Mass Transfer in the Liquid Phase in Gas Chromatography R. H. PERRETT Department o f Chemistry, College o f Advanced Technology, Birmingham 4, England
b A method proposed earlier for the evaluation of liquid phase mass transfer coefficients in chromatographic columns has been extended to allow for the use of other carrier gases, A range of carrier gases-hydrogen, helium, nitrogen, and carbon dioxidehave been employed and the method gave valid results. The value to be taken for the diffusion coefficient ratio for the various carriers has been discussed in the light of the values obtained for B' and C,' terms in the rate equation. It was concluded that the estimates for the ratios based on published diffusion data were adequate.
0.20
3
P
work (6) indicated that the contribution to elution band spreading by diffusion through the liquid phase in a gas chromatographic column could readily be measured. The method relied on the fact that this contribution should be independent of the carrier gas, and that a more or less constant ratio between the interdiffusion coefficients in two gases could be evaluated for most solutes. The two carriers used in the earlier mork were hydrogen and nitrogen, not only because they are commonly used as carrier gases, but also because they are gases REVIOUS
Table I.
10
Figure 1.
for which some interdiffusion coefficients have been measured. When these two gases were used, the method gave good reproducible results and the present study was designed to check whether the technique was limited to systems using hydrogen and nitrogen as carriers or mas useful for other combinations of carrier gases.
Do'(co~), sq. cm. see.-'
0.2716 0.1997
0.0476 0.0351 0.0573 0.0567 0.0471
0.3368
Ethyl formate
Methyl acetate Isobutyric acetate
Table II.
D~'(Hz), sq. cm. sec.-l
0.3330 0.2713
Do'(H2) Do'( COP) 5.70 5.69 5.88 5.87 5.75
Interdiffusion Coefficients of Vapors in Hydrogen and Helium
Do'( Hz), Vapor
sq. cm. sec.-l
sq. cm. sec.-l
D,'(Hz) D,"e)
%-Heptane 2,4-Dimethylpentane n-Octane 2,2,4-Trimethylpentane
0.283 0.297 0.277 0.292
0.265 0.263
1.07 1.13
0.253
1.15
1346
ANALYTICAL CHEMISTRY
Do'(He),
0.248
1.11
WC,)
Elution of n-butane by helium
Interdiffusion Coefficients of Vapors in Hydrogen and Carbon Dioxide
Vapor n-Butyl alcohol Hexyl alcohol
30
?O
d (cm./
EXPERIMENTAL
Apparatus. This is described elsewhere (5, 7). The column was 25% n-octadecane on 100 to 120 B.S.S. Sil-0-Cel packed in a &foot stainless steel column. The sample gases were propane, isobutane, and n-butane. Procedure. T h e necessary preliminary experiments to find a katharometer filament current ( 2 ) and sample size (1, 8),which gave no extracolumn effect on the shape of the elution peaks, were carried out for each of the carrier gases used. The experiments with all four carrier gases were carried out a t a column temperature of 40' C. and the H E T P was measured a t a series of different linear gas flow rates, as described earlier ( 5 ) . RESULTS
The interdiffusion data for the gases used in this study are rather few, but a selection (3, 4)is shown in Tables I and 11. The ratios of diffusion coefficients of these vapors in pairs of carrier gases are reasonably constant, and a ratio of 3.8 for diffusion coefficients into hydrogen and nitrogen has been found in many cases (6). Using this value and the ratios found in Tables I and 11, D,, (H2)/D,'(C02) = 5.8 and Dg'(H2)/
0.05
Figure 2.
I
I
20
10
u’ (cm. I stc.1
Elution of n-butane b y carbon dioxide
D,’(He) = 1.13, Table I11 has been constructed. Using these values of r , by a method analogous to that described earlier ( 6 ) , C L may be calculated H(1)
=
.1
+ B’(I)/u’(I) + + CLC(I)
Co’(1)u’(I) and H(I1)
=
A
+ B’(II)/u’(II) + Co’(II) ~ ’ ( 1 1 )+ CLC(II)
but B‘(I1)
TB’(I) and Cg’(II)
=
=
C,’(I) for a given Polute and tem-
r perature. If values of H are taken a t 1 points where u’(1) = - u’(II), then r by subtraction H(I1)
..
- H(1) CL
=
=
1
I
IO
CLG(II) - CLC(I)
dioxide. I n view of the fact that direct measurements are not available for the diffusion coefficients required, they serve as a suitable starting point in the investigation. T h e interdiffusion coefficients into helium are a t least those for higher hydrocarbons and are, therefore, more likely to conform to the same pattern as the data needed for the present study. I n spite of this reservation, the values obtained for C L agree, with one obvious exception, with the final values after refinement. I n fact, if the odd value found for the elution of isobutane from the column by hydrogen and helium is removed froin the averaging, the agreement with the refined value is even better. Since the diffusion coefficient data are rather scant, especially for diffusion into carbon dioxide, some internal evidence would appear to be relevant. The values of B’ may be written
- N(I) 7.y-m
H(I1:) u(I1.)
The values obtained at various values of u’(1) throughout the range of flow rates studied are i n good agreement. The mean values calculated by this method are shown in Table IV. The values of the other rate equation coefficients were determined by methods described earlier (5, 6 ) , and subsequent refining. The mean values of C L after refining were 15 X 11.5 X and 11.5 X loW4second, for the elution of propane, isobutane, and n-butane, respectively. The other rate equation coefficlients are shown in Table V. The fit of the coeff&mts to the experimental points is illustrated in Figures 1 and 2. DlSCUljSlON
The diffusion data quoted in Table I have not, in general., been obtained for interdiffusion, by paraffins into carbon
B’
=
Table VI shows the values obtained for this ratio in the cases studied. If these ratios are compared with those shown in Table 111, there is good agreement between the ratios deduced here and the theoretical ratios foi pairs of gases, not including carbon dioxide. Since, however, the values of CL obtained using the diffusion coefficient ratios shown in Table I11 are coiiiparable with those obtained in other gases and \vith the refined value of C L , it is probable that the discrepancy originates from inaccuracy in the measured B’ values. This is understandable in view of the difficulty in obtaining refined values for &Iand B‘ in elution by carbon dioxide. This difficulty arises froin the fact that the minimum of the HCTP curve occurs a t very low carrier gas velocities. Thus the low value of d and the consequent high value of B’ for elutions by carbon dioude are moie likely to be in error than the ,I and 13’ values obtained in experimentu with other carrier gases.
Table 111. Ratios, D,’
Gas I1 H2
He Ng
CO1
and since y is a function of the column and not of the carrier gas, the ratios of diffusion coefficients are given by
Isobutane n-Butane
Carrier Hydrogen Xitrogen Helium Carbon dioxide
He
Sz
Co2
1.0 0.89 0.26 0.17
1.13 1.0 0.30 0.19
3.8 3.36 1.0 0.65
5.8 5.13 1.53 1.0
Sz
He ?IT,
Solute Propane Isobutane n-Butane Propane Isobutane n-Butane Propane Isobutane n-Butane Propane
H,
Table IV. Mean Values of C L Obtained by Elution with Various Carrier Gases C L X 10: see. _____ Carrier Carrier Pro130nI1 I pane butane Butane H, He 15 34 10
27D,’
Table V.
Interdiffusion Coefficient (gas ll)/D,’ (gas I) = r Gas I
COz
NZ
co, coz
Rate Equation Coefficients B’, sq. A , em. em. see.-’
0.02 0.012 0.015 0.015
0.015 0.015 0.015 0.015 0.015 0.007 0.008
0.01
1.00 0.88 0.85 0.27 0.22 0.22 0.93
18 14 17
16 15 16
16
11 10
...
c,’ x
2.7
0.80 0.78 0.25
20
0.19
23
0.18
104,
see. 3.4 3.7 3.9 8.5 12.5 14.0 3.8 4.1
23
VOL. 37, NO. 1 1 , OCTOBER 1965
11 10 10 11 6
cL x
104, see. 15
16 11
13 16 12 15 16 12 13 15 12 1347
Table VI. Ratios of E’ Terms in Rate Equation for Various Carriers
Carrier I1 Hz
CarB’(II)/B’(I) rier IsonI Propane butane Butane He
Nz
CO1
He
Nz
Nz
COz
coz
1.08 3.7 4.0 3.44 3.7 1.08
1.10 4.0 4.65 3.65 4.22 1.16
1.09 3.86 4.7 3.54 4.34 1.22
If, in view of the discrepancy between the ratio of diffusion coefficients and the ratio B’(H2)/B’(COz),the value of r is taken as 4.7 and not 5.8 as in the original calculation of C L , the results show a very marked dependence on u’. Thus, since consistent values for C L cannot be obtained for all parts of the HETP curves, the correct value for r is not 4.7, so the discrepancy must be due to the error in evaluating B’ when carbon dioxide is used as the carrier gas. Further internal evidence for the ratios of interdiffusion coefficients is available from the ratio of C,’ terms, since
Table VII. Ratios of C,’ Terms for Elution of Solutes by Various Carrier Gases
Carrier I1
Carrier I
HO
He Kz COz
He
Nz
Nz
COz COP
COY1)/C,’UI)
Propane 0.8 2.5 5.9 2.6 7.4 2.3
Isonbutane butane 1.03 3.4 6.2 3.4 5.6 1.6
1.05 3.6 5.9 3.4 5.6 1.6
C,’ (I)/C0’(11) = D,‘ (II)/D,’ (I) for any given solute a t a fixed temperature. These ratios are shown in Table VII. As a result of the method of determination (5, 6 ) of Cg’, the ratios in Table VI1 most likely to be in error are those for which helium is one of the carrier gases. The values suggested for the ratio r in pairs of gases including carbon dioxide are in good agreement with the values
taken from Table I11 and used in the calculations of C L . The consistency of the values of C L obtained by this method indicate that the C L term is a genuine liquid phase mass transfer term and is independent of the carrier gas used. This consistency also suggests that the diffusion coefficient ratios contained in Table I11 are the correct ones for use in such calculations. Moreover, in view of the origin of these ratios they should apply to almost any system studied. LITERATURE CITED
( 1 ) Bohemen, J., Purnell, J. H., “Gas Chromatography, D. €I. Desty, ed., p. 6, Butterworths, London, 1958. ( 2 ) Bohemen, J., Purnell, J. H., J . A p p l . Chem. 8, 433 (1958). ( 3 ) Clarke, J. K., Ubbelohde, A. R., J. Chem. SOC.1957. 2050. ( 4 ) International Critical Tables, Vol. 5, p. 62, McGraw-Hill, New York, 1929. ( 5 ) Perrett, R. H., ANAL.CHEM.37, 1342 (1965). ( 6 ) Perrett, R. H., Purnell, J. H., Ibid., 34, 1336 (1962). ( 7 ) I b i d . , 35, 430 (1963). (8) Purnell, J. H., Sawyer, D. T., Ibid., 36, 457 (1964).
RECEIVEDfor review March 30, 1965. Accepted July 9, 1965.
Gcls Chromatographic Detector Response Using Carrier Gases of Low Thermal Conductivity JAMES
M. MILLER‘
and A. E. LAWSON, Jr.
Gow-Mac Instrument Co.,Madison, N . 1.
When performing a gas chromatographic analysis with a carrier gas whose thermal conductivity approaches that of the compound being studied, anomalous results are often obtained. The most common examples are the reverse and W shaped peaks obtained with nitrogen as the carrier gas. From an investigation of a variety of compounds these anomalies have been shown to be a function of sample size. In nitrogen, at 100” C., most of the compounds studied gave W-shaped chromatographic peaks. In argon and in carbon dioxide, under identical conditions, none of the compounds studied gave W peaks, although some responded in a positive direction and others responded in a negative direction. The effect of detector cell geometry was also investigated.
1348
ANALYTICAL CHEMISTRY
W
a gas chromatographic analysis is performed using a thermal conductivity (TC) detector, carrier gases of high T C are usually preferred because of their greater sensitivity and linear response. Hence, helium is the most commonly used carrier gas in this country. However, the cost of helium often prohibits its use in Europe and in preparative work where large amounts are consumed. Hydrogen can be used, but it is hazardous, particularly in the latter application. Xitrogen has been used, but anomalous results are often obtained because of its low T C . Early in the development of gas chromatography (GC), reverse or Wshaped peaks were reported for compounds eluted in nitrogen. The first comprehensive study was made by Bohemen and Purnell ( 2 ) . Their paper summarizes the developments to HEN
that date, and it concentrates mainly on the effect of filament temperature and flow rate on peak shape. Brief mention is made of the effect of sample size. They concluded that W peaks were caused by forced convection or a so-called heat capacity effect. This argument was extended later by Purnell (19).
Schmauch and Dinerstein (21) obtained response values for mixtures containing a small amount of organic vapor in both helium and nitrogen (and in one case, ethane). At high filament temperatures and with a flow insensitive detector, they obtained minima in plots of response us. solute concentration for n-hexane and methanol in nitrogen. They show how 1 Present address, Department of Chemistry, Drew University, Madison, N. J.
