in sample 7 neither of the fractions collected contained traces of the other solute. The efficiency is independent of the carrier gas flow rate. The technique is much simpler than total trapping methods which involve condensation of the carrier gas (4, 5 ) or the use of an evacuated trap (6) and has the advantage that the collected material may be stored at room temperature until analyzed. Moreover, since the coil
(4) P. A. T. Swaboda, Nature, 199, 31 (1963). (5) I. Hornstein and P. Crowe, ANAL.CHEM., 37, 170 (1965). (6) S. Dal Nogare and R. S. Juvet, "Gas-Liquid Chromatography," Interscience, New York, N. Y . , 1962, p 254.
is cooled only after it is attached to the vacuum manifold, the risk of contamination with atmospheric moisture when cold traps are attached to a gas chromatograph is avoided. The procedure is applicable to any compound having a vapor pressure at - 196 "C which is low compared with that of the carrier gas, and which at higher temperatures is sufficient to enable it to be distilled under vacuum. The method is limited to analytical gas chromatography to permit reasonably small coils to be used with the flow rates and peak widths which are normally encountered.
RECEIVED for review April 16, 1971. Accepted June 8, 1971.
Calibration of Low Thermal Conductivity Signals with Continuously Flowing Mixed Gases for Determining Adsorption Isotherms Stewart Karp and Seymour Lowell C . W . Post College, Long Island University, Greenvale, N . Y . 11548
THEDYNAMIC FLOW method is now a well accepted technique for the determination of adsorption isotherms and "BET Surface Areas" ( I ) . This technique involves the adsorption of nitrogen or other suitable adsorbate out of a flowing pflow mixture of adsorbate and a n inert gas, usually helium, followed A by subsequent desorption of the adsorbate back into the flowing mixed gas. This decrease and increase of adsorbate in the flowing gas mixture is usually monitored by thermal conductivity detection. The detector signal is easily calibrated by injecting a known volume of pure adsorbate into the flowing gas mixture. To minimize errors due to nonlinearity of the detector, the calibration signal should match the desorption signal. The closeness of match needed depends upon the katharometer design and the accuracy desired. When small signals are obtained, it is difficult to make accurate injections of the required small amounts of gas. This problem can be solved by injecting larger volumes of adsorbate diluted with the 'pl low carrier gas. However, when this is done, it must be recogIin N2 "mix nized that the effective volume of adsorbate injected is not Figure 1. Diagram of fractional pressures simply the volume of the mixture injected times the fraction after injections into flowing gas mixture of adsorbate in the mixture. The fact that the injected volume displaces the flowing gas, which contains adsorbate, must also proportional to the signal, S. This is diagrammatically be taken into account. described by Figure 1A. Therefore, Specifically, for nitrogen helium mixtures, if pure nitrogen is injected into flowing pure helium, the change in thermal S = kVN,'"(l - PN2f10W) (1) conductivity results in a signal which is proportional to the amount of nitrogen introduced. (Linear response is aswhere k is a constant and Pstflowis the fractional pressure sumed here and is a good approximation for small thermal of nitrogen in the flowing gas. conductivity changes.) However, if the same amount of pure Now if a volume of a mixture of nitrogen and helium, nitrogen is introduced into a flowing mixture of nitrogen and Vmiin, with a fractional nitrogen pressure of PNjnis introhelium, the change of thermal conductivity and, hence, the duced into the flowing gas mixture, the volume of nitrogen signal, must be less than in the previous case because the effective in changing the gas composition is the actual volume injected nitrogen here displaces both helium and nitrogen of nitrogen introduced, Vmi,i"PN,in, minus the volume of of the flowing gas. The volume of nitrogen introduced, nitrogen displaced by the injection, Vmi\-inP~2floW. See VNZin,minus the volume of nitrogen displaced, V N : ~ P N ~ ~ ~ Figure ~, 1B. The signal, S ' , is therefore, proportioned to this is the volume of nitrogen effective in changing the thermal difference. conductivity of the flowing gas and, hence, is the amount S' = kV,i,i"(PN,i" - P N 2 f l 0 W ) (2) (1) S J. Gregg and K. S. W. Sing, "Adsorption, Surface Area, and Porosity," Academic Press, New York, N. Y., 1967, Chapter 8. 1910
k in Equations 1 and 2 is the same if the flowing gas, i.e., is the same for Equations 1 and 2.
PN2f10w,
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
Table I. Experimental Data
PNif*oW
, cc
0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.498 0.498 0.498 0.498 0.498 0.498
0.500 2.00 4.00 1 .OO 4.00 8.00 4.00 2.67 2.00 2.50 3.34 2.50 5.00 10.0
No. of
Integrator counts +
cc
Integrator counts, av
replicates
VNiin
0.500 0.505 0.515 1.00 1.01 1.03 -0.485 -0.497 2.00 1.99 1.95 -1.97 - 1.94 -1.91
688 702 710 1450 1452 1490 - 668 - 656 1260 1248 1247 - 1093 - 1049 - 1031
3 2 2 2 1 1 1 2 4 2 2 3 2 2
1376 1391 1379 1450 1439 1447 -1378 -1319 630 627 639 - 555 - 542 - 540
VNiin
Vmi x in PNxin
1 .OO 0.402 0.303 1.00 0.402 0.303 0.103 0.0513 1.00 0.898 0.792 0.103 0.303 0.402
that To calculate the amount of pure nitrogen, VN)~, would show the same signal as a given amount of a mixture of nitrogen and helium, Vmi:n, Equations 1 and 2 are equated, i.e., S = S ’ , yielding Equation 3.
(3) Equation 3 can also be used for the calibration of nitrogen deficient signals (adsorption) with helium injections and with injections of mixtures where PKin < Pr*:2flow. Nitrogen deficient signals are indicated by negative VN;I’ in Equation 3. The data shown in Table I illustrate the validity of the above. The data were taken using the Quantachrome Corp. “Quantasorb,” a dynamic flow adsorption system. This instrument allowed for the injection of a gas sample into a
flowing gas stream and thermal conductivity detection. G a s samples were injected with Hamilton gas syringes. The mixed gases used were obtained from J. C . Baker and Company who reported their compositions t o i.1 relative. The integrated signal, column 5 , is proportional t o Vxtin, column 4, calculated from Equation 3. Therefore, the ~ ~ be ~ ratio, column 7, of this integrated signal to V N should constant for different injections into the same flowing gas mixture. The data demonstrate this. The differences between the sets of data with the same flowing gas mixtures reflect the nonlinearity of the detector system.
RECEIVED for review April 9, 1971. Accepted June 14, 1971. This work resulted from a project supported by Quantachrome Corp., Greenvale, N.Y. 11548.
Nomograph for Known Addition Methods in Analysis with Ion Selective Electrodes Bo Karlberg Department of Ana/ytical Chemistry, Unicersity of Umeh, 901 87 Urn&, Sweden
THEANALYTICAL TECHNIQUE involving standard addition is commonly used in connection with concentration determination. The growing interest in its applicability t o measurements with ion selective electrodes has produced several papers on the subject (1-6). The conventional method for analysis with ion selective electrodes is direct potentiometry. A calibration curve must be constructed using standard solutions similar to the
(1) E. L. Eckfeldt, ISA T r a m , 9, 37 (1970). (2) R . M. Carrels in “Glass Electrodes for Hydrogen and Other Cations,” G. Eisenman, Ed., Marcel Dekker, New York, N. Y., 1967, Chapter 13. ( 3 ) R. A. Durst, Mikrochim. Acta, 3, 611 (1969). (4) “Newsletter,” Orion Research Inc., Cambridge, Mass., 1, 2 (1969); ibid., 1, 4 (1969), ibid., 2, 2 (1970), ibid., 2, 5 and 6 (1970). (5) M. J. D. Brand and G. A. Rechnitz, ANAL.CHEM., 42, 1172 (1970). (6) L. G . Bruton, ibid., 43, 579 (1971).
sample. A single measurement in the sample then gives the concentration of the ion in question. Known addition methods offer the advantage that they are rapid and easy to perform. They are also diagnostic methods as they provide information about the buffer capacity of the ion t o be determined. However, nonidealities of the electrode used may cause errors. These may comprise a narrow working range, a lack of selectivity, and a non-Nernstian response of the electrode. Unfavorable conditions in the sample solution are other sources of error. The presence of complexing species in the sample solution may sometimes invalidate the methods. Two different methods will be distinguished. The first of these consists in adding a known volume of a standard solution t o a known volume of the sample and recording the potential change of the electrode system. The second method is sample addition t o a standard solution, called “analate addition” by Durst (3). Successive additions of standard and sample solutions, respectively, are generally applied
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
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