X, = AZWi(Ui - Xi)’, k
Table I. Classification Performance 10 dimensions 3 dimensions 1-Nearest Neighbor Training set 102/120 1131120 Evaluation set 23/30 28/30 3-Nearest Neighbor Training set 961120 110/120 Evaluation set 18/30 29/30
B
(7) The above process is repeated for all pairs. For the n-class problem, n(n - 1)/2 alternative variables will be defined. Finally, to equally weigh each new variable, the new pattern space is autoscaled (10). DATA
To test the technique, three classes of hydrocarbon spectra were used; the compounds within each class contained six, seven, and eight carbon atoms (denoted Cs, C;, and C8 in the figures), respectively. The spectra were selected randomly from our computerized low-resolution mass spectra library. For each class, forty spectra were used in the training set and ten were used for the evaluation set. Rather than use the intensities for each m/e value as the variables, moments were used. The recognition accuracy of similar representations has been discussed elsewhere (7). For each non-zero intensity the m/e (c,) and the square root of the intelisiiy ( W , ) were used to calculate the moments. Ten variables were defined for each spectrum.
Xi
=
A Z Wioi
=
=
2,. . . 5
(9)
l./2ci
This alternative representation slightly degrades the performance of supervised classification (no more than 5 % loss), but since the purpose of this study was to develop a method for optimum use of variables, such a loss was considered tolerable. Figure 1 shows a two-dimensional representation of the tendimensional space, using the original data. RESULTS AND CONCLUSIONS
The ten-dimensional space was reduced to three dimensions by the above-mentioned transformation. Figure 2 shows a two-dimensional representation of the new pattern space. Clearly some of the overlap between classes has been eliminated. Since the data do not appear to be linearly separable, the k-nearest neighbor classification (3) was used for evaluation of the transformation. Table I gives a comparison of the ten- and three-dimensional k-nearest neighbor classification. For this study k = 1 and k = 3 classifications were made. The results are most encouraging for two reasons; first, the performance of the classifier was greatly enhanced (at least 9 higher) and, second, a great reduction in the number of variables has been attained. The latter feature may have many implications for designing spectral information retrieval systems. Although the example given here concerns mass spectra, the same technique has proved useful in numerous other pattern recognition applications in our Laboratory.
(8)
(10) B. R. Kowalski and C. F. Bender, J. Amer. Chem. SOC.,94, 5632 (1972).
RECEIVED for review June 12, 1972. Accepted November 10, 1972. Work performed under the auspices of the US.Atomic Energy Commission.
Microdetermination of Volat iIe 0rganics by Galvanic Coulometry Alphonso Anusieml and Paul A. Hersch Laboratory for Biophysical Chemistry, Department of Chemistry, Uniwrsity of Minnesota, Minneapolis, Minn. 55455 MOST ORGANIC GASES and vapors carried by a n inert gas stream can be determined by adding a constant proportion of oxygen to the stream, passing the stream through a hot tube for complete combustion, and determining the oxygen left over in the effluent. The galvanic-coulometric monitor for traces of oxygen described by one of us ( I , 2 ) can be put 1 present address, chemistry Department, University of Ibadan, Nigeria.
(1) P. A. Hersch in “Advances in Analytical Chemistry and Instrumentation,” C. N. Reilley, Ed., Vol. 111, Interscience, New York, N.Y., 1964, p 183.
(2) P. A. Hersch in “Lectures on Gas Chromatography 1966,” L. R , Mattick and H, A, Szymanski, Ed., plenum press, N~~ York, N.Y., 1967, p 149. 592
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ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
to use advantageously in this context. This contribution shall show how the principle can be extended to hydrocarbons and other slightly soluble species in an aqueous sample. The gas train we used comprised: (1) a cylinder of nitrogen, not necessarily highest purity grade; (2) a strong capillary flow restrictor as a flow stabilizer; (3) a gas wash bottle with water for humidification; (4) a n electrolytic source for oxygen; ( 5 ) a bubbler with a septum to receive sample from a syringe; (6) a combustion chamber housing a heatable refractory; ( 7 ) a galvanic-coulometric sensor for oxygen; and (8) a flowmeter (see Figure 1). The electrolyte in (4) is aqueous KOH (e.g. 5 N ) ; the anode is a thin wire of nickel held vertically and barely touching the surface of the electrolyte; the cathode is of cadmium-impregnated porous nickel carried by nickel screen, as used in alkaline storage batteries. The electrolyte is powered by
a dry cell (9 V or more) with a resistor in series. Microscopic bubbles of oxygen leave the anode tip in rapid succession creating a smooth oxygen background. The cathode reaction is Cd(OH)2 + Cd and no hydrogen is evolved. The electrolyte level stays constant since the nitrogen entering the electrolyzer is prehumidified. Without the humidifier, loss of water by evaporation would cause eventual loss G f contact of the solution with the anode wire. combustion takes place on the outer surface of a quadruple bore ceramic tube, available commercially for sheathing thermocouples. The tube is held vertically and axially in a quartz envelope carrying in its center a gas inlet and close to the ends two gas outlets (Figure 2). Platinum wire zigzags through the bores of the ceramic tube. Each end of the wire is crimped around a 1.5-mm diameter short length of nickel-chromium rod which in turn contacts copper leads. An autotransformer supplies current to bring the ceramic to bright-red heat. The gaps between the ceramic and quartz are taken up by asbestos wool impregnated in situ with molten tin to ensure gas-tightness. As a further precaution to avoid entirely any ingress of atmospheric oxygen, the nitrogen from the exit of the gas train is directed over the upper asbestos seal keeping air away. The lower asbestos seal (two layers with tin in between) is shrouded in an extra bulb of quartz fused onto the main body of the envelope after the seal has been positioned. This configuration ensures that the gas mixture entering hits the hottest part of the chamber first rather than having to traverse a zone of intermediate temperatures as in conventional tube furnaces. Premature pyrolysis and incomplete combustion, which can cause delay and losses of signal, are thus avoided. Starting up from the cold, the furnace heats up to operating temperature within a few minutes. The oxygen sensor is attached to a four-way double bore stopcock permitting by-passing of the cell during start-up and instant insertion when the train is ready to receive a sample. The sensor is of the type graphite/immobilized aqueous KOH/Cd. The junctions between the various parts of the train are made of Tygon (Norton Co.) (polyvinylchloride) sleeves. Oxygen permeating fI om the atmosphere through the sleeves adds slightly to the base line but this is irrelevant since no noise is created. Conversely, plasticizer vapor given off by the sleeves might slightly lower the oxygen base line of the furnace effluent without, however, causing noise. The junctions to the furnace, which undergo fluctuations of temperature. are ground cones and sockets. OPERATION
The sensor terminals are bridged by a resistor ( R = a few 3hms) in parallel with a potentiometric recorder (full scale leflection E , , , = 1, 2, 5 or 10 mV). The current range Y,,,,/R is adjusted to 0.2, 0.5, 1, or 2 mA, according to need. The gas flow is set to about 30 cc/min and should remain :onstant. A background level of galvanic output, io, estabishes itself dependent on the level of trace oxygen and comiustible impurities in the cylinder gas and the minor ingress of &nospheric oxygen through fittings. For calibration, an .lectrolytic input I is applied to the electrolyzer, raising the :alvanic output to i. The ratio 17 = (i - io)/Zis the coulombic ield of the cell. A typical example is io, = 25 PA, I = 500 LA,i = 488 PA, therefore 7 = (488 - 25)/500 = 0.926. A ield as close to unity as this is stable and virtually indepenLent of the ambient temperature. Such fluctuations of yield
,‘%
I 7
N
Figure 1. Gas train 2 Flow restrictor 3 Humidifier 4 Electrolytic source of O 2 5 Sample receiver 7 Four way valve for the galvanic sensor of O 2
Figure 2. Combustion unit as may occur are in general only a minor source of error and recalibration is needed only infrequently. After calibration the furnace is brought up to bright red heat and a suitable oxygen level is established by sending through the electrolyzer an input current J , resulting in a baseline leveljl = j , 11 J . The “hot background” j , is as a rule smaller than the “cold background” io owing to combustible impurities in the gas stream. Upon injection of sample into the receiver tube ( 5 ) , the recorder trace dips to a minimum to return to its initial level within a few minutes. The current time integral of the “valley” is proportional to the weight, w microgram, of the organic in the sample. For a compound of molecular weight M with x, y , and z atoms of C, H, and 0, respectively, Faraday’s law requires
+
JIo [il
- i(t)ldt = 1.608 X lo6 x 1)
n M
x
x w milliampere-minutes
+
where n = 4x y - 2 z , a stoichiometric factor stemming from the assumptions that the products of combustion are COz, H20, and Nz. For compounds containing C1 (--+HCI), ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
593
Table I. Determination of Nitrosobenzene in 10-15 pl of Water C6H;N0 found, Relative error, C,H5N0 taken, 100 x (w - Wl)/Wl w , Pg w1, 0.542 0.0 0.542 1.059 -2.3 1.084 3.145 -3.3 3.251 4.327 -0.2 4.334 5.389 -0.5 5.418 5.890 +1.9 5.779 7.192 -0.4 7.224
C,H,NO
g i l d by welght
Figure 3. Identity plot (Data obtained
cs.
expected)
S (+SOz?) and the other elements, the stoichiometric factor can be obtained from the above equation if their w and M a r e known. The n so obtained can then be applied to samples containing the same compound in unknown concentration. It is also possible to confirm or disprove assumptions about the elemental composition of a pure compound by determining the ratio n / M from the above equation and comparing the ratio with the theoretical n / M from the hypothesis. A correction is usually necessary to account for oxygen dissolved in the sample. For a sample in equilibrium with ambient air, the quantity
A
=
0.0787 7 X
01
X (P - pw)
x
c mA min
must be added to the integral. cy is the Bunsen coefficient of solubility (volumes Or STP in 1 volume water under PO? = 760 torr), P is the barometric pressure (torr), prc the vapor pressure of water, and L! the sample volume (cm3). At 22 "C (cy = 0.0301, p w = 19.8) and P = 760 torr, with 77 = 0.92, and L' = 0.01 cm3, the correction A is 0.016 mA min. In determining solubilities in water as high as that of benzene (0.654 equivalentl in terms of oxygen demand for combustion) the presence of dissolved oxygen under air (jO.001 equivalent/l.) is barely significant. If the sample contains a nonvolatile impurity or admixture this is of course retained in the receiving vessel (5). With a n appropriate absorbent or reagent in that vessel (e.g., H2S04,KOH, NaHS03, K M n 0 4 , or CrOJ reactive volatiles may be removed while the inert volatiles are being processed. Solutions of HgS04/H2S04 or AgzS04/H2S04absorb unsaturated hydrocarbons selectively permitting their separation from the lower paraffins (3). RESULTS
Table I and Figure 3 show the results obtained with recrystallized nitrosobenzene. Stock solutions were prepared by dissolving weighed amounts of this substance in known volumes of water, sufficient for complete dissolution. The water had been purified in a Millipore system. Samples, 10 or 15 p l , were taken from dilutions of the stock solutions, (3) V. G. Berezkin, "Analytical Reaction Gas Chromatography," Plenum Press. New York, N.Y., 1968, p 77.
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Table 11. Solubility in Water of Three Aromatic Compounds (gram/liter) McAuliffe (1966; by This work, flame ionization) 22 i 1 "C 25 i- 1.5 "C Benzene 1.702 i 0.011 1.780 i 0.045 0.527 3~ 0.013 0.515 =k 0.017 Toluene ... Nitrosobenzene 0.930 i 0.014 made, and used within 24 hours. Older solutions that had turned from green to yellow gave more scatter. Integration was carried out manually by polygonization. Each point in Table I represents the average of three runs, usually reproducible within + 2 %. The solubility of benzene, toluene, and nitrosobenzene in water (Table 11) was determined similarly, using solutions saturated at 22 i 1 "C. The data on benzene and toluene agree with those of McAuliffe ( 4 ) and with the older literature surveyed by this author. The figure for benzene also agrees well with the result of Taha et al. (5), who found 1.72 g/l. a t 25 "C, but disagrees with Worley (6) (2.17 g/l. a t 25 "C) and with Eisenbrand and Baumann (7) (1.31 g11. at 20 "C). CONCLUSION
The experiments confirm that combustion of trace organics followed by galvanic coulometry of the residual oxygen yields accurate analyses in the microgram range with only modest demands on time, training, and equipment. The range can probably be extended to much smaller quantities, given electronic amplification of the signal, before limitations by various types of noise are encountered. The ultimate sensitivity of the method should much exceed that of flame ionization. In FI only one in about lo5 carbon atoms contributes to the signal. Coulometry utilizes every carbon and hydrogen atom combusted. The principle should be applicable to effluent analysis in both gas and liquid chromatography and to many microanalytical requirements of organic and biological chemistry. RECEIVED for review July 3,1972. Accepted October 30, 1972. Work supported by Grant No, HL13109 from the National Institutes of Health. This is paper No. 79 from this Laboratory. Please request reprint by number. (4) C. McAuliffe, J. Phys. Clzem., 70, 1267 (1966). (5) A. A. Taha, R. D. Grigsby, J. R. Johnson, S. D. Christian, and H. E. Affsprung, J . Clzem. Educ., 43,432 (1966). (6) J. D . Worley, Can. J. Cliern., 45, 2465 (1967). (7) J. Eisenbrand and K. Baumann, Z . Lebensm.- Unters.-Forsck., 140, 210 (1969).
