Accurate Multicomponent Analyses by Gas Chromatog raphy BUFORD D. SMITH arid WARREN W. BOWDEN1 School of Chemical Ertgineering, Purdue University, lafayette, Ind.
b Two major difficulties in the accurate analysis of multicornponent mixtures b y gas chromatography are the tendency of the calibration curves (response area vs. amount injected) to shift because of day-to-day variations in the instrument ccnditions and the dependence of thermal conductivity detector response factors on sample size. The latter difficulty results from the nonlinear nature of the calibration curves. This paper shows that more accurate analyses are obtained if calibration curves are used only i o provide relative response factors rather than used directly to give the amounts of each component present in the unknown sample. Also described i s an iterative procedure for taking into account the dependence of the response factors upon the amounts of the components present in the sample. The relative response factors often vary b y 15 to 20% over the composition range.
This paper will show how the effect of sample size can be taken easily into account and how the effect of the shifts in the calibration curves can be minimized. The latter problem will be dealt with first. Consider a three-component sample containing m1, mz, and ma mg. of the three constituents. If this sample were
A
1 Present address, Chemical Engineering Department, Rose Polytechnic Institute, Terre Haute, Ind.
then the shifted curves can be used directly to provide correct analyses. Intuitively one would expect that a more likely possibility is that K I = K2 = K3 in the set
AI’ = KiAi SULFUR DIOXIDE
-
0
An’ = KzAs Ar’ = KaAs
BENZENE
(4)
In other words, the instrument or condition change that shifted the curves would, in effect, multiply all the component areas by the same factor and A2‘ - Aa’ AZ As
&e---
TEMPERATURE-IIO ‘C HELIUM R A T E - I 3 ML /MIN
0
QVANTIrATIVEanalyses by gas chromatography units have been difficult because of the day-to-day changes in instrument components such as batteries, thermistors, etc., and the inevitable variations in operating conAlso, for multicomponent ditions. samples, there has been no convenient way to take into accoiint the dependence of the instrument response factors on the amounts of the individual components injected. Calibration curves (response area vs. amount of the component injected, as in Figure 1) will remain constant for only a short time before changes in the instrument componmts or operating conditions will rotai,e the curves upward or downward a short distance around the origin. The day-to-day variations in the instrument response can be followed by inclusion in the sample to be analyzed of a known amount of a “markckr” compound (3). However, the use of a marker is inconvenient and, when high accuracy in the analyses is desired, the reproducibility of the amount of marker injected becomes a pro’dem in itself. CCURATE
If the curves all shift in such a manner that
2
4
SAMPLE
6
8
’
,
If Equation 5 holds, the relative response factors F18 =
1 0 1 5
2 2,etc.
S I Z E , MILLIGRAMS
Figure 1. Calibration curves for sulfur dioxide, normal pentane, and benzene
injected immediately after the calibration curves were determined (before any shifts occur) response areas A I , Az, and A3 would be obtained. Sometime later after some change in the instrument conditions has shifted the curves, injection of an identical sample would provide areas AI’, Az’, and -43’. Use of the original calibration curves with these areas would give ml’, ml’, and ma’ as the milligrams present in the sample. The two samples were identical in both total mass and composition but the error in total mass is of no concern if the correct composition is obtained. The set of incorrect m’s will provide a correct set of w’s only if
and these equalities will hold only if kl = k2 = k3 in the set ml’ = klml
m2’
Ai
= k2m ma’ = krm,
(2)
and
obtained from the two injections will be constant since K3 = K1 = Ks. Messner, Rosie, and Argabright (6) found that the relative response factors remained essentially constant over rather wide temperature and flow rate changes. This indicates that Equation 5 is more likely to hold than Equation 3. Both cannot apply a t the same time. This can be shown by constructing vertical lines at ml, m2, and mS on Figure 1 and then defining the angles el, 82, and e3 as follows:
From Equation 8 tan- O1 - F1s ki- 1Kr- 1 tan 08 kr- 1 K i - 1
(9)
If Equation 5 holds, ( K 3- l ) / ( K 1- 1) is unity and Fls is a constant for any given ml and ma-i.e., Fl3 is independent of the magnitude of Ka and K1. If Equation 3 were applied simultaneously with Equation 5, then (kl - 1(/ VOL. 36, NO. 1, JANUARY 1964
87
(k3 - 1) would be unity and it would be necessary that the ratio tan &/tan e3 be equal to F13 and independent of the magnitude of K l and K3. Obviously, if the calibration curves are not linear, the angles 01 and 83 as defined by Equation 8 will not be independent of the magnitude of K I and K3. Therefore, kl = ka cannot be true simultaneously with K1 = Ks a t any given m1 and m3 if one (or both) of the calibration curves is nonlinear. Experimental results will be presented a t the end of this paper to show that Equation 5 is a better assumption than Equation 3. Before discussing these data, we must show how the dependence of the relative response factors on sample size can be taken into account. The factors often vary considerably as w i goes from 0.0 to 1.0 in the i-j binary (4). For example, Figure 2 shows that the relative response factor for heptane to toluene varied from about 0.91 to 1.1 on the iModel 154C Perkin Elmer vapor fractometer used in this work. This instrument has a thermal conductivity detector with reference and sensing thermistors. Values of F obtained from only one sample (usually a 50-50 mixture) will often be in error by 10% or more a t the ends of the composition range. These latter statements are contrary to the conclusions reached by Messner, Rosie, and Argabright (5) who found no variation in relative response factors with sample size or composition. Their conclusions were evidently based on the diisopropyl ether-benzene pair. The response of a thermal conductivity detector to benzene is essentially a linear function of sample size, as can be seen in Figure 1 . Evidently the diisopropyl ether response was also essentially linear a t these column conditions (@, causing relative response factors to be invariant with sample size. This constancy has not been found in the present work in any of the pairs among the Csto CSnormal paraffins, benzene, toluene, and sulfur dioxide. The calibration curves can be used in conjunction with the unknown sample chromatogram to obtain the F’s corresponding to the set of m’s in the unknown sample. At the time of injection the sample volume, 77, must be noted from the syringe or whatever device is used to inject the unknown gas or liquid sample. If the sample is a gas the temperature and pressure must also be known. An initial estimate of the sample composition is obtained from the uncorrected response areas on the recorder chart. For compound i in an i-j-k ternary
88
ANALYTICAL CHEMISTRY
CARRIER GAS - HELIUM AT 19 ML / MIN
W
wt-
z v w
I
09 0
20
40
60
80
100
WEIGHT PERCENT HEPTANE
Figure 2. Relative response factors for normal heptane compared to toluene as function of sample composition Data of Kaufer ( 2 )
the difference is large enough to fall within the significant digits carried in the calculations, the effect is essentially self-canceling because the partial mass volumes of all the components will always vary from the pure component volumes in the same direction and the effect on the F’s obtained will be negligible. This analytical technique was developed for an experimental project for the measurement of activity coefficients in liquid-liquid-vapor systems. I n simple form, the equation used to obtain liquid-phase activity coefficients from pressure, temperature, and phase compositions is Ti
These approximate weight fractions can be used with the sample volume, temperature, and pressure to calculate approximate values of the m’s for each component from the following equations : lntvi
+ ??a$, +
mkvk
=
v
(11)
Since
and
Equation 11 can be rearranged to
The approximate value of m obtained for each compound from Equation 13 permits the first approximate relative response factors to be obtained from the combined use of the calibration curves and Equation 6. If compound j is chosen as the reference (the reference compound should be present in relatively large amount), Equation 10 can now be written more accurately as
The procedure is now repeated with Equation 14 substituted for Equation 10. Each time through provides a better set of relative response factors until there are no further changes. It was found from experience that it is seldom necessary to obtain more than two sets of F’s and if good approximate values are known beforehand only one new set need be evaluated. About 15 minutes are required to calculate an analysis after the chart areas have been planimetered. The only assumption in the above procedure besides Equation 5 lies in the ideal solution assumption in Equation 11. Usually the difference between the pure component specific volume and its specific volume in solution is completely negligible. Even in cases where
= 2/1p/xip*t
Percentage errors in the measured values of y, and x, cause proportional errors in yi. Therefore it was desired to measure concentrations within 5% of the true value. After the calibration curves in Figure 1 were established, nine samples of known composition that ranged in size from 4 to 10 pl. !\-ere analyzed and the gas chromatography results compared with the known compositions as determined by weighing. These analyses were made from 2 to 4 weeks after the calibration curves were determined. The results based on the assumption of Equation 5 were better than those obtained from direct use of calibration curves. In other words, Equation 5 was a better assumption than Equation 3. The mean percentage errors (regardless of sign) from the nine check samples were 2.12, 2.10, and 1.03 for the pentane, sulfur dioxide, and benzene, respectively, when Equations 10 through 14 were used. The corresponding numbers obtained directly from the calibration curves and Equation l were 3.55, 3.41, and 0.57. Care had been taken to maintain the instrument conditions relatively constant to minimize shifts in the calibration curves; hence, reasonably good values were obtained from direct use of the curves. The range of errors obtained in the analyses is of more interest than the averages. The following summary of results is for the analyses based on the relative response factors. The pentane concentrations ranged from 7.33 to 37.43 n-t. % and the gas chromatography results deviated from the weighed concentrations by 0.35 to 5.49% of the true values. Six of the nine values were within 2%. For sulfur dioxide, the true concentrations ranged from 8.88 to 44.64 n-t. yoand the chromatography values deviated by 0.70 to 4.95% of the true values. Five samples were within 2%. In the case of benzene, the concentrations by weight ranged from 37.88 to 68.23y0 and the deviations ranged from 0.01 to 1.93% of the true values. The smaller deviations here
were probably due to the larger amounts of benzene present. ;Is mentioned earlier, the relative response factors vary by an appreciable amount from sample to sample. I n the nine check samples, i,he pentane factor ranged from 0.85 to 0.98 and the sulfur dioxide factor from 1.14 to 1.29 relative to benzene. The effect of a relaidvely large change in some instrument component on the applicability of the calibration curves in Figure 1 was checked by running duplicate analyses with recorder battery voltages of 1.42 and 1.56 volts. This change was sufficient to shift the calibration curves a sizsble distance but the maximum differer ce in the duplicate analyses was 2i.45 us. 27.20 wt. 7,. for sulfur dioxide. The other two compounds had smaller differences in the opposite direction. The results discuss2d above, plus the work of 2Messner,Rosie, and drgabright (j),support the hypothesis that the relative response fackors at any given sample composition remain essentially constant despite shif s in the response area us. amount injected curves. This, together n-ith the iterative procedure described above, per nits accurate analysis of multicomponent mixtures with relatively little effort. It is important to note that the calibration curves must lie consistent with each other if accurate? results are to be obtained in the itwative procedure based on Equations 10-14. They must all be determined a t the same operating conditions and instrument condition. Also, the amounts injected and the areas obtained must be known quite accurately. I n this woik the Hamilton 7OlN microsyringes used to inject the liquid samples were calibrated with high purity mercury at t i e injection temperatures. The needle volume was included in the calibration because some vaporization of the needle contents a t the oven temperaturc? of 110’ C. was inevitable. To be cer :ain of the amount injected, the syringe was left in the sampling port until all the material was vaporized. The chart areas mere planimetered a sufficient number of times to get within 17; of the true area. AUso,multiple injections (at least three) were made at each veight. Variations in operating and instrument conditions between the various calibration curves we*e not so easy t o handle. The curves should all be
determined within a relatively short period of time and injections of the various compounds intermixed. Also, large and small sample injections should be intermixed. In short, all of the usual experimental techniques to avoid the effect of time on the variables should be employed. Once a set of accurate, consistent calibration curves are obtained most of the above precautions are not necessary in the routine analysis of unknown samples. The chart areas must, of course, always be measured accurately but the size of the injected sample need not be known with the precision described above-i.e., a calibrated syringe need not be used. This does not mean that the accurate measurement of the unknown sample volume is not important. Sample volumes greater than 5 filecan be measured easily within 2% with an uncalibrated Hamilton syringe. The possible additional 1% increase in accuracy obtained by calibrating the syringes will not affect any of the significant digits in the final set of relative response factors obtained and is therefore not worth the trouble. Incorrect volume readings, n-hich are off by, say, IO%, will of course affect the results and reasonable care in the measurements should be exercised. The recorder battery should not be alloa-ed to run down completely but a change in voltage from 1.5 to 1.4volts, for example, will not cause trouble. Similar remarks hold for other instrument components. The calibration curves will shift with such changes but the relative response factors evidently remain essentially invariant. The data and techniques described in this paper are given in complete detail in reference ( 1 ) .
p : Total system pressure. pi*: Vapor pressure of compound i. IT: Volume of totalinjectedsample. vf: Specific volume of compound i. wi: Weight fraction of compoundi. Q: Mole fraction of i in liquid. yi: Molefraction ofiin gas. LITERATURE CITED
Bowden. W. W.. Ph.D. Thesis. Purdue ~University, Lafaiette, Ind., 1964. (2) Kaufer, D. M., M. S Thesis, Purdue University, Lafayette, Ind., 1961. (3) Keulemans, A. I. M.,“Gas Chromatography,” 2nd ed., pp. 32-5, 83-91, Reinhold. New York. 1959. (4) Keulemans, A. I. ’M., Kwantes, A., Rijndens, G. A,, Anal. Chim.Acta. 16, 29 (1957). (5) Messner A. E., Rosie, D. M., Argabright, P. A., AN.~L.CHEM.31, 230 (1959). RECEIVEDfor review April 2, 1963. Accepted September 30, 1963. This work was made ossible by the support of the Humble Oiyand Refining Co. 1
\ -
Corrections Determination of Molecular Weights of Proteins by Gel Filtration on Sephadex In this article by John R. Whitaker [ANAL. CHEM.35, 1950 (1963)l on page 1952, in column 3, lines 25-30, the equations of the lines should read as follows: log molecular n-eight = -0.660 ZIC 0.054(vV - 1) f 4.785 rt 0.040 for Sephadex G-75 and log molecular weight = -0.973 0.012(v0 V - 1) f
*
5.190 i 0.010 for Fephadex G-100.
ACKNOWLEDGMENT
Jonathan Amy and William Baitinger of the Chemistry Department provided invaluable assistance during the course of this work. NOMENCLATURE
Ai: Response area of compound i. Response area is chart area in square inches multiplied by instrument attenuation setting. Ff-,:Relative response factor for compoundireferred t o compoundj. Defined by Equation 6. m,: RIasc, of compoundiin mg
Coulometric Efficiency of Anodic Deposition and Cathodic Stripping of Chloride at Silver Electrodes In this article by H. -1. Laitinen and Zui-Feng Lin [ d x a ~ .C H m . 35, 1405 (1963)l on pages 1407 and 1408, respectively, in Figures 3 and 5 the units of the abscissa should be cfa./cm.* rather than ma. /cm.’
VOL. 36, NO. 1, JANUARY 1964
89
