Anal. Chem. 1990, 62, 991-994
991
Prediction of Gas Chromatography Solute Activity Coefficients in Mixed Stationary Phases Based on the Wilson Equation Joief J. Cornor* a n d Miroslav M. Kopeeni
Chemical Dynamics Laboratory, T h e Boris KidriE I n s t i t u t e of Nuclear Sciences, P.O. B o x 522, 11001 Belgrade, Yugoslavia
Gas chromatography based activity and partitlon coefflclents are reported for nine solutes, including aliphatic, alicycllc, chlorinated aliphatic, and aromatic solutes, in two mlxed stationary phases, (a) N,N-dibutyl-2-ethylhexanamide N,N-dlbutyl-2,2dimethylbutanamide and (b) N,N-dibutyl-2ethylhexanamide dodecanol, in the mole fraction region from 0 to 1, for flve temperatures spanning from 298.15 to 338.15 K. The inflnlte dilution activity coefficients of solutes In mixed solvents can be accurately described by a simple, thermodynamically founded, four-parameter equation, derived from the expression originally reported by G. M. Wilson.
+
+
Second, both parameters A 3 1 and A 3 2 contain the value X33, which is proportional to 3-3 interaction energy. In the situation when component 3 is infinitely diluted, the 3-3 interaction is not significant for characterization of the mixture. With this in mind, we proceed with the modification of eq 4 to eliminate the X3, parameter. Wilson ( I ) has empirically redefined the volume fractions of the Flory-Huggins equation into what he termed the local volume fractions,
ti=
xiV,(exPt-X,,/RT))
2
j=lxjVj
INTRODUCTION In 1964, Wilson ( I ) reported an expression for the excess free energy of mixing of nonelectrolyte solutions, based on the Flory-Huggins (2-5) theory for athermal mixtures. From this equation, the activity coefficients could be derived by using the exact thermodynamic relation
(5)
exp(-Xij/ RT)
Taking into account that component 3 is infinitely diluted, it could be assumed that its local volume fraction is approximately 0. Substituting El and E2 in the Flory-Huggins equation
4,
A G , ~ = RT&
In 2
i
(6)
Xi
and using eq 3, the excess Gibbs energy becomes
AGme = -RT(xl In (xl
+ x2Al2+ x 3 8 1 3 ) +
x p In (x1Li21+ X Z + x3A2J) (7)
Following the work of Wilson, Orye and Prausnitz (6) have shown that the activity coefficient of a component 12, for a ternary mixture, is given by the equation In Y k = 1 - In ( X l - I k l + X 2 * i k 2 X 3 ~ i k 3 ) -
+
xl.ilk Xi
+ XZAip + XgA13
x2A2k
-
XlLi21
+ X2 + x3A23
-
X3A3k xl'431
+ XZA32 + x 3
Combination of eqs 1 and 7 gives the activity coefficient of component 3 in the ternary mixture In y3 =
xi2
+ x ~ x Z A-~~ ~1 A 1 3+ x ~ x ~ A+Z X?~ - x 2 A 2 3 + x,Li12 + x 3 ~ 4 1 3 X l l i 2 1 + x 2 + X 3 h 2 3 (8)
(2)
Considering that the component 3 is infinitely diluted, eq 3 can be further simplified to In y3m= 1 -
-
x1A13
(9) + XlA21 Generalization of this result to a solution containing any desired number of components, gives x1
In the above relation, V ,stands for the molar volume of pure component i and A, is proportional to the i-j molecule perwise interaction energies. Equations 2 and 3 are derived for real concentration conditions and have been successfully tested by several authors, clearly indicating the superiority of the approach to many theoretical models proposed (6). If one of the solutes is infinitely diluted, for instance component 3 (x3 = 0), eq 2 will be reduced to In y3m=
Equation 4 is not, however, the best solution for describing the infinite dilution activity coefficients. mainly for two reasons. First, eq 4 has six parameters and their accurate determination requires a lot of experimental measurements.
+ X2A12
x2
J-1
In the case of binary mixture, eq 10 is reduced to In yZm= 1 - A,,
(11) and as such was used first by Hussey and Parcher (7), to derive gas-liquid based activity coefficients. The authors (7)used solute as an infinitely diluted component, while the column stationary phase was regarded as the second constituent of the binary mixture.
EXPERIMENTAL SECTION The equipment, techniques, and procedures pertaining the high-precision data acquisition by GLC have been summarized
0003-2700/90/0362-0991$02.50/0 1990 American Chemical Society
992
ANALYTICAL CHEMISTRY, VOL. 62, NO. 10, MAY 15, 1990
1,
OL
0.5:
a-a-o-a--o-O-a-a-~-~ *-*-+-*-+-*-*-
0
02
+-+-+-+
OL
06
08
-
+*\,
\
%a.
*.+-.*-+-;a-a-a-m]
,
+
-+++
-
+-t-+-+
0.0
10
0
0.2
0.b
XDBEHA
0.6
1.6
0.8
IDBEHA
+
+
Figure 1. Activity coefficients of infinitely diluted solutes in DBEHA DBDMBA mixture vs solvent composition at 308.15 K. The solutes are as follows: 0, hexane; 0 , heptane; A, octane; A, 2,3-DMB; 0, 2,4-DMP; E, cyclohexane; 9,benzene: 0 , CH,CI,; CHCI,. Solid lines are calculated from eq 9
Figure 2. Activity Coefficients of infinitely diluted solutes in DBEHA DDA mixtures vs solvent composition at 308.15 K. The solutes are as follows: 0, hexane; 0 , heptane: A, octane; A, 2,3-DMB; 0, 2,4-DMP; E, cyclohexane; 8 , benzene; 0 , CH,CI,; CHCI,. Solid lines are calculated from eq 9.
elsewhere (8). The GC was laboratory constructed, the hydrogen carrier gas flow was regulated by a diaphragm gauge and measured by a 50-cm3 soap bubble meter. The column, 1 m long, 4,5 mm i.d. stainless steel tubing, was thermostated in a water bath. The column temperature, monitored by a precise mercury thermometer, was constant within 0.05 K. The carrier inlet pressure was measured with a mercury manometer, and the outlet pressure (assumed to be the same as the atmospheric one) was measured with a precise barometer. The solvent N,N-dibutyl-2-ethylhexanamide(DBEHA) and N,N-dibutyl-2,2-dimethylbutanamide (DBDMBA), kindly supplied to us by G.-M. Gasparini, CNEN, Casaccia, Roma, Italy, were vaccum distilled prior to use. High-temperature capillary GC revealed purity in excess of 99%. Dodecanol (DDA), a BDH product, was of p.a. grade. The solutes n-hexane, n-heptane, n-octane, 2,3-dimethylbutane (2,3-DMB), 2,4-dimethylpentane (2,4-DMP), cyclohexane, benzene, and di- and trichloromethane were all of p.a. grade, Merck, and used without further purification. The packings prepared by rotary evaporation with sO/lOO mesh Chromosorb G AW-DMCS were placed by suction into the column. The total mass of liquid (ca. 5% (w/w) throughout) was assessed for each packing a t C11.570 relative standard deviation by ashing. Partition coefficient data were evaluated from the usual relation
Table I. CIJ Parameters of Equation 9 (in kJmmol-'), Defined by DBEHA (1)-Solute (3) Interaction, at Given
+.
(9)
where V, is the volume of the column stationary solvent, j is the James-Martin carrier compressibility correction factor, F, is the fully corrected flow rate, and t,' is the solute retention time adjusted against void space. V , was determined from the total mass of liquid stationary solvent and the solution densities, measured by an Anton Paar DMA 55 densitometer. The usual relative standard deviation in KLdetermination was at worst 2%. The solute activity coefficients at infinite dilution, y - , were deduced from eq 13 without virial corrections
+,
Temperatures solute C6HM C7H16
CBHM 2,3-DMB 2,4-DMP C6H12 C6H6
CHZC12 CHCI,
298.15 K
308.15 K
318.15 K
328.15 K
338.15 K
-1.3 -0.8 -0.3 -1.4 -1.1 -2.5 -3.8 -5.9 -6.2
-1.4 -0.9 -0.4 -1.5 -1.2 -2.6 -3.9 -6.1 -6.3
-1.5 -1.0 -0.5 -1.6 -1.3 -2.7 -4.1 -6.2 -6.4
-1.5 -1.0 -0.5 -1.7 -1.3 -2.8 -4.2 -6.3 -6.4
-1.6 -1.0 -0.6 -1.8 -1.4 -2.9 -4.3 -6.4 -6.5
The C,j parameters for all mixtures were computed by applying eq 9 t o the activity coefficient data, using a simplex (10) iteration algorithm, and are collected in Tables I-V. Equation 11 allows C13 (or CZ3)parameters to be directly obtained from simple measurements of the activity coefficient of infinitely diluted solute (3)on pure solvent (1 or 2). This procedure might be regarded as a first useful approach in evaluating C13 as pointed out by Hussey and Parcher (7). Here, each Cij parameter was obtained from the curve fitting procedure, meaning that every C, was equally weighted and, hence, that they are given with the same standard deviation. The adopted procedure enables determination of the Cij parameters with a n experimental error of f400 J-mol-'. Figures 1 and 2 illustrate a n excellent agreement of the calculated curves based on the computed C, values and eq 9, with the experimentally determined activity coefficient values. It has been already said that the C , parameters are thermodynamically justified, and as such, they have physical significance. T h e C,, parameters of the system DBEHA (1) + solute (3)are given in Table I, while C23 parameters of the system DBDMBA (2) solute (3) are collected in Table 11. A comparison of these values clearly shows t h a t these two parameters are equal (at the same temperature and for the given solute) within the experimental error. This result is expected, as these two amides are very close members of a homologous series and, therefore, they should exhibit near to identical chemical behavior. For the same reason, the C12 and C, parameters of the DBEHA (1)+ DBDMBA (2) interaction are very close t o 0 (less than the experimental error, except for 2,3-DMB at 298.15 and 338.15 K for which C1, is 0.4 and -0.6 kJ-mol-', respectively). In other words, the interaction
+
where V,,, and PO are the solute molar volume and the bulk vapor pressure, respectively. The virial corrections were omitted, since it was shown (9) that this correction is trivial under the experimental conditions adopted here.
RESULTS AND DISCUSSION Experimentally determined partition coefficients and the corresponding activity coefficients are given as supplementary material. See paragraph a t end of paper for ordering information.
ANALYTICAL CHEMISTRY, VOL. 62, NO. 10, MAY 15, 1990
Table 11. CZ3Parameters of Equation 9 (in kJ*mol-I), Defined by DBDMBA (2)-Solute (3) Interaction, at Given Temperatures solute C6H14 C7H16
CJl8 2,3-DMB 2,4-DMP C6H12 C6H6
CH2C12 CHCL
298.15 K
308.15 K
318.15 K
328.15 K
338.15 K
-0.9 -0.3 0.2 -0.9 -0.6 -2.1 -3.4 -5.6 -5.8
-1.0 -0.4 0.1 -1.1 -0.7 -2.2 -3.5 -5.7 -5.9
-1.0 -0.5 0.0 -1.1 -0.8 -2.3 -3.6 -5.8 -5.9
-1.0 -0.5 0.0 -1.2 -0.8 -2.4 -3.7 -5.9 -6.0
-1.1 -0.6 0.0 -1.3 -0.8 -2.4 -3.7 -6.0 -6.0
Table 111. C,, Parameters of Equation 9 (in kJ*mol-'), Defined by DDA (2)-Solute (3) Interaction, at Given Temperatures solute C6H14 C7H16
C8Hl8 2,3-DMB 2,4-DMP C6H12 C6H6
CHZCI, CHCI,
298.15 K
308.15 K
318.15 K
328.15 K
338.15 K
1.9 2.6 3.6 1.7 3.3 0.0 -0.7 -2.1 -2.8
1.6 2.4 3.2 1.5 2.8 -0.3 -1.0 -2.3 -2.9
1.4 2.2 3.0 1.4 2.5 -0.4 -1.2 -2.6 -3.0
1.3 2.1 2.9 1.3 2.3 -0.6 -1.4 -2.8 -3.0
1.2 2.1 2.9 1.2 2.2 -0.7 -1.5 -3.0 -3.1
Table IV. C,, Parameter of Eqatuion 9 (in kJ*mol-'), Defined by DBEHA (1)-DDA (2) Interaction, at Given Temperatures" 298.15 K
308.15 K
318.15 K
328.15 K
338.15 K
CHzC12 CHCI,
-1.0 -1.2 -1.0 -1.5 -0.3 -0.9 -0.9 0.1 0.2
-1.2 -1.0 -1.3 -0.3 -1.3 -0.8 -1.0 0.1 0.1
-1.6 -1.1 -1.4 -1.0 -1.3 -1.2 -1.0 0.0 0.0
-1.8 -1.3 -1.5 -0.8 -1.3 -1.5 -1.1 -0.1 -0.2
-2.1 -1.4 -1.5 -0.7 -1.3 -1.8 -1.2 -0.3 -0.4
mean
-0.9
-1.0
-1.2
-1.4
-1.4
solute C6H14
C7H16
C8Hl8 2,3-DMB 2,4-DMP C6H12 C6H6
Mean values are calculated without values obtained by using CH2C1, and CHCI,.
Table V. CzlParameters of Equation 9 (in kJ*mol-'), Defined by DBEHA (1)-DDA (2) Interaction, at Given Temperature9 298.15 K
308.15 K
318.15 K
328.15 K
338.15 K
CHCI,
1.0 1.2 1.4 1.8 -2.4 0.9 2.4 0.8 0.7
1.7 1.o 2.3 -0.7 2.3 0.8 2.6 0.9 0.7
2.5 1.5 2.8 1.1 2.4 1.7 2.7 1.0 1.0
3.0 2.2 3.2 1.0 2.6 2.3 2.9 1.3 1.3
3.5 2.7 3.3 1.1 2.8 2.8 3.0 1.8 1.8
mean
0.9
1.4
2.1
2.5
2.8
solute C7H16
C8Hl8 2,3-DMB 2,4-DMP C6H12
energy between DBEHA-DBEHA molecules is the same as that of DBEHA-DBDMBA or DBDMBA-DBDMBA. These findings end up with a conclusion that the two amides form a near-to-ideal solution. Table I11 shows the parameters of the DDA (2) + solute (3) interaction. These parameters are always greater than those of the DBEHA (1) + solute (3) interaction. I t should be underlined that the DDAsolute interactions are lower than the DBEHA-solute interactions, which results in poorer solubility of the solutes in DDA. The Clz and Cpl interaction parameters of DBEHA (1)DDA (2) interaction are given in Tables IV and V. Large Clz and C, values suggest the existence of a considerable DBEHA-DDA interaction, probably as a result of the H-bond formation. According to the theory, CI2and Czl should be independent of the solutes applied for their determination, because the solutes are infinitely diluted and, hence, have no effect on overall interaction. This is true for DBEHA-DBDMBA-solute systems, but only partly valid for the system comprising DBEHA-DDA-solute. Indeed, the C12and Czl parameters of the DBEHA-DDA mixture are independent of the used solute, except for di- and trichloromethane, which are capable of interacting specifically. In the case of strong solute-solvent approximation, used here, might not hold. interaction, the it The C,, parameters should have been independent of temperature (the interaction energy is barely dependent on temperature), but we found their parabolic dependence on temperature. This might result from an incompleteness of the Wilson's approximation, observed for many systems ( I I ) without definite explanation of the effect.
CONCLUSION The modified Wilson equation is successfully applied for describing the infinitely diluted activity coefficients of various solutes in mixed solvents. Experimental results for mixtures of several components (one of them is infinitely diluted) are excellently fit by a four-parameter expression 9. The parameters CI2and C, should be solute independent and, thus, invariably hold for nonreacting solutes. Hence, to evaluate the activity coefficients of a series of nonpolar components,
993
C6H6
CH2C12
'
Mean values are calculated without values obtained by using CH,CI, and CHCI,. (I
one needs only two fit parameters, viz. C13 and C23,providing that CI2 and Czl are previously located by an independent nonpolar volatile, for the given solute. As shown, the situation of a polar or of a specifically is much more complicated if y30D reacting solute is to be predicted. There, Clz and Czl are not constant and deviate from the value established by nonpolars with the magnitude assumed t o exist between the reacting solute and the stationary phase constituents. Equation 9 allows the calculation of the activity coefficients of the solutes in mixed solvents, assuming that the C,, parameters are known, and it, therefore, can be used for prediction of solute elution order from a GLC column. The Wilson equation could be easily expanded to the stationary phases of three or more components, and it was shown that the parameters of the equation have physical significance for, a t least, binary stationary phases. Supplementary Material Available: Partition coefficients and activity coefficients for solutes hexane, heptane, octane, 2,3-DMB, 2,4-DMP, cyclohexane, benzene, CH2C12,and CHC13 in DBEHA + DBDMA and DBEHA + DDA (19 pages). Photocopies of the supplementary material from this paper or microfiche (105 X 148 mm, 24X reduction, negatives) may be obtained from Microforms & Back Issues Office, American Chemical Society, 1155 16th Street, NW, Washington, DC 20036. Orders must state whether for photocopy or microfiche and give complete title of article, names of authors, journal issue date, and page numbers. Prepayment, check or money order for $34.00 for photocopy ($36.00 foreign) or $10.00 for microfiche ($11.00 foreign), is required and prices are subject to change.
LITERATURE CITED (1) (2) (3) (4)
Wilson. G M J Am Chem Soc 1964, 86. 127 Flory, P J J Chem Phys 1941, 9 , 660 Flory. P J J Chem Phys 1942, 10, 5 1 Huggins, M L J Chem Phys 1941, 9 , 440
Anal. Chem. 1990, 62, 994-996
994
(5) Huggins, M. L. Ann. N . Y . Acad. Sci. 1942, 43, 1. (6) Orye. R. V.; Prausnltz, J. M. Ind. Eng. Chem. 1965, 5 7 , 18. (7) Hussey, C. L.; Parcher, J. F. Anal. Chem. 1973, 45, 926. (8) Laub, R. J.; Purnell, J. H.; Williams, P. S.;Harbison, M. W. P.: Martire, D. E. J . Chromatogr. 1978. 155, 233. (9) Conder, J. R.; Young, C. L. Physicochemical Measurement 6y Gas Chromatography; John Wiley & Sons: Chichester, 1979. (10) Deming. S. N.; Morgan, S. L. Anal. Chem. 1973, 45, 278A
( 11) Dohnal. V., Vesely. F., VinH. J., Collect. Czech. Chem. Commun. 1982, 47, 3188.
RECEIVED for review November 16, 1989. Accepted February
E,1990. The authors are indebted to the Research Fund of SR Serbia. Belgrade, for partial financial support.
Application of Hydrogen Storage Alloy for the Determination of Trace Impurities in High-Purity Hydrogen by Gas Chromatography Hiroshi Ogino,* Yoko Aomura, a n d Masashi Mizuno Technical Research Laboratory, Toyo Sanso Co., Ltd., 3-3, Mizue-cho, Kawasaki-ku, Kawasaki-shi, Kanagawa 210, J a p a n
A hydrogen storage alloy was applied to determine the trace impurities, such as neon, argon, nitrogen, krypton, methane, and xenon, in hydrogen. This system consists of a gas chromatograph combined with a precolumn filled with the hydrogen storage alloy. The alloy efficiently retains hydrogen at room temperature and under the pressure of the carrier gas. By use of a photoionization detector, the detection HmKs achieved were as follows: 4.7, 0.02, 0.02, 0.01, 0.01, and 0.01 ppm for Ne, Ar, N,, Kr, CH,, and Xe, respectively.
INTRODUCTION For the determination of inherent gas impurities in hydrogen, gas chromatography (GC) has been widely used as the preferred method. The photoionization detector (PID), which is based on the emission from a direct current discharge in helium gas (1,2),is a universally sensitive detector ( 3 , 4 )and has especially high sensitivity for gases such as argon, nitrogen, krypton, methane, and xenon. We reported in a previous paper (5)that the P I D is suitable for the determination of trace amounts of such gases. However, it has been hard to separate and accurately determine the trace amounts of impurities a t levels less than parts per million in hydrogen. The use of a high sensitivity detector for these gases results in a huge hydrogen peak overlapping other peaks that are later eluted. It is necessary to eliminate the hydrogen peak overlap. In general, hydrogen is eliminated prior to entering the analytical column of the GC with a hydrogen transfer system (palladium alloy tube) and/or copper oxide (CuO) catalyst. T h e former method utilizes the very high and selective permeability of the palladium alloy, heated between 500 and 625 "C, to allow transfer of the hydrogen ( I ) . T h e latter method requires temperatures over 800 "C. If the hydrogen sample contains oxygen, the system causes water formation. There are some problems with these methods relative to unwanted deactivation of the column from the resultant water. The resulting water should be adsorbed by a short precolumn filled with desiccant, such as a molecular sieve (e.g. MS-13 X) column. For the last two decades, hydrogen storage alloys such as LaNi, have provided purification and storage techniques for hydrogen gas ( 6 ) ,but there have been no published methods
* Author to whom correspondence should be addressed. 0003-2700/90/0362-0994$02 50/0
Table I. Hydrogen Storage Alloys" HSA-1 MmNi4SA10.5 HSA-2 LaNi,,,Al0,, HSA-3 LmNi4.7A10.3 HSA-4 Ti,.,Zro.,,Mno.,CrCuo,~ Mm and Lm are mischmetal and lanthanum rich mischmetal, respectively; mischmetal is a mixture of lanthanoid rare earth metals extracted from ores. (I
for applying hydrogen storage alloys to gas analysis techniques. This paper describes a new analytical method for determining trace impurities in hydrogen by the use of a photoionization detector (PID)and the precolumn separation using a hydrogen storage alloy (HSA).
EXPERIMENTAL SECTION Apparatus a n d Conditions. A schematic diagram of the experimental apparatus is shown in Figure 1. A gas chromatograph with a PID (Hitachi, GC-263-30, Tokyo, Japan) was used in this experiment. A precolumn was installed between the gas sampler with a 1.5-mL loop and the analytical column, which was packed with a molecular sieve (MS-5A, 60/80 mesh) in 3 m X 3 mm i d . stainless steel tubing. The precolumn was 30 cm X 3/8 in. 0.d. stainless steel tubing and was packed with HSA (20/60 mesh) as shown in Figure 2. Silica fibers were packed intermittently in order to prevent any expansion problem of the precolumn, e.g., wall rupture, which might be caused by hydrogen absorption into the alloy. Operating conditions of the GC-PID and the precolumn were as follows: oven temperature, 80 "C; detector temperature, 100 "C; carrier gas, He, 50 mL/min; discharge gas, He, 44 mL/min; discharge potential, 750 V; precolumn temperature, a t room temperature (ca. 25 "C). Materials. The HSA used in the experiments are listed in Table I. They were purchased from Japan Metals and Chemicals Co., Ltd. (for HSA-1-3), and Daido Steel Co., Ltd. (for HSA-4), respectively. Reference gases were prepared by the gravimetric method and were supplied by Toyo Sanso Co., Ltd. Most of the experiments, which were done in order to establish the optimum operating conditions of the precolumn and gas chromatograph, were conducted with reference gases having the following compositions: [l] 9.0 ppm Ar and 9.0 ppm N, in H,; [2] 46.8, 9.4, 9.4, and 9.4 ppm for neon, argon, krypton, and xenon especically in H2. Activation of the HSA. Hydrogen absorption with HSA (e.g., LaNi,) is based on the following reaction: LaNi, + 3H2 .-+LaNi,HG + heat This is the reversible reaction of a solid alloy with hydrogen gas. C 1990 American Chemical Society
