or methane streams could be particularly difficult and even small amounts of these gases in higher boiling hydrocarbons can seriously complicate the analysis. For example, the presence of only 0.9 per cent ethane in the propane used for the solubility determinations made it necessary t o use a 36-foot squalane column to obtain an adequate acetylene/ethane ssparation. With the apparatus described acetylene contents down to ca 0.1 v.p.m. could be detected. In the absence of interfering hydrocarbons acetylene concentrations of the order 0.01 v.p.m. or less could be measured by improvements in the design of gas chromatographic apparatus (6). It is doubtful, however, if this would lead to a significant improvement in the overall sensitivity of the method since quantitative water to acetylene conversion
would be difficult to achieve a t concentration levels much below 0.1 v.p.m. Although the main objective in this investigation was to develop a method for determining trace amounts of water in propane and butane streams containing methanol, the technique is of course applicable to all gases that are inert toward calcium carbide. It may therefore be applied to a very wide range of problems. LITERATURE CITED
S. T., Smith, V. N., ANAL. CHEM.34, 1129 (1962). (2) Desty, D. H., Geach, C. J., Goldup, A., “Gas Chromatography 1960” p, 46, R. P. W. Scott, ed., Butterworths, London, 1960. (3) Duswalt, A. A,, Brandt, W. W., ANAL.CHEM.32, 272 (1960). (4) Forbes, J. W., Ibid., 34, 1125 (1962). (5) Hersch, P. A., Deuringer, R., Pitts(1) Abrams,
burgh Conference on Analytical Chemistry and Applied Spectroscopy, March 1965. (6) Huytens, F. Hii Rijnders, G. W. rl., Beersum, W. V., Gas Chromatography 1962” p. 235, M. van Swaay, e d , Butterworths, London, 1962. (7) Kirk-Othmer, “Encyclopedia of Chemical Technology,” J’ol. 2, p. 837, Interscience Encyclopedia Inc., New York, 1948. (8) Knight, H. S., Weiss, F. T., ANAL. CHEM.34, 749 (1962). (9) Kyryacos, G., Boord, C. E., 131st Meeting ACS, &$ami, April 1957. (10) hiiller, S. A., Acetylene-Its Chemistrv and Uses.” Vol. 1. Ernest Benri Ltd:, London, 1965. (11) S‘illelume, J. de, Ann. C h i m (Paris) 7, 265 (1952). (12) Walker, J. A. J., Campion, P., Analyst 90, 199 (1965). RECEIVED for review February 21, 1966. Accepted July 27, 1966. Permission t o publish this paper has been given by The British Petroleum Co., Ltd.
Solution Thermodynamics from Gas-Liquid Chromatography R. E. PECSAR’ and J. J. MARTIN University o f Michigan, Ann Arbor, Mich.
b Gas-liquid chromatography has been employed to study the thermodynamic solution properties of twocomponent volatile nonelectrolyte solutions at infinite dilution. The expressions relating chromatography to thermodynamics have been developed and the theory of hydrogen bonding has been used to order liquids into distinct classes and predict solution deviations from ideality. Homologous series of alkanes, chloromethanes, alkyl formates, aldehydes, amines, and alcohols were studied in water, 2-pentanone, and 2,3,4-trimethylpentane from 20’40” C. The resulting solution thermodynamics agreed quite well with the anticipated behavior as well as existing literature results. The data in general were successfully correlated with a linear relation between the partial molar excess free energy and the hydrocarbon chain length of the solute for a homologous series in a given solvent.
T
HE INITIALwork
deriving thermcdynamic solution properties from chromatographic measurements was that of Littlewood, Phillips, and Price ( 2 1 ) in 1955. The authors defined the concept of the specific retention volume which allowed a comparison of data between different investigators inde1 Present address, The Corp., Van Nuys, Calif.
Marquardt
pendent of chromatographic variables. Subsequent to this work, numerous thermodynamic studies have been made utilizing gas-liquid chromatography and the properties obtained by this technique have been adequately validated by measurements made employing static techniques on the same systems. Porter, Deal and Stross (16) demonstrated that the properties obtained represented true thermodynamic equilibrium and were constant for wide ranges of the chromatographic parameters. They also ran static equilibrium studies verifying the data obtained by gasliquid chromatography (GLC) . As the solvent in GLC is dispersed on a solid support, the role of this support in the thermodynamic equilibration process has been closely scrutinized. Adlard, Khan, and Whitham (1) studied benzene in dinonyl phthalate spread on a solid support in sufficient quantity to ensure complete surface coverage. Later these same authors (8) coated dinonyl phthalate in a capillary column and again studied benzene and other solutes. The agreement obtained by the two different techniques suggests that with a carefully coated inert support material the data obtained represent true vaporliquid equilibrium between the solute and the solvent. I n the present study a basic desire was to extend the technique of GLC to include studies of systems with a volatile solvent. I n all of the work just cited,
the solvent was a large organic molecule which had an exceedingly low vapor pressure a t the temperature of interest. By employing a volatile solvent the more common binary solutions may be studied, not merely those peculiar to GLC. A few attempts at studying such systems had previously been made. Purnell and Spencer (16) conducted a preliminary investigation on the separation of chlorinated methanes utilizing water as a solvent and obtained a boiling point separation. Pollard and Hardy (14) in a more thorough study determined that as the solute concentration decreased the elution order changed from that based on boiling points t o one dependent on the solubilities of the chloromethanes in water. The latter authors also considered the methanolwater system. Both of the above investigations were hampered by the nonstationary nature of the stationary phase. In order to reduce this problem Kwantes and Rijnders (10) first utilized a forecolumn or presaturator. In the presaturator, the carrier gas is saturated with solvent, either in bulk form or coated on a solid support, a t a given temperature and pressure. While this reduces bleeding in the main column to a large extent, because of expansion of the gas phase during transit through the system the problem is never completely alleviated. The two-component volatile study of Kwantes and Rijnders (10) was limited to normal paraffins in their VOL. 38, NO. 12, NOVEMBER 1966
1661
next higher homolog. Based on the success of this study, the present work employs the above described technique but applies it to a much wider scope of binary nonelectrolyte solutions. THEORY
The fundamental thermodynamic quantity in GLC is the partition coefficient defined as
The basis relation between the partition coefficient and the measured variable, the retention volume, may be evolved in a simpler manner than the standard derivations if one relies slightly upon intuition. The general concept is attributed t o Sternberg (18). Equation 1 states that the partition coefficient is the ratio of the solute concentration in the stationary phase to that in the mobile phase. S o w the total moles of solute in the column is n = nG
+
(2)
nL
and the velocity of solute movement in the colunin may be expressed as
u =u,*j
(3)
As the fraction of the solute in the gas phase is nol n, Equation 3 becomes
u = u , . -nGn
(4)
but from Equations 1 and 2
n-o = - = nG n nG n L nG VG (5) no nok VL/Va V G ~ V L
+
+
+
In addition the velocity of an unretained component may be expressed as
Therefore substituting Equations 5 and 6 into Equation 4 yields
Alternately, the velocity of solute movement may also be expressed as
analogous to Equation 6. Now by equating Equations 7 and 8, the desired relation is obtained.
Vn
Vo
+ kVL
(9)
This of course is the standard plate equation derived countless times by 1662
ANALYTICAL CHEMISTRY
other techniques in the open literature. Of course the justification here lies in the intuitive equivalence of the time average fraction of solute in the gas phase with the fractional residence time of the solute in the gas phase. Inherent in the development, however, is the concept of thermodynamic equilibrium involved by definition in the partition coefficient. As the retention volume determined from Equation 9 is still dependent on the chromatographic parameters being measured, to have a true invariant property Littlewood (11) defined the specific retention volume as
In
ym =
In
RT PO +-x V R M ~ ' jRT =-
As can be seen from a comparison of Equations 13 and 15, the latter two terms on the right side of Equation 15 represent the correction due to nonideality in the gas phase. Now that the relation between solution thermodynamics and GLC has been established through Equation 13, certain other classical solution properties may be readily obtained. The basic equation for the partial molar excess free energy is AGE = A H 8
or combining Equations 1, 9, and 10
yP
= y"xp0
(12)
In order to remove the gas phase terms from the relations the ideal gas law, P/No = RT, may be used in conjunction with Equations 11 and 12 to yield
RT
ym =
pF&o
As the pressures studied in this work are near atmospheric and helium is the chosen carrier gas, the inclusion of the ideal gas law restraint should be reasonably valid and cause little error. As in any actual chromatographic column, a finite pressure drop exists over the lsngth of the column, the expression for V R given by Equation 10 is usually corrected for the pressure gradient by the factor
The relation has been theoretically derived by numerous workers. Again, as the experimental pressures were near atmospheric and the columns employed were relatively short, the magnitude of the factor, j , was very nearly unity. At this point it should be mentioned that if nonideality of the gas phase becomes significant and it is desired to have the infinitely dilute activity coefficient represent the true deviation from ideality in the liquid phase alone, the ideal gas law assumption must be removed. The mathematical representation of the problem has been correctly formulated by Desty et al. ( 5 ) and involves representing the gas phase behavior by the virial equation of state, replacing pressure terms by the corresponding fugacities. The resultant expression is
(16)
The infinitely dilute activity coefficient is related to the partial molar excess free energy by AGE =
Now for a nonideal solution, Raoult's law may be expressed as
- TAXE
RT In
ym
(17)
By assuming ASE and A H E constant for a small change in temperature and differentiating Equations 16 and 17 with respect to the reciprocal temperature yields
Thus by studying the thermal variation of the infinitely dilute activity coefficient by GLC, the partial molar excess enthalpy may be determined. With a knowledge of the partial molar excess enthalpy and free energy, utilizing Equation 16, the partial molar excess entropy may be computed. EXPERIMENTAL
The chromatographic retention volumes of the systems studied in this work were obtained from an F and P v l Model 609 Gas Chromatograph equipped with a highly sensitive flame ionization detector. In order to obtain thermal control of the column to 10.1' C. for prolonged periods, the heating circuit was modified to provide for fine proportional control instead of the standard on-off mode of operation. The injection port and detector housing are thermally regulated independently. The schematic flow diagram of the apparatus is shown in Figure 1. The flow rate of the helium carrier gas is controlled by a Moore constant volume flowmeter and a precision needle valve. The rate is monitored by a Brooks rotameter as well as a soap bubble flowmeter. Hydrogen and air flow to the flame ionization detector are also monitored by Brooks rotameters. The carrier gas after entering the thermally modulated chamber is saturated with solvent prior to the point of sample injection. The pressure upstream of the column is registered on a Matheson Bourdon tube type gauge. Samples are injected utilizing a Hamilton 0.5microliter syringe or a Wahl-Henius
Helium Carrier
-
OCheck Valve
I A
--
Needle Valve
Gas
Carrier Gas Flowmeter
c Hydrogen Flowmeter
2 Stage Regslator
0
I
I
I I
Valve
0
. II
Needle Valve
-
1
7
Check Valve
--
Flowmeter
I
fiesaturator A 7
- -- ---Sample I n j e c t i o n
I
Port
I
2 Stage
i T t
Regulator I n l e t Pressure Gage (0-10 p s i g ) Hydrogen
V i b r a t i n g Reed Avp lif i e r
1Millivolt Recorder
Figure 1.
syringe with special volumetric spacers. The columns employed were of l/rinch diameter aluminum tubing varying from 6 to 10 inches in length. The rather short lengths were required because of the lengthy retention times of the majority of the solutes. Following elution from the column the sample components are chemi-ionized in the flame, the resulting signal being amplified by a vibrating reed electrometer and displayed on a 1-mv. Honeywell recorder. Because of the high volatility of the solvents studied, the rate of solvent depletion was significant. So as not to saturate the output to the preamplifier, the collector electrode was modified so as to be below the point of maximum ion production in the flame envelope. In this manner the high background due to solvent bleed could be overcome. Because of this high volatility, the thermal range of the study was limited from 20' to 40" C. In order to ensure that the systems studied in this investigation were broadly representative of a wide variety of solution types, the classification scheme of Ewell, Harrison, and Berg (6) was employed. This scheme, based largely on hydrogen bonding, is the one essentially presented in the numerous recent texts on gas chromatography. The various liquid classifications and the choices studied in this work are as follows: Class I. Liquids capable of forming three-dimensional networks of hydrogen bonds. Solvent: water. Class 11. Liquids containing active donor and acceptor atoms. Solutes: methyl, ethyl, and propyl alcohol; ethyl, propyl, and butyl amine.
Schematic diagram of equipment
Class 111. Liquids containing only active donor atoms. Solutes: methyl, ethyl, and propyl formate; acetaldehyde, propionaldehyde, and butyraldehyde; solvent: 2 pentanone. Class IV. Liquids containing only active acceptor atoms. Solutes: dichloro, trichloro, and tetrachloromethane. Class V. Liquids containing no active atoms. Solutes: pentane, hexane, and heptane; solvent: 2,3,4 trimethylpentane. The last class shows no tendency to hydrogen bond and thus the interactions are mainly due to dispersion forces. When considering interactions between different liquid classes, again five types arise. The first comprised of I-V and 11-V interactions shows limited solubility and always positive deviations from ideality with hydrogen bonds broken. The second limited class of 111-IV interactions shows negative deviations from Raoult's law and hydrogen bond formation. The I-IV and 11-IV interactions, composing the third class, again always shows positive deviations, but hydrogen bonds are formed and broken. A fourth very extensive class is composed of 1-1, 1-11, 1-111, 11-11, and 11-111 interactions and usually has activity coefficients in excess of unity. The remaining interaction combinations, namely 111-111, 111-V, IV-IV, IV-V, and V-V form quasi-ideal solutions. The effect of the various interactions on the partial molar excess enthalpy follows closely the above pattern also. That is, with the possible exception of the 111-IV interaction, the solutions should be formed endothernially. The reason-
ableness of the above anticipated behavior, in the light of the present experimental effort, will be subsequently discussed in detail. ils the binary solutions investigated in this work differ fiom the conventional GLC systems, it was deemed worthwhile to elaborate a bit on the technique employed. In preparing the column packing material, known weights of solid support were saturated with the solvent of interest and then evaporated sloivly while stirring to obtain the desired percentage coating. These coatings were then stored in closed containers. When packing a column the quantity of contents was determined by deciease in tare \+eight as well as increase in column weight. *It the conclusion of a run, the column is reweighed to ascertain the rate of solvent depletion. As the total quantity of solvent in the column u as not large, 0.04-pl. samples were used to obtain infinitely dilute data. This actually represented a solute mole fraction of the order of 10-6, yielding linear absorption icotherms as evidenced by the peak symmetry. The solid supports chosen for each solvent were determined by the solvent wetability and the support inertness. For water. Chroinosorb W was used, for 2 pentanone the support was HMDS-treated Chromosorb W, u hile Fluoropak 80 was employed 1% ith 2,3,4-trimethylpentane. In the case of the former two, initially 4Oye w./w. of solvent existed and no data was accepted below 15% w./w. In the latter case because of the loner specific surface area only 20% w./w. of solvent elisted initially and data were taken to a limit of 5ye w./w. coating. VOL. 38, NO. 12, NOVEMBER 1966
1663
Infinitely Dilute Activity Coefficients for VariousSolutes in Water, 2-PentanoneI and 2,3,4-TMP at 20", 30", and 40" C.
Table 1.
Solute CJLz C6Hl4 C~HM CHzCL CHCla
cc14
MeFo EtFo PrFo CHICHO CiHjCHO CaHiCHO EtAm PrAm BuAm MeOH EtOH PrOH
Table II.
Solute
Water 30' C. 796 2225 6160 201 568 2150 17.4 51 168 4.36 17.6 73 0.69 2.85 4.70 2.53 6.15 26
20" c. 945 2940 8050 209 57I 2870 16.6 46 150 3.59 14.7 63 .. 0.37 2.33 4.00 2.69 6.51 24
Water 30" C. 4.0 4.6 5.3 3.2 3.8
4.0 4.7' 5.2 3.1 3 .7
CH3CHO CzHiCHO C3HiCHO EtAm PrAm BuAm MeOH EtOH PrOH
BuAm EtOH PrOH
1664
0
3.00 4.40 5.60 6.52 7.21
6 7 6
3 3 6
0.9 1.0
1.0
0.8
1.1
1.1
-0.4 0.6 0.9 1.0 1.1 1.2
0.3 0.4 0.6
1.7 2.6 -0.5 0.5 0.5
1.9
2.0
2Pentanone 20'40" C.
Water - %?& 20°20"4OOC.
1.3
0 1 1 1
4OoC. 0 0 1 0 0
1 1 1 0 -1 0
2 4 2 2 2 2 2 5
-3
0
1
-1
1 0 0 0 0
-1 --I 1
ANALYTICAL CHEMISTRY
-4
1 0 0 0 0 1
2 2
0.1
0.8
0.4 0.5
0.6
1.9
1.1
2-Pentanone 30" C.
0.8
0.6 1.1
20" c. 0.9 0.1
0.9 1.7 2.6 -0.2 0.6
0 1 1 1
MeOH
0.50
2-Pentanone 30' C. 3.99 4.65 5.36 0.95 1.13 2.73 1.95 1.96 3.24 1.73 2.01 2.59 0.41 2.14 4.31 3.93 4.24 4.60
0.0 0.1
0.7 1.6 2.4 -0.6 0.5 0.8
40" C. 3.9 4.5 5.1 3.1 3.8
Table 111. Partial Molar Excess Enthalpy (kcal./mole) for Various Solutes in Water, 2-Pentanone, and 2,3,4-TMP from 2 0 " to 40" C.
PrAm
20" C. 5.27 6.53 8.51 1.18 1.19 3.61 2.58 2.66 3.66 2.06 2.25 3.97
40' C.' 5.36 6.16 7.36 1.21 0.93 2.41 2.18 2.25 3.65 1.65 1.77 2.66 0.50 2.50 4.58 5.12 6.01 6.27
'20' C. 0.99 1.10 1.07 2.26 1.59 5 51 5.57 3.52 3.11 5.17 4.14 4.04 2.18 2.23 1.76 39.9 28.1 23.0
2,3,4-TMP 30" C. 0.97 1.13 0.98 1.97 1.35 6.48 5.11 3.40 2.70 5.00 3.77 3.62 1.80 2.15 1.45 39.4 22.6 12.8
40" C. 0.97 1.09 0.98 2.23 1.56 8.63 4.92 3.78 3.13 5.24 4.18 3.72 1.85 2.48 1.84 33.9 22.4 18.3
Partial Molar Excess Free Energy (kcal./mole) for Various Solutes in Water, 2-Pentanone, and 2,3,4-TMP at 20", 30", and 40" C.
2OOC.
Solute C&iz C6Hl4 C7H16 CHLL CHCla CCl4 MeFo EtFo PrFo CHiCHO CzHjCHO CaHGHO EtAm
40" C. 517 1465 3925 153 425 1490 14.2 41 131 3.71 15.4 61 0.44 2.44 3.70 2.30 5.50 22
0.8
-0.5
0.5 0.9
2,3,4-TMP 40" C.' 1.0 1.1
1.2 0.1
20°C. 0.0
30OC. 0.0
0.0
0.0
0.1
0.0
0.5 0.3
0.3 0.4 0.6 -0.4 0.6
0.8 0.8
0.8
0.9 0.9
The effect of GLC operating variables was also investigated on a limited scale. Using water as a solvent, Chromosorb R, Firebrick, and Chromosorb W were employed as support material and provided that 10% w . / ~ or . more of solvent was maintained, no effect was noticed. The carrier gas flow rate made no noticeable change in the activity coefficient when varied over a threefold range. Likewise the properties remained unchanged, irrespective of whether or not the presaturator was used. The percentage coating of solvent was varied from 10 to 5Oy0 w./w. and the total amount of solvent was varied from 0.1 to 4.0 grams, all of which produced a constant value of the thermodynamic properties. Also the column length was varied from 6 inches to 6 feet with negligible results while small variations in inlet and outlet pressure produced invariant results. From Equation 15 it can be seen that large variations in the mean column pressure will produce changes in the gas phase behavior, but this effect was not visible in this work because of the ideality of helium. Finally, no difference in the value of the gas phase volume of the column was
1.0
1.o
1.0 1.1 1.1
0.5 0.5 0.3 2.1 1.9 1.8
0.1 0.4 0.2
1.0 0.8 0.8
0.4 0.5 0.2 2.2 1.9 1.5
40" C. 0.0 0.1 0.0
0.5 0.3
1.0
0.9 0.8
0.4 0.6 0.4 2.2 1.9 1.8
obtained by the two techniques of geometrical calculations and determination of the retention time of an unretained component, in this case helium. The above studies indicate that the thermodynamic properties obtained are independent of the GLC parameters and represent true vapor-liquid equilibrium. RESULTS AND DISCUSSION
The actual process of determining thermodynamic solution properties from GLC consists of measuring the chromatographic parameters experimentally and then employing Equations 13, 17, 18, and 16 to compute the desired results. The infinitely dilute activity coefficients derived in this manner are presented in Table I. The data represent average values for a number of runs on each binary system. The overall average error was 15y0, the trimethylpentane systems being slightly better while the 2-pentanone systems were somewhat worse. Utilizing the data in Table I and Equation 17, Table I1 is derived. As the partial molar ex-
20
I
I
I
I
I
I
I
I
I
I
-
109-
-
8-
-
76
00
5- 0
0 5
0
w
I 0 I- 4-
0-
h W
-
3-
2-
I-
oo
I
I
I
0.00400
m
I
I
I
1
0.01200
0.00800
I
I
8
.
0.02200
0.0200
0.01600
XETOH
Figure 2.
Activity coefficient of ethanol in water as a function of concentration in the dilute solution region at 30" C.
cess free energy is exponentially related to the activity coefficient, the trends observable in Table I are somewhat normalized in Table 11. From the thermal variation in the activity coefficient the partial molar excess enthalpy can be determined utilizing Equation 18, as given in Table 111. As the overall temperature range investigated was
Table IV.
fairly narrow and AHE is determined by differentiation of the data, a single constant value of DH" over the 20" C. range is obtained from a linear fit of the experimental results. Finally utilizing Table I1 and Table 111 with Equation 16, the partial molar excess entropy as presented in Table IV is computed. An inspection of the activity coeffi-
Partial Molar Excess Entropy (cal./mole
cients shows that large deviationa from ideality are usually accompanied by decreasing solubility as in the case of the alkanes in water. This is due to the inoreasing chain length of the hydrocarbon radical. As the %pentanone has properties near the mean of the solutes, none of its binary solutions exhibit large deviations from Raoult's law. At the op-
for Various Solutes in Water, 2-Pentanone, and 2,3,4-TMP at 20",
OK.)
30°, and 40' C. Solute
CJHlZ C&14 C7Hl6 CHzC1.z CHCla CCL MeFo EtFo PrFo CHsCHO CzHpCHO C,H,CHO EtAm PrAm BuAm MeOH EtOH PrOH
c.
20°
8 7
4 -1 -4 5 -2 -5
-7
-3
-8
-9 -7 -5
-2 3 1 -3
%Pentanone
Water 30" C. 8 6 4
-1 -4 4 -2 -5 -7 -3 -8 -9 -8 -6 -3 3
1 -3
40" C.
8 7 4 -1
2OoC. -4 -2 0 3
3OOC.
-3 -1 1 3 8
8
-4 5 -2 -5
4OOC. -4 -2 0 2 8
c.
20°
1 0
2 -1 0
-17
-1
-3
-7 -3 -8
5 6
6
15
15 0
6
-9 -6 -5 -2
3 -4
3 -4
3 1 -3
-2 -3 -3
-2 -2 -2
0
6 6 15 0 3 -4 -2 -2 -3
-2 -4 -3 0 3
-4 -3 -3
2,3,4-TMP 30' C. 1 0 2 -1
0
-17 0
-3
-2 -4 -3 0 3 -4
40' C. 1 0 2 -1 0 -17 0 -4 -2 -4 -3
0 3 -4
1
-1
VOL 38, NO. 12, NOVEMBER 1966
1665
posite end of the scale, the alkanes form nearly ideal solutions in trimethylpentane as little excess solute-solvent interaction exists. It should be noted in Table I1 that for a given homologous series of solutes the partial molar excess free energy varies in a regular manner with increasing hydrocarbon chain length. This observation is the basis of an interesting correlation to be subsequently presented. From Table IV it can be seen that AS* is negative for the majority of the solutes in water. This is due to the restricted solute motion in solution caused by hydrogen bonding with the solvent. On the other hand the negative values for the trimethylpentane solutions are due to the solute motion being hindered by the larger solvent molecules. Other trends due to hydrogen bonding will shortly be discussed. The validity of the resulting data aa equilibrium conditions can be substantiated by comparsion with existing results in the literature. As water is a common solvent, most comparisons will be made with that solvent system. Copp and Everett (4) investigated the amines in water at 25"C., quoting values of the partial molar excess free energies as follows: ethylamine, - 500 cal./mole; propylamine, 300 cal./mole; butylamine, 800 cal./mole. As seen in Table I1 this agrees quite well with the present data. Pierotti et at. (IS) have studied alkanes in water by static techniques a t 25°C. The values of the infinitely dilute activity coefficients of pentane and hexane are 1250 and 3150 as compared to 945 and 2940 at 20" C. in this study. Brown and Martin (3) give ym = 2.3 a t 0°C. for methanol in water which is in accord with the present value, as is the value of 2.2 given by Pollard and Hardy (14) a t 27" C. No direct data for comparison exists with either 2-pentanone or 2,3,4trimethylpentane. However Kretschmer and coworkers (9) studied ethanol in 2,2,4trimethylpentane reporting an activity coefficient of 31 a t 25" C. as compared to 28 for ethanol in 2,3,4-trimethylpentane a t 20" C. in this work. This comparison for similar solvents is quite favorable. Likewise the data obtained by Kwantes and Rijnders (IO) for polar solutes in hexadecane can confirm trends in solute-solvent interactions. Their results are y=
Solute Methanol Ethanol Propanol Acetaldehyde Propionaldehyde Ethyl formate
at
25" C. 71.5 47.0 31.5 7.3 4.0 3.7
40D C. 45.0 30.5 19.5 6.1 3.4 3.2
Realizing that hexadecane has a longer hydrocarbon chain length but similar polarity, the comparison between the above data and the present work is ex-
1666
ANALYTICAL CHEMISTRY
CARBON NUMBER
I
I
I
I
I
I
2
3
4
I
CARBON NUMBER
Figure 3. Incremental relation between excess free energy and molecular structure for solutes in water at 20" C. 0 Alkanes 0 Alkyl formates A Aldehydes
Amines
V Alcohols 0 Chloromethanes
some degree with Jones et al. and the I.C.T. As this discrepancy existed, it was decided in this work to investigate the variation of activity coefficient with ethanol concentration a t 30°C. This was accomplished experimentally by varying the quantity of water in the column as well as the size of the injected ethanol sample. In this manner the ethanol mole fraction was varied from 20°C.,6.1at400C.,6.8at550C.,and7.6 7.6 X to 0.022. As can be seen a t 75°C. On the other hand Jones, from Figure 2 the data can be fitted with Schoenborn, and Colburn (8) report a smooth continuous curve over the eny" = 4.4 a t 50°C. and 5.2 a t 60°C. tire region. Now the above quoted Also Rao, Achsrya, and Rso (17) list literature values generally represent an extrapolation to infinite dilution from a y" = 4.8 a t 65"C., 4.3 a t 70"C., and 3.2 a t 80°C. Finally Hansen and Miller ( 7 ) finite concentration of the order of 0.02 give ym = 4.0 at 25" C. concurring to mole fraction. At this value the present
ceptionally good. As the 2,3,4trimethylpentane is a smaller hydrocarbon, the values given in Table I should be lower than the above results. The remaining system for which data are available is the ethanol-water system. In fact a significant discrepancy exists between the various sources. The International Critical Tables (19) quotes the following values: y" = 4.5 at
data yield an activity coefficient of 3.8 which is in close accord with much of the literature results. As a mole fraction of 0.02 represents a maximum value in the present study, it is felt that there is more justification for a smooth interpolation to infinite dilution through this data than a nonlinear extrapolation of the literature work to zero mole fraction. I n the discussiop of the experimental program the classification scheme of Ewe11 (6) was used to predict the deviations from ideality based on hydrogen bonding. The degree to which the experimental results verify the hypotheses proposed will now be investigated. The interaction between all classes of solutes and water, a class I solvent, should yield positive deviations from ideality. From Table I it can be seen that this is true with the exception of ethylamine and water. This indicates that the association between the solute and solvent is the predominant effect. The effect of limited solubility can be depicted by the large values of ym for alkanes and chloromethanes in water. When considering the class I11 solvent, 2-pentanone, again positive deviations are anticipated except for the chloromethanes which are a class IV solute. The data bear out this prediction fairly well. As before, ethylamine exhibits negative deviations due to association with the 2pentanone. In the case of dichloromethane, and trichloromethane, although the deviations are slightly positive in some cases, they generally substantiate the results anticipated. The carbon tetrachloride in reality does not have active acceptor atoms and thus should not be expected to deviate neg& tively from Raoult's law. Finally for the class V solvent, 2,3,4-trimethylpentane, with the exception of the alcohols most of the solutes exhibit weakly positive deviations from ideality as expected. By an inspection of Table I11 one may deduce that the partial molar excess enthalpy is endothermic for nearly all solutions with the notable exception of the amines in water. However, for the amines in water solute association with the solvent was seen to be a major factor. As the difficulty of obtaining calorimetric properties from vapor liquid equilibrium data has often been pointed out, the values for the partial molar excess enthalpy can only be interpreted in a qualitative sense. Computation of AHE involves differentiation of the activity coefficient data and thus any experimental discrepancies in the actual data are greatly magnified. Because of this the tabulated values should be used only to deduce the exothermic or endothermic nature of the solution formation. In this respect the linearized differentiation of the experimental results yields trends which are in good agreement with the predictions based on hydrogen bonding considerations.
Likewise the partial molar excess entropies derived utilizing the A H E values are useful in indicating the relative degree of mobility gained or lost by the solute in forming the solution. I n addition, as over extended ranges dAHE/ dT#O, no extrapolations of the computed values into other regions should be attempted. With the above considerations in mind, it is felt that the anticipated results have been confirmed quite well by the majority of systems investigated. Finally a word should be said concerning the magnitude of the nonideality in the gas phase. As helium was the carrier gas employed, the deviation was anticipated to be slight. For a worst possible binary solution, namely ethanol in water, the more exact Equation 15 was used to compute the infinitely dilute activity coefficient. The value obtained in this manner deviated from the result obtained utilizing Equa-
tion 13 by 2.4%. As the overall average error in y a was =t5%, the assumption concerning the ideality of the gas phase was substantiated and Equation 13 was justified for use with helium carrier gas under the present conditions. CORRELATION
Pierotti, Deal, and Derr ( l a ) , while studying the infinitely dilute activity coefficient of a large number of solutes in a variety of solvents, evolved a correlating expression based on the interaction between functional terminal groups on the solute and solvent, and on the size of the associated hydrocarbon radicals. The resulting expression is
l60C
140C
120c
IOOC
800
600
400
200
0
- 200
-400
0
-600 1
1
1
1
1
,
1
CARBON
1
,
1
1
~
,
,
,
(
)
NUMBER
Figure 4. Incremental relation between excess free energy and molecular structure for solutes in 2-pentanone at 20' C. 0 Alkanes 0 Alkyl formates A Aldehydes Amines Alcohols
v
VOL 38, NO. 12, NOVEMBER1966
e
1667
For a given solute Cs/nz is a constant while for a specific solvent Cs/nl is invariant. The constant C, is characteristic of the solute functional group while C, represents the solvent functional group. The interactions between solute and solvent functional groups are characterized by the constant Ca. The C6 term is usually quite small and accounts for solution effects,between the respective hydrocarbon radicals. Applying Equation 19 to the present systems under study yields the following specific results. For alkanes in water, as alkanes have no active terminal group and water no hydrocarbon radical, C5, C,, C7, and Ce are either zero or can be lumped into a single parameter to be combined with Cas Thus
In r :
=
+ Bnz
A
(20)
":
1200
For the other solutes in water the Cg term must be considered In
ym =
A
+ Bn2 + CS(i)
In a similar manner for alkanes in 2,3,4trimethylpentane In y m =
c 6
(n2
- nJ2
(22)
as no terminal groups exist on either solute or solvent. For other solutes in
8001 800-
-
600 6001
. I
c
-
400 4001
U
trimethylpentane the anticipated relation is
lny=A+B
(3+ -
I
Finally for alkanes in Zpentanone the infinitely dilute activity coefficient may be represented by
In y"
=
A
+ B 712 + C6
(nz - nJ2
(24)
while for the remaining solutes the full Equation 19 must be used m all contributing groups are present. From an inspection of Equations 20 to 24 it would appear that a plot of RT In y m as a function of 122 would provide a good correlation within a given homologous series of solutes in a particular solvent. Such plots are shown in Figures 3,4, and 5 for water, 2-pentanone, and 2,3$-trimethylpentane, respectively. The excellent linear relations obtained for the homologous series of solutes in water is to be expected as Equation 20 is that of a straight line while Equation 21 is nearly so. The correlation indicates that the magnitude of CS is suitably small. Similarly for the solute series in trimethylpentane, because of the known small values of cg,the resulting relations are nearly linear. This also can be anticipated from the fact that no hydrogen bonding exists in these binary solutions and the physical interactions can be expected to be determined primarily by
1668
ANALYTICAL CHEMISTRY
4
I
5
6
t
,
I
7
J 8
CARBON NUMBER
Figure 5. Incremental relation between excess free energy and molecular structure for solutes in 2,3,4-TMP at 20" C. 0 Alkanes 0 Alkyl formates A Aldehydes Amines V Alcohols
the solute functional terminal group. I n the case of the various solutes in 2pentanone a different situation exists. Based on Equation 24 the linear relation for alkanes is quite plausible. An inspection of Equation 19, however, makes it readily apparent that many nonlinear terms exist. Thus the linearity of the alcohols in Zpentanone appears to be fortuitous. A further interesting yet unexplained correlation is the linear relation obtained for the chloromethanes in water when the partial molar excess free energy is plotted as a function of the number of chlorine atoms in the solute molecule. Thus by utilizing the proposed equation of Pierotti (18), with the exception of certain solutes in 2-pentanone, the data of the present study are quite adequately correlated.
NOMENCLATURE
A
= arbitrary constant
B Bo
= second virial coefficient, cc./
= arbitrary constant
mole BOint = second interaction virial coefficient, cc./mole Ct = arbitrary constant F = carrier gas flow rate, cc./sec. f = fraction of time solute is in gas phase AGE = partial molar excess free energy, cal./mole ME = partial molar excess enthalpy, cal./mole j = pressure correction factor defined in Equation 14 k = partition coefficient defined in Equation 1 L = column length, cm. M = molecular weight of solvent m = mms of solvent, gram
NG N L
n
= molar density of gas, moles/cc. = molar density of liquid, moles/
z
y
= solute liquid mole fraction = solute gas mole frac,tion
cc. total number of moles of solute = number of moles of solute in gas = number of moles of solute in liquid = number of methylenic groups in solvent = number of methylenic groups in solute = total pressure, atm. = column inlet pressure, atm. = column outlet pressure, atm. = solute vapor pressure, atm. = gas constant = partial molar excess entropy, cal./mole OK. = temperature, O K . = velocity of solute, cm./sec. = velocity of unretained component, cm./sec. = gas phase volume, cc. = liquid phase volume, cc. = retention volume, cc. = specific retention volume, cc./ gram = solute molar volume, cc./mole
ym
=
=
nL
nl 12.2
P
Pi P* P O
R
ASE T U v u
VG VL TiR
VR
V0
infinitely dilute activity coefficient LITERATURE CITED
(1) Adlard, E. R., Khan, M. A., Whitham,
B. T., “Gas Chromatcgraphy 1960,” R. P. W. Scott, ed., Butterworths, London, 1961. (2) Adlard, E. R., Khan, M. A., Whitham B. T., “Gas Chromatography 1962, M. Van Swaay, ed., Butterworths, London, 1963. (3) Brown, W. S., Martin, D. S.,U . S. At. Energy Comm. Rept., I.S.C. 235, June 1951. (4) ,Copp, J. L., Everett, D. H., Discusaons Faraday SOC.15, 268 (1953). (5) Desty, D. H., Goldup, A., Luckhurst, G. R., Swanton, W. T., “Gas Chromatography 1962,” M. Van Swaay, ed., Butterworths, London, 1963. (6) Ewell, R. H., Harrison, J. M., Berg, L., Ind. Eng. Chem. 36, 871 (1944). (7) Hansen, R. S., Miller, F. A., J . Phys. Chem. 58, 193 (1954). (8) Jones, C. A,, Schoenborn, E. M., Colburn, A. P., Ind. Eng. Chem. 35, 666 (1943). (9) Kretschmer, C. B., Nowakowska, ‘J.,
Wiebe, R., J. Am. Chem. Soc. 70, 1785 (1940). (10) Kwantes, A,, Rijnders, G. W. A., “Gas Chromatography 1958,” D. H. Desty, ed., Butterworths, London, 1959. (11) Littlewood, A. B., Phillips, C. S. G., Price, D. T., J. Chem. SOC. 1955, p. i----. 4 ~n (12) Pierotti, G. J., Deal, C. H., Derr, E. L., Ind. Eng. Chem. 51, 95 (1959). (13) Pierotti, G. J., Deal, C. H., Derr, E. L., Porter, P. E., J. Am. Chem. SOC. 78, 2989 (1956). (14) Pollard, F. H., Hardy, C. J., “Vapor Phase Chromatography,” D. H. Desty, ed., Butterworths, London, 1957. (15) Porter, P. E., Deal, C. H., Stross, F. H., J . Am. Chem. SOC. 78, 2999 11956). (16) Puhell, J . H., Spencer, M. S., Nature 175, 988 (June 4, 1955). (17) Rao, C. V., Acharya, hl. 1‘. R., Rao, hl. N., Trans. Indian Inst. Chem. Engrs. 2 , 6 ‘(1948). (18) Sternberg, J . C., Beckman Instruments Inc., Fullerton, Calif., personal communication, 1966. (19) Washburn, E. W., ed., “International Critical Tables,” Vol. 111, RlcGraw-Hill, New York, 1928. RECEIVED for review February 3, 1966. Accepted September 6, 1966.
Gamma-Gamma Coincidence Counting Applied to Chlorine Analysis by Neutron Activation EDWARD T. BRAMLITT Atomics International, A Division of North American Aviation, Inc., P .
b Gamma-gamma coincidence techniques for radionuclide determination have been shown to facilitate activation analysis. A routine neutron-activation method for determining trace quantities of chlorine in organics has been developed which eliminates the effect of interfering impurity activities. The method has significantly extended the experimental sensitivity for chlorine detection and at the same time has improved the precision and accuracy of the determination. Chlorine can b e determined down to a concentration of about 10 p.p.b. j= 5070 relative standard deviation. In the 0.4- to 2p.p.m. chlorine concentration range a relative standard deviation of about 7% is attainable.
A
problem in instrumental activation analysis is that elements other than the one(s) of interest also become activated. Consequently, one must resolve either complex spectra by “spectrum stripping” or composite decay curves by successive subtraction after decay is followed to background. When the activities have similar properties, neither technique may yield satisfactory results. This is often the MAJOR
0.Box 309, Canoga Park, Calif.
case in the activation analysis for trace chlorine. Generally, the activating reaction used for this analysis is C137 (n, y)C138. The 37-min. C13* is determined by detecting either its 1.64 or 2.16 m.e.v. gammas. Accurate detection of these gammas, however, can be prevented by either Mn66, Na,24 or Ar4I (3, 7,8,10,12). The major goal of this investigation was to develop a method for determination of chlorine in organic materials, especially, terphenyls, which would be accurate, precise, and not be limited by these interfering activities. The analysis is important for organic nuclear reactor technology because impurity chlorine is thought to cause or contribute to problems of film formation, zirconium hydriding, and corrosion (13). Although the activation analysis method extensively used gives better results than do other methods-Le., chemical or x-ray fluorescence (IO)-it is now especially inadequate for terphenyls because (1) improvements in reactor grade quality have reduced their chlorine level to only a few p.p.m. and (2) use in a nuclear reactor causes additional chlorine loss plus contamination by corrosion products.
Coincidence counting is possible for many radionuclides (9, 16) but, perhaps because of its low inherent efficiency, it has not been commonly used in activation analysis for detecting the desired activity. Owing to the “inert” matrix of terphenyl samples and because cascade gammas are emitted by Cl”, it was anticipated that activation of large amounts of terphenyls would give sufficient C138 activity for determination by coincidence counting. The specificity of coincidence counting should permit achieving the desired goals. EXPERIMENTAL
Materials. Chlorine standard solutions were prepared from reagent grade calcium chloride and sodium chloride, dried at least 24 hours in an oven a t 110’ C. and cooled in a desiccator over Drierite before weighing. A weighed amount of these salts was added to a 1-liter volumetric flask and dissolved with deionized distilled water to give 1000 p.p.m. chloride ion stock solutions. The deionized distilled water was obtained by passing distilled water through a Deem-A-Jet mixed resin. One- to 10-ml. aliquots of these stock solutions were taken and diluted to 1 liter to give a series of VOL. 38, NO. 12, NOVEMBER 1966
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