Table 111.
GLC Repeatability and Accuracy Data for Hydrocarbon Impurities in Benzene
yo Volume Paraffins
% Volume Toluene Found Deviation Addedu Found Deviation +o, 02 0.24 +0.01 0.11 0.13 0.23 0.00 0.13 +0.02 0.38 0.35 -0.03 0.24 0.23 -0.01 0.38 0.00 0.24 0.00 0.59 0.57 -0.02 0.32 0.31 -0.01 0.58 -0,Ol 0.33 $0.01 0.82 0.84 0.02 0.41 0.39 -0.02 0.86 + O , 04 0.39 -0.02 Av. dev. 0.016 Av. dev. 0.014 o Includes 0.03% volume paraffins and 0.02% volume toluene in benzene base stock as determined by GLC. Addeda 0.23
+
Table IV.
GLC Repeatability and Accuracy Data for Hydrocarbon Impurities in To1uene
yoVolume Benzene Deviation Added0 Found Deviation i-0.01 0.11 0.12 +0.01 $0.02 0.11 0.00 0.42 0.44 +0.02 0.21 0.21 0.00 0.44 +o. 02 0.22 +0.01 0.30 0.32 $0.02 0.62 0.59 -0.03 0.61 -0.01 0.32 0.02 Av. dev. 0.018 Av. dev. 0.010 Includes 0.02% volume paraffins and 0.01% volume benzene in the toluene base stock as determined by GLC. % Volume Paraffins
Addeda 0.22
Found 0.23 0.24
+
to be 0.014 and 0.01670 volume, respectively. The standard deviations for paraffinic and benzene impurities in toluene were found to be 0.014 and 0.012% volume, respectively. Results of 10 determinations were used to calculate the standard deviations cited. Results of duplicate determinations of several benzene and toluene samples to which 0.33 to 1.23y0 volume impurities have
been added are given in Tables I11 and
IV. Determinations of paraffinic impurities in high purity aromatics by the ASTM Kattwinkel reagent test are systematically low by 0.6% volume due to absorption of paraffins in acid and for this reason concentrations below 0.6% volume cannot be detected (10). From this fact and from the precision,
accuracy, and sensitivity data presented above, the gas chromatographic method is concluded to be superior to the ASTM Kattwinkel reagent test for determining hydrocarbon impurities in high purity benzene and toluene. ACKNOWLEDGMENT
The author expresses his appreciation to R. G. Eveld for his assistance in the preparation of the paper and to A. H. Cherry, M. C. Simmons, and M . Nager for critical reviews thereof. LITERATURE CITED
(1) Adlard, E. R., “Vapor Phase Chromatography,” pp. 98-114, D. H. Desty, ed., Academic Press, New York, 1957. (2) Am. Soc. Testing Materials, Philade!phia, Pa., “Aromatic Hydrocarbons in Olefin-Free Gasolines by Silica Gel Adsorption,” D 936-55, 1955. (3) I b i d . , “ASTM Standards on Benzene, Toluene, Xylene, and Solvent Naphtha,” D 851-47, 1947. 14) Zbid.. ‘IASTM Standards on Petro‘id., “Hydrocarbon Types
D 1319-581’. 1658 (6) Eggertsen: F. T., Groenninge, S., ANAL.CHEM.30,20 (1958). ( 7 ) Fabrizio, F. A., King, R. W.,Cerato, C. C.. Loveland. J. W., Ibid., 31, 2060 (1959). (8) Tenney, H. l l , , Ibid., 30, 2 (1958). (9) Whitham, B. T., ‘‘Vapor Phase Chromatography,” pp. 395-410, D. H. Desty, ed., Academic Press, Sew York, 1957. (10) Wood, J. C. S., Martin, C. C., Lipkin, M. R., ANAL. CHEM.30, 1530 (1958). RECEIVED for review March 14, 1960. Accepted May 23, 1960. Division of Analytical Chemistry, 137th Meeting, ACS, Cleveland, Ohio, April 1960.
END OF SYMPOSIUM
Factors Affecting the Use of Gas-Liquid Chromatography for the Separation of Large Samples The Column Dimensions W. J. de WET Central Tobacco Research Station, Kroondal, Transvaal, South Africa VICTOR PRETORIUS Department o f Physical Chemistry, University of Pretoria, South Africa
b Theoretical and experimental evidence is put forward to show that for a given column efficiency the maximum sample volume increases as either the column diameter or the column length is increased. 1396
ANALYTICAL CHEMISTRY
I
T H . ~ Sbeen
shown (8) that the efficiency of a gas-liquid chromatography column decreases as the sample volume is increased and that the rate of decrease is affected by the method used for introducing the sample, b y the
amount of liquid in the stationary phase, and by the distribution coefficient of the solute. I n this paper the study is extended to include the effect of the dimensions of the column. An equation relating the column
'?
/
a,/b
,
,
/'
2Or
/
M
0
2 .o
1.0
LIOUID SAMPLE VOLUME
CML.1
Figure 1. Effect of sample volume on efficiency for columns of various diameters Experimental curves a. d = 4 mm. c. d = 6 mm. e. d = 1 2 mm. g. d = 1 8 mm. Calculated from Equations 5 and 6 far Km = 7 b. d = 4 mm. d . d = 6 mm. f. d = 1 2 mm. h. d = 1 8 mm. Column length, 2 3 0 cm.; column temperature, 90' C.; preheater temperature, 1 3 0 ' C.; linear gas velocity, 2.5 cm./recand
efficiency to the sample volume for columns of various diameters may be derived as follows. It has been shown (9) that
for V,K, n = [
4 now 4
+ 2 V,K, vdn, for V,K,
I
20
10
0
30
I
40
LIQUID SAMPLE VOLUME (ML.3
Figure 2. Effect of sample volume on efficiency for various column diameters Experimental curves b. d = 38.2 mm. d. d = 60 mm. Calculated from Equations 5 and 6 a. d = 38.2 mm.; Km = 7 c. d = 60 mm.; K m = 7 e. d = 60 mm.; Km = 5 Column conditions same as in Figure 1
Substitution of Equation 4 in Equations 1 and 2 yields
(HETP)=
> 3v 4%(1)
1
< 0.5 v V'L
(2j
where number of theoretical plates obtained using a gaseous sample volume V,K, no = number of theoretical plates obtained using infinitely small samples v = effective plate volume V, = volume of undiluted vaporized sample K," = a dilution factor representing the degree of dilution of sample Fyith carrier gas before entering the packed portion of column n
Since where
V,
0'
=
=
L'
=
Vp + V i / K ( 1 )
(3)
volume of mobile phase per theoretical plate
1-1 = volume of liquid phase per theo-
retical plate 6 = distribution coefficient of sample between gas and liquid phases = (concn. of solute in gas phagej/(concn. of solute in liquid phase) it follows that 2: =
rd21(F,
+ Fi,/K)/4n,
(41
There d = column diameter I = length of packed portion of column F,, F i = fraction of cross-sectional area of column per unit area occupied by gas and liquid phases, respectively
where (HETPj = mean height equivalent per theoretical plate. Equations 5 and 6 show the effect of the sample volume on the column efficiency for various column diameters. T o test the accuracy of these equations the following experiments were carried out using the apparatus previously described (2). Various volumes of a test mixture consisting of equimolar amounts of benzene and toluene were separated on oolumns of different diameters. The columns were packed to a density of 0.53 gram per cc. with a mixture of Celite 545 (100 to 200 mesh British Standard Scale) and dibutyl phthalate (30y0by weight of the liquid). The column parameters were adjusted to give maximum efficiency for small samples (column temperature 90' C., preheater temperature 130' C., linear gas velocity at the column outlet 2.5 em. per second). The column efficiency in each case was calculated from the toluene peak in the chromatogram by the method previously described (a). The efficiency expressed as the mean height equivalent per theoretical plate, (HETP) has been plotted against the corresponding liquid sample volume (Figures 1 and
015 L I Q U I D SAMPLE VOLUME
0.30
( M L ~
Figure 3. Effect of sample volume on efficiency for various column lengths in centimeters as calculated from Equations 9 and 10 I = 500 I = 2000 c. I = 3500 d. I = 5000 a. b.
2) where the experimental conditions are also given. T o compare Equations 5 and 6 with the experimental results it is necessary to calculate the values of the parameters in these equations which pertain to the experimental conditions. Although, in principle, no may be calculated from Equation 7 , this is not yet practicable. For this reason the various values of no have been obtained from the experimental data by extrapolating the curves in Figures 1 and 2 to zero sample volume. The values F,=0.728 and F~=0.112 have been calculated directly from the known characteristics of the packing. The gaseous sample volume, V 8 , has been determined from the liquid sample volume by the van der Waals equation. VOL. 32, NO. 11, OCTOBER 1960
1397
I
1
\a
0.5
____ _____--_ax+ 3_ _ _ - - -
IO0
0'
1
200
LIQUID SAMPLE SIZE CMICROLITRES)
2500
0
5000
Figure 5. Effect of sample volume on column efficiency determined experimentally for various column lengths in centimeters
COLUMN LENGTH CCM.)
a. b.
Figure 4. Wect of column length on column efficiency for various liquid sample volumes determined from data in Figure 3 X 10-2 ml. a. b. c.
d.
9 4.5 3 1.5
The effective plate volume, u, has been calculated (4) from the retention volume V i = n,u which may be obtained experimentally from the chromatogram. Using the equation V," = 1/4n3d2i(F, Ft/K) the distribution coefficient of the toluene between nitrogen and dibutyl phthalate has been estimated to be 0.0048. The value of the dilution factor, Km, has been taken to be 7 (2) for all columns. The values of the various parameters are given in Table I.
+
Table I.
Column Diameter, Cm. 0.4
0.6 1.2 1.8
3.82 6.0
Values of a Number of Column Parameters
no 884 ~~
766 639 495 383 314
v,Cc.
vi,cc.
0.78 1.99 9.47 27.51 160.0 480.50
680 1,528 7,050 13,620 61,340 151;500
The dashed curves in Figures I and 2 have been drawn using Equations 5 and 6 and the data given above. The theoretical and experimental curves in Figures 1 and 2 show satisfactory agreement, especially for the narrow columns. I n a sense this agreement is fortuitous, since the shape of the curves is strongly dependent on the value chosen for the dilution factor, which in turn depends on the characteristics of the preheater at the sample inlet ( 8 ) . The dilution factor will be constant only if the rate of evaporation per unit volume of the sample is constant. I n practice this is very difficult to achieve, so that it is not surprising that the dilution factor must 1398
ANALYTICAL CHEMISTRY
c.
d. e.
180 540 860 1430 1760
Column diameter, 4 mm.; column temperature, 90' C.; preheater temperature, 1 3 0 ' C.; inlet pressure, 88.6 cm. of Hg; outle pressure, adjusted to optimum value
be reduced from 7 to 5 to obtain satisfactory correlation with the experimental results (Figure 2) in the case of the widest column. However, these results show that the decrease in the column efficiency which accompanies an increase in the sample volume be3omes less as wider columns are used. If no is assumed to be independent of the column diameter, it follows from Equations 5 and 6 that the volume of sample which can be handled by a column a t any chosen efficiency is proportional to the square of the column diameter. An interesting fact which emerges from the experimental results in Figures 1and 2 is that n odecreases as the column diameter is increased. Theoretically no should be independent of the column diameter (Equation 7 ) . Scott (6) has attributed this effect to increased eddy diffusion. I t is generally accepted ( I ) that the tortuosityf actor is independent of the column diameter, provided the packing is random and "wall effects" are ignored, which will be the case in the columns used in the present study. Therefore. it is difficult to accept the explanation given by Scott. A more probable esplanation is that the granular support tends to settle, causing vertical density and vertical gas velocity gradients in a horizontally mounted column. Band spreading is thus promoted and the efficiency is decreased. This effect would be expected to become increasingly pronounced as the column diameter is increased, which is in agreement with the experimental results. Furthermore, if the support does settle, the amount by nhich no is decreased as the column diameter becomes larger should depend on the type of granular support. By comparing the results given by Khitham
(6) with those obtained in this study, it may be inferred that crushed firebrick provides a firmer support than does Celite. The decrease in nowith an increase in the column diameter seriously detracts from the usefulness of very wide columns for the separation of large samples. The conclusions given in the previous paragraphs suggest that this disadvantage may be overcome by employing a number of columns of relatively small diameter in parallel. From Equations 5 and 6 it follon-s that for any chosen constant efficiency the sample volume may be increased without detracting from the efficiency if the column length is increased. This is particularly true, since the limituig number of theoretical plates, no, is a function of the column length. Thc precise relation between n, and I is given by (3)
(7,
where A
d,
= a packing factor = average diameter of granular
support
D,,
= =
d,
= = =
Dl
=
y
a tortuosity factor diffusivity of solute in gas phase at pressure of 1 atm. viscosity of carrier gas permeability coefficient "effective" thickness of liquid filni diffusivity of solute ill liquid phase
P , , Po = gas pressures a t column inlet and outlet pressurcs, re-
spectively It is now convenient to assume that all the column parameters, other than
s
04:
5 2
30 >
0:
W
d
I
d
20.15
0 i 1 2000
I
1000
.
c /
COLUMN LENGTH CCM.)
Figure 6. Effect of column length on column efficiency for various sample volumes (MI.) as obtained from data in Figure 5 a. b. c.
200 150 75
C
2500
Figure 7. Effect of column length on sample volume which may be handled at various efficiencies as determined from data in Figure 3
(HTP~)~, cm. a. b.
the column pressures and the column lrngth, are held constant. Equation 7 then reduces to Equation 8. The values which have been chosen for the various column parameters are hypothetical. Although they are not intended t o apply exactly to the columns used in the present study they are of the same order. 1.5 x 10-41
where
2Xd, = 0.03 cm.
4-/D0.11/8 =
1.5 X 10-4 g. atm. cm.-’
E‘, = 2
x 106 dynes cm.-*
I t follows from Equation 8 that for cach value of the column length there ill be an optimum outlet pressure-an outlet pressure which will lead to a maximum number of theoretical plates. The simplest method of calculating the optimum outlet pressure is to plot the number of theoretical plates against the outlet pressure for each column length using Equation 8. The corresponding maximum number of theoretical plates, n , may then be obtained by substituting the optimum outlet pressure in 1:quation 8. The values shown in Table I1 have been obtained in this way. Equations 1 and 2 may now be nrittcn in the following form:
(HETP)’ = [4
;l;;gm]-* (10)
for V a K m< 0.5 v 6 , wheren,.,~ = V i kl, k is volume of gas per unit length of column, and for convenience it has been assumed that k = 3 ml./cm. and (HETP)” = minimum mean height equivalent per theoretical plate corresponding to sample volume V,K, 6
Equations 9 and 10 and the data in Table I1 have been used to plot (HETP)’ against the liquid sample volume for various column lengths. K , has been taken to be 7. The results are shown in Figure 3. I n Figure 4 the (HETP)’ has been plotted against the column length for various sample volumes.
> 3 u.\/n,,
1.2
c.
0.3
0.6
d.
0.25
qualitative agreement with the theory. The agreement is as good as might be expected, since the values of the parameters chosen for the calculated curves are only of the order of the actual experimental values. The column lengths on which particular sample volumes may be handled at a given efficiency have been calculated from Figure 3 and are shown in Figure 7. Although the amount of material which can be separated on a column operating a t a low efficiency increases with the column length, the increase is not directly proportional to the column length and depends on the chosen efficiency. For high efficiencies the amount increases with column length until a maximum is reached, after which a decrease occurs. LITERATURE CITED
(1) Carman, P. C., in “Flow of Gases Table II. Maximum Number of Theoretical Plates Calculated from Equation 8 for Various Column Lengths
Column Length, Cm. 500 2000
3500 5000
Maximum No. of Plates, 2,404
8,888
14,000 17,605
(HETP)’ = 1
for V , K ,
5000
COLUMN LENGTH CCM.3
The results in Figures 3 and 4 have been experimentally checked using the apparatus and methods described above. The results (Figures 5 and 6) are in
through Porous Media,” p. 45, Butterworths Scientific Publications, London, 1956. (2) de Wet, Vi-. J., Pretorius, V., ASAL. CHEM.32,169 (1960). (3) Haarhoff, P. C., de U‘et, R. J., Pretorius, V., in press. (4) Keulemans, A. I. M., in “Gas Chromatography,” pp. 135, 172, New York, 1957. ( 5 ) Scott, R. P. W., in “Gas Chromatography,]’ D. H. Desty, ed., p. 189, raphy,” Butterivorths Scientific Scier Publications, 145% Londnn 1958. London, (6) Rhitham, B. T., Ibid., p. 194, 1957. R RECEIVEDfor review October 26, 1959. Accepted June 7, 1960. The senior author (V. P.) is indebted to African Explosives and Chemical Inds. Ltd., for the award of a Research Fellowship and to the Council for Scientific and Industrial Research for financial assistance.
VOL. 32, NO. 1 1 , OCTOBER 1960
1399
