Susan Kenworthy' and James Miller Drew University Madison, New Jersey D. E. Martire Stevens Institute of Technology Hoboken, New Jersey
II
Determining Activity Coefficients by Gas Chromatography A physical chemistry experiment
classical methods of determining activity coefficients of non-electrolytes are laborious (1) and not as accurate or precise as desirable (8). On the other hand, the use of gas-liquid chromatography affords a fast, simple method for making these measurements. A simple, gas-liquid chromatographic experiment which can be performed by students in undergraduate physical chemistry is outlined for the determination of the activity coefficients of benzene, cyclohexane, and cyclohexene in dinouylphthalate. Since the column of the gas chromatograph can be considered the site of a dilute solution, a correlation exists between gas-liquid chromatographic data and the activity coefficient of a solute in solution. The necessary link is found in the specific retention volume, V,, which by definition is the volume of carrier gas reduced to zero OC which is necessary to elute a given solute, per gram of liquid phase. This quantity is independent (to a first approximation) of any of the operational variables of the column; it is a function of the temperature alone. It measures the amount of time spent by the solute in the moving gas phase, which in turn is determined by how easily the solute can "escape" from the solvent into the moving phase. The "tendency to escape" is simply vapor pressure. Like other solution properties, it is altered by non-ideal behavior, and therefore activity coefficients are necessary in order to reconcile observed behavior with ideal behavior. Various investigators have successfully demonstrated this relationship between activity coefficients a t infinite dilution and the gas chromatographic retention volume (8-7). The simplicity of the gas chromatographic technique makes the measurement of activity coefficients by this method attractive for student instruction. The data which are obtained are accurate and can be used to explain some of the deviations from Raoult's Law; i.e., the nature of intermolecular forces in solution and the resultant deviations from ideality. Overall, this represents an ideal teaching situation. Two very different instruments were used in this study; an F&M model 720 dual column gas chromatograph, and a home-made one. The latter was built around a Gow-Mac model 9285, Cfilament thermal conductivity cell2 and used a Sargent Model SR recorder for readout. Using the same home-made column in both instruments, good results were obtained. Column temperature was maintained between 40 and
' Abstracted in part from an honors thesis submitted by Susan Kenworthy to the faculty of Drew University, 1963. This cell is part of a kit from which the gas ohromatograph was built.
60°C and had to be accurately measured. This was accomplished with either an accurate thermometer or a thermistor incorporated into a wheatstone-bridge type circuit. The injection port (and in the case of the F&M instrument, the detector as well) was kept a t about 150°C. Helium was used as the carrier gas; flow rate was about 60 ml/min and was measured on the exit side of the carrier-gas line with a soap-bubble flow meter. A student-made manometer, placed in the carrier-gas line on the inlet side served to measure the inlet pressure. Samples were kept as small as practical (about 0.5 @I)and were injected with a 10 p1 syringe. Column. It is necessary that the liquid phase be pure, and that the exact amount of liquid phase in the column be known. Dinonylphthalate (molecular weight = 418.6) was obtained from Analytical Engineering Laboratories, Inc. and was used without fnrt,her purification. The column packing contained 25.0% dinonylphthalate on 80 to 100 mesh Chromosorb. For the 3 ft of '/4-iu. copper tubing used, this required a mixture of 2.50 g dinonylphthalate and 7.50 g ovendried Chromosorb. The efficiency of this column was found to be 525 theoretical plates. Such a column, if used below 125OC should be good for a minimum of 100 hr. A new column should be preconditioned for about 4 hr at 80°C before use. The Experiment The instrumental conditions prescribed earlier should he set at least I hr before any runs are made, in order to allow the column to come to equilibrium. With the recorder running, a 0.5 sample (including some air) is injected. The instrument sensitivity is adjusted so that the peak which is obtained is a t least 20% of full scale. Samples of benzene, cyclohexane, and cyclohexene are run. The following measurements are required: Flow rate., F:. av. of values taken before and after the run: in ml/min. Adjusted retention time, ta'; measured from the air peak; in cm. Column temperature, T,; in 'K. Room temperature, T,; in OK. Atmospheric pressure (outlet pressure), PO; in em Hg. Column pressure (manometer reading), P,; in cm Hg. Total inlet pressure, P* = PO
+ Pz.
C a l ~ u l a t i o n . ~The specific retention volume, V , (in ml/g), can be calculated from equation (1) : A sample calculation is available to instructors upon request to Dr. Miller.
Volume 40, Number 10,
October
1963 / 541
r P w X v, = P------Po
1 j ~ ? ! X F ~tn'- X - X T. 2.54 Wr.
(1)
where W , = 2.50, the weight of the liquid phase in grams, P, is the vapor pressure of water at room temperature, (T.);and j is pressure gradient correction factor and equal to
The factor, tZ1/2.54,is used because the recorder speed was 1 in./min and tR' was measured in centimeters. If a different recorder speed is used, a new term will he needed in equation (1). The units on this term (taking into account the recorder speed) should be minutes. Activity ~oefficient,~ -yo, is related to specific retention volume by equation (2) (8):
where M = the molecular weight of the liquid phase, and fO = the fugacity of the pnre solute vapor in millimeters of mercury. To a first approximation, vapor pressure of the pnre solute, po, a t the column temperature, can be substituted for fugacity, and can he calculated from data found in several reference works (9). Typical results are shown in the table. Discussion
Benzene, cyclohexane, and cyclohexene were chosen for this experiment because comparable activity coefficients were already in the literature and showed a wide range of values. The close agreement between literature values and student values is shown in the table and indicates the reliability of this simple method. A low activity coefficient (yo
