268 Analyst, April, 1967, Vol. 92, p p . 268-270 A Note on the Determination of Vapour-Liquid Equilibrium for Multi-component Systems BY K. A. PIKE AND D. C. FRESHWATER (Imperial Smelting Co. Ltd., Avonmouth) (Loughborough University of Technology, Loughborough, Leicestershire) The use of a gas chromatograph connected to a data-logging system is described for analysing samples taken in the determination of ternary vapour - liquid equilibria. Data are produced in a form that is ready for processing by digital computer, and therefore their accuracy may be determined within a short time of sampling. There is a distinct improvement in the accuracy of the method over more traditional methods for ternary system analysis. ONE of the major hindrances to experimental investigation of the vapour - liquid equilibrium of multi-component systems is the time-consuming and usually tedious analysis of experi- mental samples.Many of these difficulties disappear if gas - liquid chromatography is used, but by itself this is still a lengthy technique for the many samples that have to be examined. However, we have developed a method that not only reduces the time of operation to a minimum but also gives the actual composition results directly from the detector output. These results can also be produced in a one-step operation from sample injection, in a form suitable for immediate processing by digital computer. The method has been developed for a three-component system which was of particular interest for other purp0ses.l The method can be easily adapted to analyse four or more components.The main components of the equipment used are shown in the form of a flow-chart (Fig. l).. The data-logging system is multi-purpose and is used for recording experimental results in the Chemical Engineering Laboratories of Loughborough University of Technology. ANALYSIS PROCEDURE A = Air supply t o combustion chamber B = Carrier gas supply, 75 per cent. hydrogen and 25 per cent. nitro- gen (as recommended by Shandon Scientific Co. Ltd.) C = Sample introduction point D = Thermocouple E = Combustion chamber F = Jet G = Chromatograph column H = Output from thermocouple t o I = Sunvic recorder J = Signal voltage t o data-logging system K = Data-logging system L = Data scanner unit M = Digital voltmeter N = Paper tape punch recorder Fig. 1.Flow-chart of analytical equipmentPIKE AND FRESHWATER 269 The gas-liquid chromatograph used was a Shandon universal model with a flame thermocouple detector. The chromatograph column (20 feet x $ inch, external diameter) was packed with Celite, and diglycerol was used as the stationary liquid phase. This column was maintained at 100" C. The detector output was fed simultaneously to a chart recorder and also the data-logging system. At the conditions chosen, samples of the system, acetone - methanol - isopropyl alcohol, which were to be analysed, gave three well separated peaks on the recorder chart. The areas of these peaks were measured by recording several peak height values, read at regular time intervals and then performing an integration to obtain the area. A trans- mitting potentiometer was incorporated in the chart recorder, which enabled the alterations in the thermocouple output to be read and then recorded by the data-logging system.The peak height was recorded at precise 1-second intervals by the data-logging system. Each peak had a duration of about 100 seconds, and considerably more readings for each peak were obtained to ensure that the whole peak was sampled. Peak areas were obtained by integrating the precisely recorded peak heights by using a form of Simpson's rule- h h h f (4 dx = 3 (Yo + 4% + YZ) + 3 (9% + 4y3 + y4) + 3 (y4 + 4y5 + y6) + error function (1) (where h = increment 1 second, and y = peak height above base-line), which gives- h f (x) dx = 3 (yo + 4y1 + 2y2 + 4y3 + 2y4) + error function .. By sampling the peak height above a base-line, which is calculated for each peak in turn, the method allows for the slight drift of base-line that can occur when using an amplifier over an extended period. For the type of peak obtained with the signal voltage equal to the base-line voltage immediately before and after a peak, the first and last terms of equation (2) tended to zero and were neglected. The error function was also negligible for the size of increment being considered. The peak areas so obtained were normalised by using heats of combustion, with methanol being considered as the basic component. The normalised peak areas were then converted into mole fractions of the components present. All of the computations necessary to produce an analysis result were carried out by a digital computer programme compiled in Fortran for the I.B.M.1620 data processing system. Other functions of the programme were to compare an analysis result with previously defined accuracy limits. If the results were of the required accuracy a data tape was compiled for use in other programmes. Data of insufficient accuracy were simply printed out and not punched out as a data-source tape. When operating the analysis procedure for the systems composed of acetone - methanol - isopropyl alcohol, it was necessary to accumulate a number of vapour - liquid equilibrium samples that required analysing to make optimum use of the system. The peak height information was then accumulated as a continuous reel of paper tape that could be stored until processing time was available on the digital computer.The processing time for the longest reel of data containing some thirty ternary analyses was about 20 minutes. The same programme as that used for ternary samples was also used for binary samples. This was possible because the programme would integrate the signal voltage Less the base-line voltage for a period where a peak should have occurred and obtain an area of zero, as during this period the base-line voltage was equal to the signal voltage. ACCURACY OF THE METHOD- Besides the distinct advantage of the convenience of the method over more traditional techniques, there are significant improvements in other directions. With the physical property measurement technique for a ternary system, Jones2 has quoted an accuracy of analysis of k0.2 per cent., while the procedure outlined here has an accuracy of better than k0.1 mole per cent.This is a small but significant improvement when considering vapour - liquid equilibrium results. The gas - liquid chromatograph was calibrated with standard samples made up by weight to the fourth decimal place, the total weight of a sample being about log. In the event of a contaminant entering the system, which is unlikely in a vapour - liquid equilibrium study where very high purity components are required, the digital computer270 PIKE AND FRESHWATER programme would identify the whole analysis result as being of insufficient accuracy for further processing. Again in a vapour - liquid equilibrium study this would not be too serious as the experimental point could be repeated.OTHER APPLICATIONS- In addition to its use for analysing complex multi-component mixtures, gas - liquid chromatography can be used to obtain, by direct measurement, activity coefficients under conditions tending towards infinite dilution. The method depends upon obtaining retention volume data, which, in turn, require the determination of retention times. Retention times are variously defined as being the time taken from actual sample injection to the emergence of the maximum peak height, or as the time between emergence of an inert-gas peak and the emergence of the maximum peak height. A feature of the analysis procedure described in this paper is that the emergence of peaks can be accurately recorded to small time intervals. Thus the timing operation for retention volume determination can be carried out auto- matically and to a high degree of accuracy. The technique could also be used advantageously linked to an equilibrium still along the lines of the suggestion by Wichterle and HAk3 Resides providing analyses of a high accuracy, the continuous analysis of the mixture could be used to ensure that equilibrium between liquid and vapour phases was being achieved. REFERENCES 1. 2. Jones, T. H., Ph.D. Thesis, University o f Birmingham, 1962. 3. Pike, K. A., Ph.D. Thesis, Loughborough University of Technology, 1965. Wichterle, I., and HAlB, E., Ind. Engng Chew. Fundamentals, 1963, 2, 155. Received Augztst lst, 1966