 CHCN; MW = 53 Molar Volume = 3 x 14.8 + 3 x 3.7 + 15.6 = 71.1 Amyl acetate, CH3 COO (CH2)4 CH3; MW = 130 Molar Volume = 7x 14.8 + 14 x 3.7 + 2x9.1 - 173.6
Examples (Diffusion Coefficients):
Benzene
/1 crrr
D = 22.120 x /-- + 0.0345 = 0.0815-----
V 78
sec
(3.103+ 96.01'3)2
Acrylonitrile cm'
D = 22.120 x 71.1 x 0.0345 = 0.0928 sec
(3.103 + 71.1l/3)2
Amyl acetate
D = 22.120 x /-U + 0.0345 = 0.0603 --
v 130
sec
(3.103+ 173.61/3)2
Comparison with experimental values [Lugg, G. A., Anal. Chem.,40, 1072 (1968)] are shown in Table II.
Compound Benzene Acrylonitrile Amyl Acetate
TABLE II CALCULATED VS. EXPERIMENTAL
DIFFUSION COEFFICIENTS
Calc. 0.0815 0.0928 0.0603
Exp. 0.0932 0.1059 0.0610
% Deviation From Exp. -14 -14 -1
R&S166307
For more information on Du Pont's PRO-TEKTM badge system, contact: E. I. du Pont de Nemours & Co. (Inc.)
Fabrics and Finishes Department Applied Technology Division Concord Plaza -- Clayton Bldg. Wilmington, DE 19898 Phone (302) 772-5989
NOTICE The recommended procedures and product performance described herein have been developed and are the result of primary research completed by Du Pont, as well as the current state of the art knowledge. The systems are designed to be used under the supervision of knowledgeable technicians and the Du Pont Company does not offer any warranty expressed or implied for the products or their performances. Further, Du Pont does not assume liability and will not be responsible for any injuries or damage to persons or property which result from the improper use of this system.
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