DAVIDC. LOCKE
3768
Gas-Solid Partition Chromatography with Real Carrier Gases1’Sb
by David C. Locke2 Department of Chmistry, Stevens Inetitute of Technolooy, Hoboken, New Jersey 07030 (Received April 81, 1966)
The effects of gas phase nonideality and mean column pressure on sample retention have been considered in several gas-solid partition chromatographic systems defined in terms of the observed sample and carrier gas isotherms. As in gas-liquid partition chromatography, the distribution coefficient is dependent upon the mean column pressure, decreasing slightly with increasing pressure of thermodynamically imperfect carrier gases. I n the limiting case of gas phase ideality, the distribution coefficient is proportional to the sample adsorption constant. Considerable potential is seen for the extraction of second virial coefficients, adsorption constants, and quantities calculable from these parameters from gas-solid partition chromatographic data.
Introduction Gas-solid partition chromatography (g.s.p.c.) has been used for the separation of gaseous mixtures somewhat longer than gas-liquid partition chromatography (g.1.p.c.). However, being restricted mainly to the analysis of the fixed gases and simple organic compounds, the study of g.s.p.c. became submerged in the deluge of theory and application following the introduction of g.1.p.c. in 1952. More recently, renewed interest has arisen in the theory and practice of linear elution g.s.p.c. In this paper, several systems defined in terms of the observed sample and carrier gas adsorption isotherms are considered. Quantitative predictions are made as to the effect of mean column pressure and gas phase nonideality on the retention behavior of adsorbates in , ~ a given carrier gas in the g.s.p.c. As in g . l . ~ . c .for simpler adsorption systems, absolute sample retention is linearly related to the mean column pressure; at constant pressure, the distribution coefficient decreases slightly with increasing gas phase nonideality. It is anticipated that g.s.p.c. will provide a simple, reasonably accurate method for the determination of the second virial coefficients which characterize these gas phase imperfections. Furthermore, the utilization of small changes in partition ratio with mean column pressure or carrier gas nonideality may have important analytical consequences for the resolution of difficultly separable mixtures. Since the distribution coefficient is proportional to the adsorption constant ’of the sample, Tha Jou~nalof Phyeical Chemistry
it is apparent that g.s.p.c. offers a means for obtaining information about gas-solid interactions.
Theory We define the fundamental adsorption distribution coefficient, K,, by
K,=
1
number of moles of component adsorbed per unit weight of adsorbent number of moles of component in the gas phase per unit volume of gas phase
( (
)
(1) The distribution coefficient is related to the partition ratio, k,, defined as the amount of component in the adsorbed phase divided by the amount of component in the gas phase, according to
K , = k,(Vg/W,) (2) where V g is the interstitial volume of the column, the retention volume of an unadsorbed component, and w s is the weight of adsorbent in the column. Note that K , has units of cubic centimeters per gram of adsorbent, while k , is dimensionless. We could have as (1) (a) Work supported by the National Aeronautics and Space Administration under Contract No. NSG-494; (b) presented a t the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Pittsburgh, Pa., March 1-5, 1965. (2) Analytical Rasearch Division, Esso Research and Engineering Co., Linden, N. J. 07036. (3) D.H.Desty, A. Goldup, G. R. Luckhurst, and W. T. Swanton, “Gas Chromatography,” M. van Swaay, Ed., Butterworth and Co. Ltd., London, 1963,p. 67.
GASSOLID PARTITION CHROMATOGRAPHV WITH REALCARRIER GASES
easily defined K , in terms of the number of moles of component adsorbed per unit area of adsorbent, in which case K , would have units of centimeters. However, the weight of adsorbent is more readily measured than its surface area. In any case the final numerical values will differ only a constant. Often we need to know both quantities anyway. k, can be determined experimentally from the sample retention time, t,, since t, = (L/u) (1 k,), where L is the column length and u is the carrier gas velocity. K , can be obtsined from eq. 2 and is related to the corKawa, rected retention volume, VRO, by VRO = V g and to the heat of adsorption, AH,, by K , = c exp (- AH,/RT). In this paper we shall be mainly concerned with the effect of gas phase nonideality on retention ( K , or k,). The development used here relies heavily on the similar treatment of g.1.p.c. by Luckhurst, who with Desty, et aL13considered this effect in gas-liquid partition chromatographic systems. The case of g.s.p.c., however, is slightly more complicated: both the component of interest and the carrier gas may be adsorbed, and each may follow a different adsorption isotherm. Furthermore, the carrier gas may behave ideally for all practical purposes, as is effectively the case with helium at high temperatures, but the adsorbate vapors may deviate appreciably from ideal behavior. It is apparent that several distinct situations need to be considered. It will be assumed in most cases that the adsorbate obeys Henry’s adsorption law, Le., that the amount of component present is so small that its adsorption isotherm is linear. Experimentally, this qualification is easily met since very small samples can be used in conjunction with sensitive ionization detectors or microvolume thermal conductivity cells. The carrier gas may not be adsorbed, or it may follow a linear or a Langmuir-type adsorption isotherm, depending upon the experimental conditions, the characteristics of the adsorbent, and the nature of the carrier gas. Situations involving multimolecular adsorption will not be considered in this paper. Although mean column pressures may be as large as several atmospheres, normal operating temperatures are considerably higher than the critical temperatures of the usual carrier gases. Thus, carrier gas adsorption usually will occur only to an extent which can be described by a linear or a Langmuir-type isotherm. It will be necessary in all cases to consider that second-order adsorbed phase interactions are negligible. This assumption will be valid if we restrict our attention to situations where only very small quantities of sample are present. I n such cases, lateral interactions
+
+
3769
between adsorbed molecules and interactions between the bulk gas and the adsorbed species will be negligible.*~~ This is an important point if the deviations of our measurements from ideality are to reflect gas phase interactions only. The first case to be considered (case I) is the simplest : the carrier gas is not adsorbed, the adsorbate follows a linear isotherm, and the gas phase is considered ideal. In practice, such a situation could be approximated with very small samples of simple adsorbates, He carrier gas, and moderately high column temperatures. Letting n2’ and nZg be the number of moles of component adsorbed and the number in the gas phase, respect ively nza/w, nzg/Vg
Ka = -
(3)
Following Barker and Everett’s d e r i ~ a t i o nwe , ~ find an expression for Henry’s adsorption law
nZa= kHApzg (4) where ~ I I .(in mole atm.-l cm.-2) is the adsorption constant, a function of the gas-solid interaction potential energy; A is the surface area of the adsorbent present; and pzg is the partial pressure of sample component above the adsorbent. Adsorption is linear with the quantity of sample. For ideal gases
nzg/Vg= pZg/RT
(5)
Thus
Ka = k ~ A p z ~ R T / ~=, p~z H ~ART/w,
(6)
I’n terms of the adsorption partition ratio, k, = kHA R T / V g . k, is dimensionless, as it should be. The next situation to consider (case 11)is the same as case I except that the gas phase behaves nonideally. These conditions may be experienced with, for example, Hz carrier gas and a low activity adsorbent (such as graphitized carbon black6) at moderate column temperatures. The adsorbate of interest follows a linear isotherm, but the carrier gas is not adsorbed. For real gases, we have in place of eq. 4.
nz’ = k ~ A orf In~ nza ~ = In HA
+ In
fig
(7)
where fig is the fugacity of the adsorbate above the adsorbent, related7 to the partial pressure according to (4) J. A. Barker and D. H. Everett, Trans. Faraday SOC.,58, 1608 (1962). (5) J. F. Hanlan and M. P. Freeman, Can. J. Chem., 37, 1575 (1959). (6) A. A. Isivikyan and A. V. Kiselev, J . Phys. Chem., 65,601 (1961). (7) E. A. Guggenheim, “Thermodynamics,” North-Holland Publishing Co., Amsterdam, 1950,p. 179.
Volume 69, Number 11 November 1966
DAVIDC . LOCKE
3770
In fig = In pzg
+ (P/RT)[B22- ( 1 - y)2(B112B12
+ B22)I
(8)
I n this equation, y is the mole fraction of adsorbate vapor in the gas phase, P is the mean column pressure (see Discussion), and Bll and B22 are the second virial coefficients of the pure carrier gas and adsorbate vapors, respectively. B12is the interaction second virial coefficient, characterizing the interactions between unlike molecules, in this case, those of the carrier gas and sample vapor. B12 is given by the expression8 relating Bll and Bz2to the second virial coefficient of a gaseous mixture, Bm
Bm
=
- y)B12 + (1 - y)'B11
(9)
+ nlg) = pZg/(pzg + ne)= pZg/i3
(10)
y2B22
+
Since y = n2g/(n2g
where nle is the number of moles of carrier gas present in the column and plg is the carrier gas partial pressure and since
P V g = (n2'
+ nlg)(RT+ BmP)
( 1 1)
eq. 3 becomes
K,
=
+
+
(nz"/w,)( P / P ~[ R~T) / P y2B22 2y(l - Y)&2 (1
+
- Y)2Bl11
(12)
Combining eq. 7, 8, 10, and 12, we have
2y(l
+
- y)B12 + ( 1 - Y ) ~ B u I (P/RT)[B22(1 - Y)2(Bii- 2B12 + &)I
(13)
For very small samples, y + 0. Then after rearrangBII. ing eq. 13, expanding the resulting term in'ln ( 1 PIRT), and neglecting all but firsborder terms in the expansion
+
In (k*ART/w,) + 2B12P/RT (14) A plot of In K , vs. P should be linear, with a slope of
In K,
=
2B12/RTand an intercept identical with eq. 6. Another case of lesser importance might also be considered. I n case 111, the carrier gas closely approximates ideal behavior while the adsorbate vapors are thermodynamically imperfect. Such a circumstance might effectively arise if He were used as a carrier gas at high temperatures. Equation 11 now becomes PVg = (nzg nle)RT. Assuming,7 furthermore, that In fig = In pzg B22 P / R T , substitution into eq. 3 gives
+
+
In K , = In (kHART/w,)
+Bd/RT
nla
=
+ + nm2b2p2'/(1+ bipi' + nmlbipig/(l b l p f
(15)
At ordinary operating temperatures, it is expected
bzp2')
(16) where nmiis the number of moles of the ith component required to produce a monolayer on the surface of the adsorbent, and b, is its over-all adsorption constant, the ratio of the adsorption/desorption rate constants. Each gas or vapor decreases the amount of adsorption of the other according to the relative magnitudes of the btptg products. In g.s.p.c., component 2, the adsorbate of interest, will in general obey a linear isotherm (b2psg
