Harry 1. Pardue, Michael F. Burke, and Jack R. Barnes Purdue University Lafayette, Indiana 47907
Quantitative Gas Chromatography An experiment
conventional experiments involving gas chromatography have emphasized the usefulness of this technique as a separation tool for qualitative identification ( 1 , 2). Little emphasis is placed on obtaining significant quantitative data. However, in present day analytical chemistry, the making of quantitative measurements on complex mixtures is as important as the qualitative identification of the components present in the mixture. Formal training of chemistry students in this area is extremely worthwhile. This report describes an experiment which is designed to illustrate and evaluate several methods of handling chromatographic data, as well as to demonstrate the desirability of automatic instrumentation. These methods range from rrra~hicalmeasurement and manual computation of the data to electronic measurement and computation with direct readout of the data in digital form. The experiment illustrates the use of operational amplifiers for measurement and analog computation and, depending on how the experiment is presented, it can also illustrate details of circuit design. The experiment also emphasizes the proper use and understanding of detector response in chromatographic analyses. The experiment consists of the determination of relative response factors for a multicomponent mixture and the use of these factors in determining the percent composition by weight of an unknown mixture.
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Quantitofive Gas Chromatography Detector Response
A thermal conductivity (TC) detector was used in this experiment since it offers sufficient sensitivity for student use. These detectors employ either a heated metal filament or a thermistor (a semiconductor of fused metal oxides) as the resistance e1ement:for sensing changes in thermal conductivity. A detector element and matching reference element are opposed to obtain a diiei-ential signal. The heated elements are cooled by the pure carrier gas stream and assume a definite resistance. As the binary mixture of the eluted solute and the carrier gas passes over the detector element, the mixture of diierent thermal conductivity changes the rate of heat loss, and the change in temperature causes a change in resistance of the element. This difference in resistance between detector and reference is a function of the instantaneous concentration of the component in the gas stream. The reference and sensing resistance elements are incorporated in a Wheatstone bridge, and the out-of-balance signal is applied to a recorder. The response of a TC detector due to temperature change is
a complex function of such things as heat capacity of the solute, free and forced convection, and radiation heat losses, as well as thermal conductivity. However, by proper cell design and assuming the rate of heat loss to be constant, the TC cell output voltage, I&, is given by Eo
= cAT(k./k,
- 1)
(1)
where c is a constant, and k , and k , are the thermal conductivities, respectively, of the carrier gas and the mixture. Thermal conductivity, in general, decreases with increasing molecular weight. The approximate relationship between molecular weight and thermal conductivity for members of an homologous series is given by the proportionality k d h = (MUMI)'/* (2) Therefore, the thermal conductivity will decrease rapidly for the first few members of such a series and the higher members will be detected with increasing sensitivity. For higher molecular weight molecules, this difference in response approaches a limiting value and the cell response closely corresponds to the weight of solute emerging from the column (3). For good quantitative work, therefore, it is necessary to compensate for these differences in response. A fairly exact relation between the response of a TC cell and the amount of solute eluted from the column may be obtained bv the use of a relative resnonse factor. This approachrequires the determination of a specific peak area per unit weight for each component of the mixture. These values are then normalized with respect to a chosen standard reference compound under the same detector conditions. The resulting relative response factor may then be used over a reasonable temperature range to yield highly accurate analyses (4). Correction for detector response to various molecules is also necessary with all other types of detectors commonly used for gas chromatography. The use of relative response factors is recommended for all truly quantitative work. Measurement o f Peak Areas
With the weight percent of the solute being proportional to the percent area of the recorded peak, it is now necessary to determine the area beneath each component peak. Several graphical methods have been suggested; however, the most accurate is that described by Cremer and Muller (5), which shows the area beneath a Gaussian (bell shaped) peak to be best approximated by multiplying the peak height by the width a t half height. Volume 44, Number 7 7, November 1967
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An electromechanical approach to integration is that of a ball and disc (6) where the number of rotations of the disc is displayed by a sweeping recorder pen tracing. In t,his case, a full swing of the integrator pen is assigned an arbitrary value of 100 and partial swings a proportionally smaller value. The sum of the pen sweeps during the recording of a peak represents the area of a peak and is reported in "Disc Units." A third and very powerful technique of integration of peak areas to he discussed is that of electronic in& gration using an operational amplifier as described elsewhere (6). In this case, when the output potential of a T C detector is to be integrated, a basic operational amplifier feedback circuit is used (see Fig. 1) with a capacitor in the feedback loop. A resistor is
Figure 1.
Figure 2.
Block diagram of direct reading inlegrotor.
Direct Reading Integrator. A block diagram representmg the functions of the instrument is illustrated in Figure 2. The signal resulting from a chromatographic peak is connected a t E;. and compensated for detector response by the sensitivity compensator. The signal is then integrated with respect to time and the integrated signal for each peak is stored. After all the peaks of a chromatogram have been processed in this manner, the sum of all the stored integrals is measured and adjusted until a reading of 1.000 is observed on the digital voltmeter (om). Each individual integral is then sequentially measured and the digital voltmeter presents the data in the form of weight percent for each component. The circuit layout illustrated in Figure 3 contains components which perform the functions described below.
Basis operational amplifier integrator circuit.
put in the input circuit so that the input current is proportional to the signal voltage. The output voltage is then given by
DYM.
Since the potential of the charge stored on the capacitor is equal to Eo,this charge can then be measured and is proportional to the area under the peak. These three methods of area measurement are used and con~paredin the experiment reported. The Experiment
Reagent grade hydrocarbons were used without further purification. Mixtures of known composition by weight are made up in 2 ml vials which are capped with rubber septums. Care must be taken to insure that the composition of the sample is not changed by evaporation of the lower boiling components. The column used is a 5 f t by '/,-in. od aluminum column packed with 15% Apiezon L on 60/80 mesh Chromocoil W (Johns-Manville). The column oven is maintained a t SO%, with the detector and injector a t 200°C. Helium is used as the carrier gas at a flow rate of 40 ml/miu. The detector filament current is 140 ma. Chromatograph. A Variau-Aerograph Model 202 (Varian-Aerograph, Walnut Creek, Calif.) gas chromatograph with a thermal conductivity detector is used. Reco~rler. A Leeds and Northrup Model (Leeds and Northrup, Philadelphia, Pa.) potentiometer recorder equipped with a Disc integrator (7) is used to record the peaks and the areas measured by the ball and disc type integrator. 696
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lournal of Chemical Education
Figure 3.
Circuit diogrom of direct remding integrator.
SWI SWZ SWI SWa
Single-pole-single-throw switch Four.pole-six-position rotory switch Four-pole-single-throw rotory switch Normallv ooen wsh-bullon swibh RI-R; 10K ten'turn poientiometer Rs 1K 10% resirtor 1 OOK ten turn potentiometer RD C L - 6Mylor, 2/rf. ZOO-w.v.d.c. capacitors (Goodoll) O.A. Heath Model EUW-IOA operational amplifier (Heath Co., Benton Harbor, Michigan) FOL Unit No. 1 of above system in the follower position
Response Compensation. The signal from each peak must he modified to compensate for differences in relative response of the detector to the different sample materials. According to the integration Eqn. (3), the output voltage is proportional to (l/Ri,) and the output is increased by decreasing the input resistance for a given voltage-time integral. The effect of dialing the relative response factor on the input potentiometer is to increase the output potential for materials of less d e
tector response so that the same weight of each material results in the storage of equal charges on the c a pacitors. This function is performed by a bank of five 10-turn, 10-kilohm potentiometers (RI, etc.) used in the input to the integrator. These potentiometers are switched, by a set of contacts on the resistor-capacitor (RC) selector switch (SWJ into the integrator circuit one a t a time to receive the integration signal arising from the individual peaks. Integration. The operational amplifier (O.A.) is one section of a Heath Model Em-1OA operational amplifier system (Heath Co., Benton Harbor, Mich.) stabilized with a Phibrick K2-P chopper stabilizer (8) (Philbrick Researchers, Boston, Mass.). This ampliier is connected in the conventional integrator configuration (Fig. I), with capacitor in the feedback to accumdate and store the integrated signal. After each peak, the selector switch is set to a new RC combination for integration of the signal for the next component. It should be noted that each potentiometer is always associated with the same capacitor. The capacitors must be closely matched in capacitance value and must be made with very low-leakage dielectric. Those used in this work are 10% tolerance Mylar, 2-pf 200-wvdc (Goodall) matched to within +0.5% by smaller parallel capacitors. When the INT-READ switch (ST3) is placed in the READ position, a 1K resistor (Re) is placed in the feedback loop of the amplifier to prevent i t from limiting. Cmnputation. The integrals are summed by connecting the capacitors in series a t the input of amplifier No. 1 in the follower configuration. The high input impedance of the follower prevents drainage of charge from the capacitors during readout. The output from the follower is sampled by a ten turn, 100 kilohm potentiometer. This potentiometer is adjusted to divide the output giving a reading of 1.000 v on the digital voltmeter representing 100.0%. Leaving the potentiometer a t this setting, each capacitor is switched individually into the input to the follower and the output voltage, representing percent of that component,istabulated. Digital Readout. A DigiTec Model 201 (United Systems Corp., Dayton, Ohio) digital voltmeter with a 2.000-volt full-scale range is used to convert the analog data into digital data. Procedure Determination of Relative Response Factors
The chromatograph must be allowed sufficient time to reach thermal equilibrium and the recorder and integrator should be allowed to warm up for approximately one hour. With the output of the chromatw graph connected to the recorder, and the ON-OFF switch of the direct readmg integrator set to OFF, a 0.5 p1 sample of the mixture of known composition is injected in the chromatograph. As the peaks are traced by the recorder pen, the chromatograph attenuator is adjusted such that the largest peak approaches full scale on the recorder. Several attempts may be necessary to obtain the correct setting. Then replicate chromatograms of the known-composition mixture are run by making anew injection of 0.5 pl after thelast peak of the previous injection is eluted. The areas of the peaks are then measured by taking peak-height times width at half height and by counting
the number of "Disc Units." Using these areas and the known weights of the components, response facton (&/unit area) are calculated and then normalized with respect to the largest factor. The input of the direct-reading integrator is connected in parallel with the recorder. The chromatograph attenuator is set on the XI position, the response compensating potentiometers are all set to 100 and the INT-READ switch (SW3) is set to INT. With the ON-OFF switch (SW2) set to OFF, the integrating ampliier balance control is set for zero output to the DVM. The ON-OFF switch is then set to ON, and the detector bridge zero control is used to obtain zero output to the DVM. A 0.1 pl sample is injected and the peaks i n t e grated by switching to an empty capacitor after each peak when the recorder pen returns to the baseline. After all peaks have been integrated, the ON-OFF switch is set a t OFF, and the INT-READ switch is set to READ. The RC selector switch (SF2) is moved to the various capacitors used and the voltages recorded. The response factor for each component is determined by dividing the mass of that component in the sample by the output voltage for that component. Relative response factors are calculated by dividing each individual factor by the largest. This procedure is repeated in triplicate. The average numerical value of each relative response factor is then dialed on the corresponding potentiometer. Determination of Compositions of Unknown Mixture
The weight percent composition of an ~ n k n 0 mix~n ture is determined using the relative response factors obtained above. Using the same procedures, three replicate samples of an unknown mixture are chromatographed. The areas of those peaks are measured by peak height times width at half height and the "Disc Units." The areas are then corrected by multiplying by the appropriate factor (&/unit area X area) summed and the percent composition by weight calculated. For the direct-reading integrator the procedure is the same as that used in the determination of the response factors except that after all of the peaks of a given sample are integrated, the RC selector switch is moved to the SUM position. The voltage divider (Ro) is then adjusted to give a readmg of 1 . 0 0 0 ~on the D ~ M . Now the RC selector switch is rotated to each of the capacitors used, and the value shown, which is the percent by weight of each component, is noted. All of the capacitors used are discharged by depressing the RESET switch (SW4) as the RC selector switch is set to each position. Results and Discussion
The student is first impressed with the need for using response factors by comparing the known percent by weight composition with the area percent determined by simply summing the areas and calculating their percentages. With this in mind he then determines the relative response factors and then uses these to determine the mixture of unknown composition. In reporting his results, the student is expected to discuss the limitations and advantages of the various methods. Results obtained by the various methods are compared with respect to repeatability, accuracy, Volume 44, Number 1 1 , November 1967
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Table 1.
Relative Response Factors by Each Method Manual
Disc
Dinct Reading Int.
Heptane Octane Decane
0.92 i 0.02 0.96 f 0.02 1.000
0.93 & 0.02 0.95 i 0.01 1 ,000
0.910 i 0.015 0.949 10.010 1.I100
Table 2.
Percent by Weight of a Mixture Determined by Each Method -
Actual
-
D/, .
Heptane Octane Decane
32.0 33.6 34.4
Direct Readine Int.
-
Disc
-
Manual
32.110.21 31.710.35 31.5i0.72 3 3 . 3 i 0 . 3 5 32.7*0.38 3 3 . 8 i 0 . 4 5 34.6 &0.51 3 5 . 6 i 0 . 4 0 3 4 . 5 1 0.60
relative ease, and speed of obtaining the final result. Typical numerical results obtained by an undergraduate student performing the experiment are given in Tables 1 and 2. The experimental work described in the report required about three hours for completion. It should be noted that the chromatographic equip ment, as well as the samples used, are not limited to those presented in this report. Caution should be used in selecting a system from two different points of reference. First the components should be selected such that all can be chromatographed in less than ten minutes in order that all of the required runs can be completed in the alloted time. Also highly volatile samples will change composition by evaporation of the lighter components over a three-hour period. The direct reading integrator can be used in suh-
698 / Journul of Chemical Education
sequent periods for studying experiment variables. These variables can be either chromatographic, such as the effect of changes in flow rate, temperature, etc., on the response factors as well as variations in the rlcctronics. Sever31 students havt! nsrd this upparutu* for k~llowincthe kineticsol esterificatio~~ of ethanol with acetic acid.- This was done by measuring the increase in ethyl acetate simultaneously with the decrease in the ethanol and acetic acid concentrations. Clearly, the range of problems which can be examined profitably is limited only by the time available. There is much to be said for illustrating the use of automatic equipment in quantitative analysis as described herein. Literature Cited (1) , , MEMAN.C. E.. AND KISER.R. W.. "Problems and Emeriments' ~&trume& 'Ak,lys&," Charles E. M&~U Books, Inc., Columbus, Ohio, 1963. D. T., "Experimenh for In(2) REILLEY,C. N.. AND SAWYER, strumental Methods," McGraw-Hill Book Co., Inc., New York, 1961. (3) D u NOQARE, S., AND JUVET,JR.,R. S., "Ga~LiquidChre mrttography," Interscience Publishers (division of John Wiley & Son, Inc.), New Ymk, 1962. (4) Rosm, D. M., MD GROR,R. L., Anal. Chem., 29, 1263 (1957). (5) CREMER,E., AND MUKLER,M., Krochem. A&., 36, 553 (1951). (6) BARNES,J. R., AND PARDUE,H. L., Anal. Chem., 38, 156 (1966). (7) Disc Instruments Ine., Sents Anq Calif., Bull. 200. (8) P~RDOE, H. L., AND DAHL,W. E.,J. Eleetroanol Chem., 8 , 264 (1964). ~~
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