I CORRESPONDENCE
I
Gas Chromatographic Measurement of Adsorption Characteristics of Isobutylene-Activated Alumina System with Nonlinear Isotherm SIR: Although the theory of chromatography has been dealt with in numerous articles, few studies have been reported on nonlinear chromatography which is encountered in the majority of gas chromatographic processes. Houghton reported the theoretical analysis for the case where a nonlinear isotherm is the polynomial form ( I ) . The solution obtained, however, is too complicated to compare directly with the experimental data. Extending Houghton's analysis, Haarhoff and van der Linde recently showed the analytical solution in which nonlinearity, nonideality, and sorption effects were taken into account ( 2 ) . This solution seems to be applicable to analyzing an elution curve to obtain adsorption characteristics such as an adsorption isotherm and a heat of adsorption. In order to test the applicability of Haarhoff's treatment, the present experimental study was carried out on the adsorption of isobutylene on activated alumina. In this system, the adsorption isotherm is known to be nonlinear (3, 4).
0
Y
10
mi
20
I 30
Figure 1. Typical example of adaptability for Haarhoff's master curves Column temperature, 70°C; carrier gas flow rate, 30.4 ml/min
THEORETICAL
The nonlinear isotherm is represented by the use of a polynomial form of solute mole fraction in the mobile phase, X . k When the solute is in small concentration, X is given by Pipm. In such a case, the nonlinearity is not too great, and Equation 1 could be approximated as following
On the other hand, k is generally given by
(3) Substitution of Equation 3 into Equation 2 yields
(4) Therefore the adsorption isotherm can be determined from Equation 4 if the value of Cm/Ckis known. Figure 1 shows master curves presented by Haarhoff and van der Linde. In the Figure, the elution curve parameters such as H I I 2 / HH, a / H ,s, and r are plotted as a function of mi which is a dimensionless number proportional to the amount of solute defined by the following equation: (1) G. Houghton,J.Phys. Chem., 67, 84(1963). (2) P. C. Haarhoff and H. J. van der Linde, ANAL.CHEM., 38, 573
(1966). (3) R. D. Oldenkamp and G. Houghton, J . Phys. Chem., 67, 303 (1963). (4) Ibid.,p 597. 1540
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ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
m. =
'
2kONMi (1 k")zMm(1
+
+
2)
From the measurements with various M i , the value of rni/Mi is determined in such a way that the best agreement between experimental data and master curves is obtained. Then the value of C,/Ct is calculated from m f / M iand Equation 5. EXPERIMENTAL
The apparatus consisted of the injection system, the packed column, and the thermal conductivity cell which were con80 mesh activated nected in series. The adsorbent was 48 alumina (Kishida Kagaku) with a pore volume of 0.4 ml/g and a BET area of 225 m2/g. Helium (Matheson, 99.99%) was used as a carrier gas at the flow rate of 9 30 ml/min. Isobutylene (Takachiho Kagaku, C.P. grade, >99.0%) as an adsorbate was diluted with helium in the range of 0.005 1 mole fraction and 1 ml of the diluted gas was injected into carrier gas stream. In order to verify the isotherm obtained by chromatographic method, the volumetric measurements were carried out for the same system by usual method.
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RESULTS AND DISCUSSION
In Figure 1, an example of adaptability of our experimental data for the Haarhoffs master curves is shown. Similar results were obtained at the other temperatures of 60 and 80 "C. From the Figure, the value of rn,/Mi was determined and, subsequently, C m / C K . The value of k" was found from the extrapolation of retention times to infinitesimal samples. The experimental conditions and parameters required in calculations are given in Table I. In Figure 2 , the adsorption isotherms obtained from Equation 4 and the data in Table I are shown. In the Figure, the isotherms obtained by the volumetric measurements are also
Table I. Experimental Conditions and Parameters. Column 80 temperature, "C 60 70 Mass flow rate, mol/sec M,, mol C,, mol/ml t , sec
2.26 x loa5 2.26 X 2.39 x 10-5 2.39 x 10-5 7.53 x 10-5 7.46 x 10-5 444 741 k" 710 422 N 75 80 rn,/Mi, mol-' 5.39 x 105 4.13 x 105 C,ICk 0.0164 0.0382 a Symbols are the same as those in reference (3).
2.26 x 10-5 2.39 x 10-5 7.42 x 10-5 312 296 84 4.61 x 105 0.0515
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sponding to coverages in the range of 4 12 was obtained from chromatographic measurement using the approximation by linear isotherm. The lower values in the later measurement are probably owing to the neglect of nonlinearity. In conclusion, we found that the theoretical solution reported by Haarhoff and van der Linde is applicable to analyzing practically the experimental data. However, the approximation of adsorption isotherm to be parabolic as shown in Equation 4 necessarily yields a limit in application. The relation between experimental conditions and applicable ranges should be studied in the future. LIST OF SYMBOLS a
C, C, h
C, -
H x
Hb
k 0.01
0.02 0.03 0.04 0.05 of isobutylene ( atm )
Partial pressure
Figure 2. Adsorption isotherms of isobutylene on activated alumina Solid lines: isotherms obtained by gas chromatographic method Dotted lines : corresponding isotherms obtained by volumetric method
plotted. Apparently both are in good agreement at the small coverage. Furthermore, for both the solid line and dotted line, the heats of adsorption at the initial stage of the adsorption were estimated by extrapolating the isosteric heats of adsorption to infinitesimal amounts of adsorption. In the course of estimation, some isosteric heats of adsorption were calculated in the range of 0.003 0.01 ml/m2 of adsorption by using the Clausius-Clapeyron equation and the values of P and T at the same amount of adsorption in Figure 2 . The initial heats of adsorption thus obtained for the chromatographic and volumetric measurements are 10.2 f 0.2 and 10.1 i 0.3 kcal/mol, respectively. They are also in good agreement with each other. Oldenkamp and Houghton have worked with the similar system of isobutylene-activated alumina (Alcoa F1) using both volumetric and chromatographic methods (3, 4). The initial heat of adsorption obtained from volumetric measurement was 9.8 kcal/mol, which is very close to the value in the 8.5 kcal/mol correpresent study. On the other hand, 8.1
-
N
k" Mt M, mi
N P P, r s
i Vvoid
X
Isotherm parameter defined by Equation 1 = Isotherm parameter defined by Equation 1 = Average carrier concentration in the mobile phase in the absence of solute = Amount of solute adsorbed in the stationary phase per unit volume of the bed = Height equivalent per theoretical plate for infinitesimal samples = Effective plate height determined from the peak base width = Effective plate height determined from the peak width at half height = Ratio of the amount of solute in the stationary phase to that in the mobile phase at equilibrium and at a given mole fraction = Value of k for infinitesimal samples = Amount of solute injected = Amount of carrier in the mobile phase in the absence of solute = Dimensionless number proportional to the amount of solute defined by Equation 5 = Number of theoretical plates for infinitesimal samples = Partial pressure of solute in the column = Average total pressure in the column = Peak maximum displacement parameter = Asymmetry ratio = Retention time for infinitesimal samples = Interparticle void fraction in the adsorbent bed = Radial average of the solute mole fraction in the mobile phase =
SHUICHI KAGAWA The Faculty of Engineering Nagasaki University Nagasaki, Japan KATSUMI FUJITA KENJITADA ISSEINAKAMORI The Faculty of Engineering Kyushu University Fukuoka, Japan RECEIVED for review August 2 , 1971. Accepted January 13, 1972.
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