Calculation of Weight Per Cent Ring and Number of Rings per Molecule for Aromatics 31. R. LIPKIN AND C. C. JIARTIN, Sun Oil Company, Norwood, Pa.
Per cent ring and aierage number of rings per molecule for mixtures of alkyl aromatic hydrocarbons are determined from density and density coefficient, which may be derived from mid-boiling point and density. The methods have been found accurate, on pure compound data, within 39’0 ring and 0.1 ring per molecule. Aromatics with naphthenic or olefinic side chains cause some interference but are usually not present in sufficient concentration to affect significantl? the accuracy of the methods for petroleum fractions boiling below 400’ C.
T
HIS paper continues the general investigation in this laboratory of the temperature coefficient of density for hydrocarbons, and the relation of this physical property to other physical properties and to hydrocarbon structure. .1 series of papers on the temperature coefficient of density has now been presented. This particular paper is concerned with methods for the analysis of aromatics for number of rings per molecule and for proportion of ring and side chain. The first paper in the density coefficient series related this property to molecular v-eight-a single curve was found applicable to nearly all hydrocarbons. Recently Grisrold and Chen (6) have developed separate relationships for the different classes of hydrocarbons. For practical purposes, there is little difference between the relationships except for benzene and toluene. Since toluene and especially benzene are usually present in small concentrations in petroleum products. the general correlation (11) is satisfactory for most purposes. The small differences in density coefficient betv-een hydrocarbon classes do not affect the later correlations in this series because the temperature coefficient of density is not determined experimentally, but is derived from approximate molecular lyeight in both the derivation and application of these correlations. By plotting density coefficient against density, there n-as developed a hydrocarbon class “map” which showed linear relationships for paraffins and for naphthene rings without side chains. d similar hydrocarbon class “map” was developed by plotting the temperature coefficient of density against refractive index. Vsing these maps, it, was possible to develop methods for determining the proportion of ring and chain in mixtures of paraffins and naphthenes ( I d ) , and an equation relating density, refractive in-
0
I
1
I
RIKG-CHAIN A S A L Y S I S
Derivation. The first method, analysis of aromatics for proportion of ring and chain, is similar to the method of ring-chain analysis developed for naphthenes. Per cent ring is defined as 100 times the number of ring carbon atoms divided by the total number of carbon atoms. The method was developed from the hj-drocarbon class map shown in Figure 1. I n this figure, aromatics with no side chain are shown in addition to the paraffin and naphthene ring lines s h o m in a previous paper (14). .3 noncondensed aromatic ring line is drawn through the points for benzene and diphenyl, and a condensed aromatic ring line branching from this line is drawn through the points for naphthalene and phenanthrene. The addition of side chain to an aromatic ring causes the properties to approach those of a paraffin of infinite molecular weight, and the distance of approach is approximately proportional to the percentage of chain. There are few aromatics viithout side chain on v.-hich reliable densities are reported in the liquid state, because the melting points of these compounds are so far above room temperature. (Anthracene and the terphenyls are among those aromatics on which no liquid densities are available.) The densities of the high-melting aromatics used in Figure 1 viere corrected to 20”, using the correlation of Lipkin and Kurtz (11).
ics, Figure 3 for the noncondensed typp, and Figure 4 for the average mixture assuming an
50v)
w
dex for the D line of sodium, and the temperature coefficient of density (1W). This equation permits the calculation of the refractive index of paraffin-naphthene mixtures with an accuracy nearly that of the Abbe-type refractometer. When aromatics or olefins are present, the calculated refractive index is lower than the experimental value, and the specific dispersion is a linear function of the difference ( I S ) . The hydrocarbon class map obtained on plotting density against the temperature coefficient of density is the basis for the two methods of analysis developed in this paper: analysis of aromatics for proportion of ring and chain and for number of rings per molecule.
1
1
ANALYTICAL CHEMISTRY
184 Coordinates for Construction of Figure 2
Table I.
(For condensed ring aromatics. 0% ring point: d = 0.856; A = 55.2) Radial Lines Drawn from 0% Ring t o Following Points: NO.
S O .
of rings 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
d 0,857 0.883 0.909 0.934 0.960 0.986 1.012 1.037 1.063
A 95.0 95.0 95.0 95.0 95.0 95.0 95.0 95.0 95.0
Table 11. Coordinates for Construction of Figure 3 (For noncondensed ring aromatics. 07; ring point: d = 0.856; A = 55.2) Radial Lines Drawn from 0% Ring t o Following Points: ' 50.
of rings 1.8 1.9 2.0 2.2 2.4 2.6 2.8 3.0
KO.
~~
d 1,089 1.114 1.140 1.140 1,140 1,140 1,140 1.140
A 95,o 95.0 95.0 87.7 82.7 79 1 76.2 74.0
of rings 0.9 1.0 1.1 1.2 1.3
1.4 1.5 1.6 1.7
Intersections of Per Cent Ring Lines with Radial Lines With 1 . 5 With 3.0 With 1.0 ring line ring line ring line % ring A A A 73.8 94.5 84.9 100 72.0 82.0 90 90.8 70.1 79.0 87.0 80 68.2 76.0 70 83.3 66.4 73.0 60 79.3 so 64.5 70.1 75.4 .. 62.6 67.1 71.4 40 6 0.7 6 4 . 2 30 67.4 58.8 61.3 63.4 20 57.0 58.3 59.4 10
d
A
0.854 0.883 0.912 0.941 0,970 0,999 1.028 1.056 1.085
95 0 95 0 95 0 95 0 95 0 95.0 95 0 95 0 95.0
of rings
d
A
1.8 1.9 2.0 2.2 2.4 2.6 2.8 3.0
1.114 1.143 1.140 1.140 1,140 1.140 1.140 1.140
95.0 95.0 91.0 85.5 81.5 78.4 76.0 74.0
Intersections of Per Cent Ring Lines with Radial Lines With 1.0 With 1.5 With 3.0 ring line ring line ring line 70 ring A A A 83.0 80.2 77.5 74.8 72.0 69.2 66.4 63.6 60.8 58.0
94'. 5 90.8 87.0 83.3 79.3 75.4 71.4 67.4 63.4 59.4
100
90 80 70 60 50 40 30 20 10
70.0 68.4 67.0 65.5 64.0 62.5 61.0 59.6 58.1 56.6
Table 111. Coordinates for Construction of Figure & (Average for condensed and noncondensed ring aromatics. 0% ring point: d = 0.856; A = 55.2) Radial Lines Drawn from 0% Ring t o Following Points:
-
3
50t
NO. of rings 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
,
I
085
090
I
I
I
095 I00 105 D E N S I T Y AT 2 O ' C
I
I
110
115
of rings 1.8 1.9 2.0 2.2 2.4 2.6 2.8 3.0
A 95.0 95.0 95.0 95.0 95.0 95.0 95.0 95.0 95.0
A 95.0 95,o 92.8 86.5 81.9 78.6 75.9 74.0
d 1,102 1,130 1,140 1.140 1.140 1.140 1.140 1.140
Intersections of Per Cent Ring Lines with Radial Lines With 3.0 With 1.0 W i t h 1.5 ring line ring line ring line % ring A A A
Figure 2. Rings per RIolecule and Weight Per Cent Ring for Condensed Ring Aromatics
single carbon-to-carbon bond or separated by one or more carbon atoms.) The data necessary for the construction of Figures 2, 3, and 4 are given in Tables I, 11, and 111, respectively. I n the derivation of these figures, the 100% ring lines are slightly different from those shown in Figure I, because adjustment was necessary to fit the data for the aromatics containing paraffinic side chains. The density of the limiting paraffin point used in this paper is slightly different from the value used previously ( 2 4 ) . The density of the limiting paraffin point is derived by dividing the molecular weight by the molecular volume of a CH2 increment in a paraffin. The values of the limiting paraffin density derived from the molecular volume correlations of Huggins (R), Calingaert ( 2 ) , and Kurtz and Lipkin (9) vary between 0.851 and 0.861. The value 0.856 used in the present paper fits the data for aromatics better than the value 0.861 used previously. The data used in this paper were collected from Doss ( d ) , Eaton (6), Thorpe and Larsen @ I ) , and Ward and Kurtz ( 2 3 ) , and densities were corrected to 20" C. where necessary using (If). Procedure. I n order to obtain an analysis by this method, it is necessary to obtain density and temperature coefficient of density of the aromatics. The temperature coefficient of density is always calculated from the approximate molecular weight (Table I, I d ) , xhich in turn may be obtained from density and
SO.
d 0,856 0,883 0,910 0 938 0 965 0 993 1 020 1 047 1 075
so ~. 40 30 20 10
3
83.6 80.8 78.0 75.3 72.4 69.5 66.7 63.8 60.9 58.1
94.5 90.8 87.0 83.3 79.3 75.4 71.4 67.4 63.4 59.4
100 90 80 70 60
71.9 70.2 68.5 66.9 65.2 63.5 61.8 60.1 58.4 56.8
1
I 0.85
Figure 3.
I
0.90
I 0.95
I
I
1.00 1.05 D E N S I T Y AT 2 0 ° C .
I 1.10
I
1.15
Rings per RLolecule and Weight Per Cent Ring for Noncondensed Ring Aromatics
V O L U M E 19, NO. 3, M A R C H 1 9 4 7
185
L
5 0 t
I
I
085
090
I
I
I
095 100 I05 DENSITY AT 2 0 ' C .
I
t
I10
115
Figure 4. Rings per Molecule and Weight Per Cent Ring for 3Iixtures of Condensed and Noncondensed Ring Aromatics
-t
'u'
% E p 5 -0.3
-39
mid-boiling point (Mills, Hirschler, and Kurtz, 19). This means that only two physical properties are necessary, density and boiling point. The aromatic material usually occurs mixed with other hydrocarbon types, such as paraffins, naphthenes, and olefins. There are two methods of obtaining physical properties on the aromatic material: (1) by determination on aromatics which have been separated from other hydrocarbon types; ( 2 ) by calculation from the properties of the sample before and after removal of the aromatics, in which case the aromatics are not recovered. Where olefins are absent, as in straight-run petroleum products, the aromatics can be separated from the other hydrocarbon types
0
Figure 5 .
5 10 I5 20 .NUMBER OF CHAIN CARBON ATOMS
Agreement of Aromatic Analysis for Alkyl Benzenes
by the silica gel methods of RIair and Forziati (lo',l6)l. Solvent extraction is a less satisfactory method for obtaining a quantitative separation of the aromatics. I n the gasoline boiling range, again where olefins are absent, it is possible to rcmove aromatics quantitatively and determine them volumetrically by acid treatment ( I ) , and to calculate the properties of the aromatics from the volume per cent Table IV. Agreement of Data for Aromatic Hydrocarbons with Paraffinic aromatics, the densiiy and mid-boiling Side Chains point of the original material, and the Kumber of Rings Per RIolecule NO. Weight % Ring density of the raffinate remaining after of 4 v . DeviaMax. Av. DeviaMax. acid treatment. Comdevia- tion of deviadeviation of deviaAromatic Type pounds tion av. tion tion ai-. tion For the analysis of petroleum products, i t is desirable to have some k n o d A. Using Recommended Graphs edge of the type of aromatic present, Nonocyclic 221 3 0 t24 0.1 0 +0.6 Condensed dicyclic 41 2 -1 - 5 0.1 -0.1 -0.5 since this method is dependent on the deNoncondensed dicyclic 30 3 -1 +- 74 0.1 0 +0.5 Condensed tricyclic 6 2 0 0.1 0 -0.2 gree of condensation of the aromatic. Koncondensed tricyclic 1 +a 0 The selection of the proper graph to be Average b y class 3 0 0.1 0 used is made on the following basis: B. Using Average Graph (Figure 4)'3
+- 98
2;
1. Where only monocyclic aromatics are present, either Figure 2, 3, or 4 may be used, because they are identical for monocyclics. a For monocyclics all graphs give the same results 2 . For cracked petroleum products, where polycyclic aromatics are present, Figure 2 is recommended because meager Table V. -4greement of Analyses of Aromatic Extracts from Petroleum with Analyses information on hand indicates after Hydrogenation that the condensed type of No. of aromatic predominates. Approximate 50% Weight DifferRings Condensed dicyclic Koncondensed dicyclic Condensed tricyclic Soncondensed tricyclic
Fractions E a s t Texas straight-run A Hydrogenated A E a s t Texas straight-run B Hydrogenated B E a s t Texas straight-run C Hydrogenated C Catalytic cracked D Hydrogenated D
41 30 6 1
4 5 9
+9 -9
Deviations do not differ from those shown above
+11
To
Boiling Range,"C.
B,.P., C.
d:'
nk0
Ringa
90-180
146 128 232 210
0.8625 0.7754 0.9231 0.8394
1.4943 1.4272 1.5330 1.4576
69 77 67 69
329 307
0,9744 0.8943 1,0856 0.9330
1.5601 1.4841
66 72
6
1.5008
80 83
3
180-260 260-390 310-400
C C
ence,
a 2
per DifferMoleculeb ence 0.9 0.9 1.4 1.5
0.0
2.1 2.4 3.1 3.3
0.3
0.1
0.2
Weight per cent ring of hydrogenated fractions calculated with estimated accuracy of 8% ring b y method of Lipkin. Martin, a n d Kurtz ( 1 4 ) . b Rings per molecule of hydrogenated fractions calculated with estimated accuracy of 0.2 ring by method of Vlugter. Waterman, a n d Van Westen ($3). 50% boiling point could not be obtained by Engler distillation a n d molecular weights were estimated from riscosities a t 100" and 210' F., using method of Hirschler ( 7 ) . Fraction D : vislDo= 109.2 a n d viszlo = 5.37 cs. Hydrogenated fraction D : visloo= 14.0 and viszlo = 2.74 cs.
1 After this manuscript was submitted, a paper entitled "Separation a n d Determination of Aromatics from High-Boiling Petroleum Fractions by Adsorption", b y 11.R . Lipkin, 1%'. A. Hoffecker, C . C. Martin, a n d R . E. Ledley was prepared for presentation before t h e Division of Petroleum Chemistry a t the Atlantic City A.C.S. Meeting, April 1947. This paper describes t h e complete separation of aromatic concentrate L from cracked as well as straightrun petroleum products using silica gel.
ANALYTICAL CHEMISTRY
186
fact that the noncondensed and condensed aromatic ring lines (Figure 1) become more Vol.. TTidely separated. ume Dearomatized K e i g h t Cc RingRings per Nolecule _____ Figure 5 shows that there is % Boiling AreFractions TheDifferRtnge, little systematic d e v i a t i o n C. d:' n'D" maticb dzo ?,aa Theory0 Ca1cd.c Difference ory" Ca1cd.c ence t h r o u g h o u t t h e molecular Nixed Straight-Run Crudes weight range. The difference 96-121 0,7561 1.4186 9 0.7453 86 81 -5 1 1.0 0 1.4135 121-150 0.7721 1.4305 16 0.7528 1.0 0 1.4192 75 75 0 1 between calculated and theo150-175 0.7914 64 -3 1 1.0 0 1.4411 16 0.7765 1.4296 67 retical per cent ring, averaged 175-200 0.8037 58 -2 1 1.0 0 1.4469 14 0,7923 60 1.4377 200-218 0.8232 1.4571 15 0.8086 1.4453 65 .., 1-2 1.2 . .. 54-100 for each group of isomers, is 218-225 0.8165 1.4520 9 0,8084 1,4458 50-100 59 .., 1-2 1.2 . .. plotted against number of chain University Crude carbon atoms for monocyclic 125-150 0.7687 1.4259 6 0.7631 1.4230 75 68 -7 1 0.9 -0.1 aromatics. 67 65 -2 1 1.0 0 150-175 0.7905 1,4410 15 0.7759 1.4298 175-200 0.8050 1.4483 14 0,7924 1,4391 60 61 2 1 1.1 0.1 Table V shows an e\ample of 200-225 0.8129 1.4515 6 0.8048 1.4457 54-100 78 ... 1-2 1.4 .., the accuracy of this method Determined from molecular weight of aroniatics which can be present in boiling range of each fraction. of analysis for three fractions b A.S.T.M. Method D875-46T ( 1 ) . C From calculated properties of material removed by acid treat. llolecular weight is calculated by method of of aromatics boiling fiom 90" to Mills, Hirschler, and Kurtz ( 1 9 ) from mid-boiling point of cut a n d density of aromatic. Density of aromatic is calculated from density before and after acid treatment and volume remored b y acid treatment, assuming volume 390" C. separated from East per rent additivity. Texas straight run, and a 310" _~__ to 400" C r aromatic fraction from c a t a l y t i c a l l y cracked stock. A comparison is made of the per cent ring determined on the aromatic extracts and the per cent ae naphthene ring determined by t,he Imethod of Lipkin, Martin, and I . . Kurtz (14) on the aromatic extracts 60 $ after hydrogenation. The average difference is 5 %. METHYL TETRALINS Table VI demonstrates an analysis .XYLENES obtained on the aromatics in several gasoline fractions without recovery of these aromatics. The density of the aromatic is calculated from the density before and after acid treatment and the volume per cent aromatics, assuming volume per cent additivity of density. I n the boiling range where only monocyclic aromatics can exist, the per cent ring from aromatic analysis and per cent ring calculated from molecular weight agree very closely. Figure 6 demonstrates a n applicaAPPROXIMATE 50% BOILING POINT "C. tion of this method of analysis to n a r r o w - b o i l i n g aromatic fractions Figure 6. Analysis of Aromatics Separated from East Texas Crude from East Texas crude boiling below 350" C. The graph shows the percentage of ring decreasing t,hrough 3. For straight-run petroleum products, where polycyclic the monocyclic and dicyclic boiling ranges, and increasing in aromatics are present, Figure 4 is recommended for the present the boiling range where dicyclic aromatics begin to appear. because it is believed that both condensed and noncondensed There arc sharp increases in the amount of ring a t certain boilaromatics may be present. 4. Where only monocyclic and noncondensed polycyclic ing points, but in this particular example the boiling points were aromatics are present, Figure 3 should be used. Present informacorrected from about 9-mm. pressure and are not sufficiently action does not indicate that any petroleum product normally curate to warrant drawing conclusions as to the individual found in the refinery contains a predominance of noncondensed aromatics present. polycyclic aromatics. Limitation of Method. This method has been developed for Results. Pure compound data on 299 unsubstituted aromatics aromatics with paraffin side chains. I n petroleum, aromatics and alkyl aromatics ranging from one to three rings per molecule containing a naphthene ring or olefin double bond in the same show a n average deviation of 3% ring as shown in Table IV,A. molecule interfere \Tit,h this method of analysis. The recommended graphs were used for the condensed and nonTables VI1 to S show the deviations in per cent ring for the condensed polycyclics. available data on these mixed-type aromatics. I n general, a Table IV, B, shon s the results which are obtained by the use of naphthene ring in t'he aromatic molecule causes low results, and the average graph (Figure 4) instead of the recommended graphs. a n olefin double bond causes high results for per cent ring. The Using the average graph, the calculated percentage of ring is too theoretical per cent ring as used in this paper includes both arohigh for the condensed type of aromatic and too low for the nonmatic and naphthenic carbon atoms by definition. condensed type by about 5% for dicyclics and 107, for tricyclics. The following is an attempt to evaluate a few of the trends The increasing error, as number of rings increases, is due to the shown by mixed-type aromatic molecules. Table VI1 s h o w that Table VI.
Agreement of Analysis with Theory' for Aromatics in Straight-Run Fractions of Petroleum
@
a
V O L U M E 19, NO. 3, M A R C H 1 9 4 7
187
Table YII. Deliations of Pure Compound Data Formula
Weight % Ring Calcd. Calcd. theoretical
S o . of R i n g s Calcd. Calcd. theoretical
Formula
86
81
(,A/ Ethyl tetralin Propyl tetralin Butyl tetralin ejt-Butul tetralin
- 8
- 14
-10
1.5
1.6
1.7
i
99
- 1
2.5
-0.5
90
- 10
2.6
-0.4
77
- 23
2.2
-0,s
79
-21
2.3
-0.7
67
- 7
2.6
-0.4
-0.3
1.6
-0.4
72 67 61 62
- 11 - 10
1 6 1 6
-0.4 -0.4 -0.4 -0.4
30
- 6
1.4
-0.6
24
- 7
1.4
-0.6
26
- 5
1 5
-
i
Aromatics Condensed with Cyclo-olefins
CsHe
CnHs
ring^
Calcd. rheoretical
-0.4
- 13
1 6 1 6
S o . oi
Calcd.
__I
'
-0.5
78
- 10 - 9
Calcd.
.4romatics Condensed with S a p h t h e n e Rings, Tricyclic-
Aromatics Condensed with S a p h t h e n e Rings, Dicyclic6 92
Keight yo Ring Calcd. theoretical
'
-0.5
-
99
1
1.7
-0.3
/+\A -0.2
22
- 6
1.4
-0.2
-0.6
Table VIII.
~
a naphthene ring or a cyclo-olefin condensed x i t h the aromatic nucleus causes results roughly 10 and 57, too low, respectively. Table VIII shows that the deviations of the noncondensed aromatic naphthenes and aromatic-cyclo-olefins are about twice as large as for the corresponding condensed compounds. Table IX shows that the effect of a double bond in a two-carbon chain attached to a benzene nucleus is + l o % ring, and that the deviation decreases with increasing molecular weight. Table X shows that the effect of two double bonds in the side chain is about I: tIvice as great as one double bond. The deviation of these mixed-type molecules is usually about 10 to 15YG,and the maximum deviation shown in these tables is about 25y0. Assuming 12% to be the average deviation, i t would be necessary for these compounds to be present in more than 257, concentration to c a u d a s much as 37, deviation, which is the average deviation for aromatics with paraffinic side chains. There are practically no aromatic-olefins or aromatic-naphthenes which are likely to be present in petroleum fractions boiling below 175" C. In the kerosene boiling range, Mair and Streiff ( 1 7 ) and Rossini (20) have shown the presence of mixed aromatics such as tetralins and phenyl cyclopentane. I n the lube oil range, Mair, Willingham, and Streiff (18) have shown that most of the aromatic molecules contain naphthene rings. Therefore, this method of analysis is limited to petroleum fractions boiling below 400' C.
Deviation of Pure Compound Data Weight 7% Ring S o . of Rings Calcd. Calcd.
Formula
Calcd. theoretical
Calcd.
-
theoretical
Soncondensed Aromatic Naphthenes -0.7
-0.6
I and .,Carleton, L. T., IND. ENG.CHmf., .$SAL. ED.,14, 220 (1942). Doss, M. P., “Physical Constants of the Principal Hydrocarbons”, 4th edition, Kew York, Texas Co., 1943. Eaton, J. L., “Science of Petroleum”, 1701. 2 , London, Oxford University Press, 1938. Griswold, J., and Chem, J. N., Ind. EILQ.Chem., 38, 364 (1946). Hirschler, A. E., J . Inst. Petroleum Tech., 32, 133 (1946). Huggins, M., J . A m . Chem. Soc.. 63, 116 (1941). Kurtz, S. S., Jr., and Lipkin, 11. R . , Ind. Eng. Chem., 33, 779 flCJ41). \ - -
~~
Leendeme, J. J., and Kreulen, D. W., J . Inst. Petrorei~mTech., 25, 801 (1939). Lipkin, M. R., and Kurtz, S.S.,Jr., ISD. ESG. CHEM..Ax*L. ED., 13, 291 (1941). Lipkin, M. R., and Martin, C. C., Ibid., 18, 380 (1946). Ibid., 18, 433 (1946). Lipkin, M. R., Martin, C. C., and Kurtz, S. S.,Jr., Ibid., 18, 376 (1946). &lair,B. J., J . Research, Natl. Bur. Standards, 34, 435 (1945). Mair, B. J., and Foreiati, A. F.,Ibid., 32, 165 (1944). Mair, B. J., and Streiff, H. J.. Ibid., 27, 343 (1941). Mair, B. J., JTillingham, C. B., and Streiff, A . J., Ibid., 21, 581 (1938). Mills, I. W., Hirschler, A . E., and Kurtd, S. S., Jr., Ind. Eng. Chem., 38, 442 (1946). Rossini. F . D., Petroleum Engr., 14, 41 (Feb. 1943). Thorpe, R. E., and Larsen, R. G., Ind. Eng. Chem., 34, 853 (1942). Tlugter, J. C., Waterman, H. I., and Van Westen, H. A., J . Inst. Petroleum Tech., 18, 735 (1932). TVard, A . L., and Kurtz, S.S., Jr., IXD.ESG. CHEW,ASAL. ED.,10, 559 (1938).
Standardization of Chromatographic Adsorbents Rate of Flow of Developing Solvent ARTHUR L. LEROSEN, Coates Laboratory, Louisiana S t a t e L‘nicersity, B a t o n Rouge, La. The usefulness of permeability in characterizing an adsorbent is pointed out and a convenient grouping of terms (kA/760a), for this purpose is suggested; with standard packing it is possible to calculate the rate of flow for different values of the pressure, column length, and soltent viscosity.
T
HE author has introduced several terms for the characterization of chromatographic adsorbents ( 3 ) . Among these is V c ,which is defined as the rate of flow of the solvent through the column after a steady state is reached. I n order to use this term to compare the permeability of adsorbents, the solvent, column length, and applied pressure must be specified. Generally benzene, a full water-pump vacuum, and a 75mm. column furnish sufficiently good data; however, i t is often necessary to estimate the usefulness of an adsorbent in columns of different dimensions viith a variety of solvents and pressures; for this purpose a more general term is needed to describe a n adsorbent. Ideally, a knowledge of the particle size of a substance and the use of a standard degree of packing should permit the direct calculation of V, for any set of conditions. I n most adsorbents, however, there is generally a wide range of particle sizes and shapes, so that, this procedure is not practical. The “permeability” of a porous solid is derived from Darcy’s lan- ( 5 ) and expressed by the equation: k = qQ/A(Pi- P d / L where k is the permeability in darcys, q is the viscosity in centipoises, Q is the flux through the column in milliliters per minute, A is the cross-sectional area in square centimeters, ( P I - Pz) is the pressure difference in atmospheres between the ends of the
column, and L is t h e length in centimeters. When the driving pressure, P , is expressed in millimeters of mercury and Q is replaced by VCa,where (Y is the interstitial volume of the column in milliliters per millimeter, the equation can be arranged as:
V, = If A is calculated and
k ( A / 7 6 0 ( ~P/qL )
is experimentally determined, it is now possible to calculate V,for any values of q , P , and L. The need for the determination of A and (Y can be avoided by groupifig i h e constants:. ( L 4 / 7 6 0 ( ~ ) .When the value of this expression is determined experimentally by measuring V , under one set of conditions for a standard degree of packing, the value of V cfor any other conditions may be calculated from the values of P, L , and q without further measurements. The adsorbent is poured into the column under the full water pump vacuum and settled by tapping the sides of the column, the surface of n-hich is made smooth without applying pressure. In describing an adsorbent, the values for both k and ( k A / 7 6 0 ( ~ ) should be stated. (Y
The linear relation bet&en V,and pressure, and the reciprocal of the column length, suggested by several authors (2, 5),follows from Darcy’s law. Flow in relation to these variables is illustrated in Figures 1 and 2 for the systems benzene-silicic acid and benzene-lime. From these graphs and the experimental values of A and a, it is possible to calculate the values of k and ( k A / 7 6 0 ( ~ for ) the adsorbents. I n additional experiments, given herewith, the independence of diameter, the relation of vis-
