The ordinate of the frequency distribution is obtained by substitution of Equations 5 and 7 into 4:
The beta distribution least squares fit to the cumulative distribution is given in Figure 1. The frequency distribution represented by Equation 10 is given in Figure 2. As a means of checking the procedure used in fitting the density distribution, the average density, 6, is calculated. Only the total volume, V , of the particles must be calculated from the frequency distribution since the total weight, W , was obtained experimentally: V
=
L"""du
It is assumed that an infinitesimal interval change in the volume is given as : dw du = d The right hand side of Equation 12 may be obtained by equating the right hand sides of Equation 10 and Equation 4. Then the relationship in Equation 7 is used. The final result is written 1 zP-1(1 - z)B-l %nsX dz du = z(dmax - d r a i n ) dmin
s,
"s,
+
(13)
This equation was solved with the aid of the 16 point Gaussian quadrature formula ( 5 , 9 ) . To check the values of the shape parameters, p and q, as obtained from least squares fitting of the experimental cumulative density distribution to the cumulative beta distribution, the values of p and q were changed by & 1%, i5 %, and =klOx, The average density was recalculated with the new values of p and q. With a change of + 1 % in p and q the calculated density remained unchanged. All calculations were performed on an IBM S/360, Model 44 computer. Double precision (16 significant figures) was used and was necessary for the evaluation of the beta function, the least squares procedure, and the evaluation of the integral in Equation 13. The pertinent data for two independent determinations on the same lot of glass beads are given in Table 111. From the results summarized in Table 111, it is clear that the least squares cumulative and frequency distributions, when used to calculate a mean density of the glass beads, give results in good agreement with the pycnometer results. The error in the calculated mean densities is comparable to that expected when densities are determined by Equation 1. Also, examination of Figure 1 indicates rather good agreement between the calculated and experimental distributions. Comparison of the results for the two independent determinations indicates good agreement between these two sets of measurements. RECEIVED for review July 15, 1969. Accepted August 21, 1969. The U. S. Atomic Energy Commission, Health and Safety Laboratory provided a fellowship for one of the authors (G.H.F.) and partially supported the research. This work is taken in part from the Ph.D. research of Gordon H. Fricke.
Vapor Pressure Determination by Differential Thermal Analysis Herbert R. Kemmel and Saul I. Kreps Department of Chemical Engineering and Chemistry, Newark ColIege of Engineering, 323 High Street, Newark, N . J. 07102
DIFFERENTIAL THERMAL ANALYSIS (DTA) equipment for the determination of normal boiling points has been described by Vassalo and Harden ( I ) , Chiu (2)) and Kemme (3). The extension of these techniques to determine the temperaturevapor pressure function for pure liquids has been described by Krawetz and Tovrog (4, and Barrall, Porter, and Johnson (5). The latter workers reported measurement of vapor pressure between 30 and 760 Torr, and claimed an accuracy of 1 0 . 2 "C. The use of commercially available DTA equipment involves several modifications in hardware and special attention to operating techniques if the fullest capabilities of the method in time and material economy and precision are to be realized. Present address, American Cyanamid Company, Bound Brook, N. J. (1) D. A. Vassalo and J. C. Harden, ANAL.CHEM., 35, 132 (1962). (2) J. Chiu, ibid., 27, 1102 (1955). (3) H. R. Kernme, M. S. Thesis, Newark College of Engineering, 1963. (4) A. A. Krawetz and T. Tovrog, Rec. Sci. Instrum., 35, 1465 f 1962). ( 5 f - E - M . Barrall, E. S. Porter, and J. Johnson, ANAL.CHEM., 37, 1053 (1965).
DIFFERENTIAL THERMAL ANALYSIS EQUIPMENT
The DuPont 900 DTA instrument was the basic equipment used. This instrument has been previously described ( I ) . Thermocouple Circuits. The thermocouple circuits originally supplied use gold-plated brass feed-through plugs to connect the thermocouples to circuitry. Spurious potentials amounting to 1 0 . 4 mV are caused by temperature variations in the vicinity of the plugs. They were eliminated by installing a separate Chromel-Alumel, shielded extension line to the ice reference junction, connected through a ChromelAlumel plug. The use of a single bath for the ice point reference for both the furnace control and temperature measuring circuits produced interactions amounting to hO.02 mV. Separate ice baths eliminated this source of error. Potentiometer and Recording System Modifications. The manufacturer supplies an X-Y recorder with maximum sensitivity to the sample temperature signal from ChromelAlumel thermocouples of 0.4 mV per inch, equivalent to 0.01 inch per 0.1 "C. Determination of sample temperature to within 0.1 "C was impossible without modification. To achieve this discrimination, a Leeds & Northrup K-3 potentiometer and 2430-D galvanometer was connected in parallel with the recorder circuit (Figure 1). The X-Y
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Shleldea Chrornei-Aldrnel E x t c n s ' o n Cab!e
Moni Old
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1 I
I I I I
Zimmerli
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I I
Prcarrp I
I I
Ice Reference I
m Manoe
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Sample Block
I I 1
Cold Trop Mercury Trap Mono S t a t F ' i 1 t e r -Trap
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Aux 1 1 tory vocuurp Pump
Figure 1. Circuit diagram of DTA system
recorder was used primarily as an indicator of boiling and sample purity; the K-3 potentiometer was switched into the system and was balanced as isothermal boiling occurred. This gave EMF readings accurate to 0.001 mV (10.025 "C) between -40' and 320 OC. Pressure Control System. Figure 2 is a schematic of the pressure control and indicating system. Flexible connections between piping, the glass manifold, and the system components were made with Tygon tubing fitted with metal band clamps and sealed with low vapor pressure silicone-based pipe dope. Disconnects were O-ring sealed, semi-ball ground glass joints. A high capacity pump was used to hold the system pressure constant in spite of any minor leakage, and a small roughing pump operated directly on the sample chamber to avoid upsetting the vacuum control system. A relatively large surge tank served as ballast to smooth out the operation of the Cartesian manostat pressure controller. Pressure measurements in the range of 5 to 100 Torr were made by a precision Zimmerli gauge (10.05 Torr) connected directly to the sample chamber to avoid a pressure drop between the chamber and the manifold which amounted to 0.15 Torr. This pressure drop was insignificant above 50 Torr. The accuracy of the Zimmerli gauge was checked against a mercurial barometer which was used to measure pressures from 100 to 760 Torr; it has an accuracy of k0.033Z of the full scale range and a sensitivity of 10.004 Z , SAMPLE PREPARATION
Each sample was placed in a 4-mm diameter glass tube which was inserted in the aluminum heating block. A calibrated Chromel-Alumel thermocouple was then inserted in the sample. The boiling point is measured at the thermocouple junction, and at this point it is essential that superheating be avoided, that there be a negligible pressure change, that the correct rate of heat input be provided, and that the quantity of sample shall be sufficient to achieve dynamic equilibrium between liquid and vapor. Samples used ranged from 4 to 12 pl of compound, mixed with 40 mg of 100-p diameter borosilicate glass beads. This produced a dry mixture in which the liquid is distributed over the bead surfaces but does not fill the interparticle voids. The beads provide nucleation sites for boiling and minimize liquid head. A roughly equal mass of glass beads was used as the inert reference material. The effect of the curvature of the beads on the boiling point is negligible. The shape of the boiling endotherm depends on sample size. If insufficient sample is taken, the endotherm has a gentle downgrade slope (Figure 3a) and often a slight backward slope 1870
Figure 2. DTA vapor pressure system
SAMPLE
TEMPERATURE
Figure 3. Effect of sample size
at the bottom which indicates that the sample is superheated. The maximum endothermic temperature may be several degrees below the true boiling point. Too large a sample may result in superheating as much as 10 "C above the true boiling point, evidenced by a large, curving endotherm trace (Figure 36). The true boiling endotherm (Figure 3c) breaks sharply and is vertical from that point until recovery commences. Optimum sample size depends to some extent on the required latent heat; at low pressures the latent heat of most liquids increases and smaller samples may give a satisfactory trace. It was necessary to modify the sample thermocouple to prevent a pressure drop during the boiling period at pressures below 50 Torr. The ceramic spacer on thermocouples supplied by the manufacturer serves to insulate the leads and to center them in the sample. However, at low pressures the mean free path of the vapor approaches the dimension of the annular space through which the vapor must escape. To avoid the pressure drop caused by this resistance, the ceramic insulator was shortened to 1 mm and the thermocouple was centered by a short length of glass tubing, 3 mm 0.d. X 1 mm i.d. X 4 mm, which was placed over the bare leads close to the junction. Vapors escaped freely through the large bore of this sleeve. T o further decrease the possibility of a pressure buildup, the size of the glass dome housing the sample furnace was doubled, and the vacuum exhaust line was increased to 6 mm i.d.
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Sample Purity. A pure sample is of the utmost importance for determination of vapor pressure, and DTA provides a powerful tool for judging the purity of samples used. In general, the method described here requires samples of greater than 99.5 mole per cent purity to produce a constant boiling point. The DTA endotherm reveals several kinds of departure from requisite purity : some fractionation occurs in the sample and both more and less volatile impurities are revealed by changes in the slope of the endotherm trace. When the amount of impurity is large, there is a continuous increase in the sample temperature as it vaporizes; should there be several impurities, the trace is characterized by a number of vertical segments. While this method does not indicate the amount of impurities present, it can reveal whether the sample is sufficiently pure for physical property determinations. A pure sample shows less than 0.1 "C variation in the vertical endotherm trace ; this temperature variation is equal to the sensitivity of the X-Y recorder. THERMOCOUPLE CALIBRATION Thermocouples were calibrated by measuring the EMF produced at the boiling points of a number of pure reference materials whose vapor pressures were accurately known, at 10 " to 20 "C intervals between -40 "C and 305 "C. Table I lists the materials used, their overlapping temperature ranges, an estimate of the data accuracy and the literature reference. All materials were spectroscopically and chromatographically pure, and showed no perceptible boiling range on the DTA. Triplicate determinations were made at each point, and the mean values of the EMF was correlated with the known boiling point of each material studied. The differences between the observed EMF values and the E M F calculated by assuming a linear temperature response of 0.04 mV/"C are markedly nonlinear and irregular. Calibration at the customary 100 "C-intervals would not reveal the irregularities in the calibration curve. HEATING RATE The effect of the heating rate on the boiling point was investigated by determining the boiling point of distilled water at 760 Torr. A temperature difference of 0.1 "C corresponds approximately to 0.004 mV; the data summarized in Table I1 indicate that heating rates between 2 " and 20 "C per minute produce boiling points which lie within this limit. At lower heating rates, equilibrium between heat input and dissipation by rapid evaporation is established without true boiling. In practice, heating rates between 5 " and 15 "C per minute are satisfactory for vapor pressure determinations. EXPERIMENTAL VAPOR PRESSURE PROCEDURE For the pressure range from 5 to 760 Torr, about 15 samples of a single compound are prepared. The total amount of material which will suffice ranges from 60 to 180 p1. Pressures are chosen so that boiling points of successive samples are spaced about 15 "C apart. Samples are cooled about 50 "C below the expected boiling point by inserting the assembled furnace block in powdered dry ice if necessary. The block is positioned in the DTA working chamber which is then evacuated by the small roughing pump to within several Torr of the test pressure, and is finally connected through the manifold to the previously adjusted vacuum system. The temperature of the furnace is programmed to rise at a constant rate while the DTA trace is recorded. At the first
Table I. Calibration Standards
h4aterial n-Pentane n-Hexane Water m-Xylene n-Octanol Benzophenone
Data accuracy
Calibration temp range, "C
Purity mole
Data reference
99 (a) 99 (4 AO.1O 99.9 (6) A0.01" 99 (C) A0.01" 99 (C) &O.0lo 99 (C) F. D. Rossini, "Selected Values of Physical Properties of Hydrocarbons and Related Compounds," Carnegie Press, Pittsburgh, Pa., 1953. * "Handbook of Chemistry and Physics," 40th ed., Chemical Rubber Publishing Company, Cleveland, Ohio, 1958. N. S. Osborne and C. H. Meyers, J. Res. Nut. Bur. Stand., 13, l(1934). *0.1"
*o. 1
-40 to 35 2 to 63 60to90 110to 132 140 to 195 200 to 305
Table 11. Effect of Heating Rate on Observed Boiling Point of Water at 760 Torr Heating rate "C/min 0.5 1 .o
2.0 5.0 10.0
15.0 20.0
Thermocouple EMF, mV 4.0536 4.0698 4.0713 4.0806 4.0819 4.0780 4.0776
Corrected temp, "C 99.32 99.73 99.91 l~.00
100.03 99.93 99.92
indication of an endotherm, the K-3 potentiometer is switched into the circuit, and it is balanced during the constant boiling period indicated by a vertical endotherm trace. The precise EMF is thus obtained from the K-3 potentiometer, and the vapor pressure is read from the appropriate vacuum gauge. A series of runs was usually undertaken by starting at low pressure and temperature. Replicates were run at identical pressure settings to avoid disturbing the main vacuum system between samples. Pressure varied by no more than 0.1 Torr in 90 minutes, while three boiling point measurements at one pressure required no more than 30 to 40 minutes. Precision of Determinations. The boiling point of a single sample of distilled water was determined at 233.9 Torr over a period of 15 months. During this time, the calibrated thermocouple was in constant use with a wide variety of samples, subject to repeated thermal cycling between -60" and 320 "C. The system pressure was reset each time to 233.9 Torr and, based on eight determinations, accuracy and precision of the method are indicated by the following statistics: Temperature range, 0.0053 mV (0.13 "C) including 70 .O "C Standard deviation 1 0 . 0 0 1 8 mV ( 1 0 . 0 0 5 "C) 95 Z Confidence interval * O . 0047 mV ( * O . 01 "C) The capabilities of this technique are illustrated by the results obtained by Kemme and Kreps (6), who applied the method described here to the determination of vapor pressures of 1(6) H. R. Kemme and S. I. Kreps, J . Chem. Eng. Data, 14, 98
(1969).
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chloroalkanes and 1-alkanols over wide temperature and pressure ranges. The results reported there have an accuracy of better than 0.1 “Cfor most of the compounds studied. CONCLUSION
The DTA method of vapor pressure determination provides economy, ease, and speed in manipulation. Only very small amounts of compounds are needed to determine a complete vapor pressure curve between 5 and 760 Torr. The inherent
ability of DTA to indicate impurities or breakdown in a compound under test provides a valuable check on the validity of the vapor pressure determination. RECEIVED for review August 17, 1967. Resubmitted June 9, 1969. Accepted August 19, 1969. H. R. K. was recipient of an NDEA Fellowship grant. This work was also supported by a grant from the Foundation for Advancement of Graduate Study at Newark College of Engineering.
Determination of Mercury in Apples by Spark Source Mass Spectrometry S . S . C . Tong Research and Deceloprnent Laboratories, Corning Glass Works, Corning, N . Y . 14830
W. H. Gutenmann and D. J. Lisk Pesticide Residue Laboratory, Cornell University, Ithaca, N . Y . 14850 MERCURY COMPOUNDS have long been used in agriculture as effective agents for control of fungus diseases of plants. Owing to the continued use of these toxic systemic fungicides, sensitive analytical methods are required for determining traces of mercury in food commodities. Several methods have been applied to determination of mercury in biological material following sample ashing. These include spectrophotometric determination of mercury as the dithizonate ( I , 2), determination of mercury with a mercury vapor meter ( 3 - 3 , and determination of mercury using microelectrolysis (6), atomic absorption (7-9), and neutron activation analysis (10-12). Specific analysis for intact organic mercury compounds in food has also been accomplished by a combination of thinlayer and gas chromatographic methods (13, 14). Spark source mass spectrometry is a sensitive method for the determination of many elements. It has been applied to determination of elements other than mercury in biological samples to only a very limited extent (15, 16). In the present work, determination of mercury in apples is performed by Schoniger combustion of the sample and analysis by spark source mass spectrometry. (1) “Official Methods of Analysis,” 8th Ed., Assoc. Offic. Agr. Chemists, Washington, D. C., 1955, p 441. (2) W. H. Gutenmann and D. J. Lisk, J. Agr. Food Chem., 8, 306 (1960). (3) 0. Lindstrom, ANAL.CHEM., 31, 461 (1959). (4) M. B. Jacobs, S. Yamaguchi, L. J. Goldwater, and H. Gilbert, Am. Ind. Hyg. Assoc. J., 21, 475 (1960). (5) M. M. Schachter, J. Assoc. Ofic.Agr. Chem., 49,778 (1966). (6) D. Pavlovic and S. Asperger, ANAL.CHEM.,31, 939 (1959). (7) W. R. Hatch and W. L. Ott, ibid., 40, 2085 (1968). (8) E. G. Pappas and L. A. Rosenberg, J. Assoc. Ofic.Agr. Chem., 49. 782 (1966). (9) Ibid., p 792.. (10) B. Siostrand. ANAL.CHEM., 36, 814 (1964). (11) M. Szkolnik; K. D. Hickey, E: J. Broderick, and D. J. Lisk, Plant Disease Reporter, 49, 568 (1965). (12) C. K. Kim and J. Silverman, ANAL.CHEM.,37, 1616 (1965). (13) G. Westoo, Acta Chem. Scand., 20, 2131 (1966). (14) Ibid., 21, 1790 (1967). 40, 869 (15) C. A. Evans, Jr., and G. H. Morrison, ANAL.CHEM., (1968). (16) W. A. Wolstenholme, Nature, 203, 1284 (1964). 1872
EXPERIMENTAL Sample Combustion. Several apples were thoroughly chopped using a Hobart food cutter and blended to obtain a representative sample. A 10-gram portion of each sample was combusted according to the procedure previously described (2) except that the total volume of absorbing solution (0.1Nhydrochloric acid) was 50 ml. One-tenth milliliter of a silver nitrate solution (50 Fg silver per ml) was added as an internal standard to the absorbing solution. Extraction of Mercury. Ten milliliters of the absorbing solution was transferred to a 60-ml separatory funnel. The following solutions were, in turn, added to the funnel: 1 ml of 20% hydroxylamine hydrochloride, 0.6 ml of 30% acetic acid, and 1.5 ml of dithizone in chloroform (2 mg per liter). The solutions were shaken vigorously for a minimum of 3 minutes. The chloroform layer was drained off and the aqueous solution was again partitioned with 1 ml of the dithizone solution and finally 1 ml of chloroform. The chloroform solutions were combined in a 5-ml beaker and evaporated slowly to about 1 ml during storage in the dark in a well-ventilated hood. About 15 mg of spectrographically pure graphite powder (SP-1C spectrographic powder, Union Carbide Corp.) was added to the solution, and the remaining chloroform was allowed to evaporate in the hood. Preparation of Electrodes. The graphite powder was transferred to a small vial using a tantalum spatula and was thoroughly mixed using a Wig-L-Bug to ensure even distribution of the sample. The usual method (17, 18) was used for preparation of electrodes. In this procedure the electrode is molded in a polyethylene slug. A hole was made by drilling axially into the slug after freezing it in liquid nitrogen. About half of the graphite powder containing the sample was placed in the hole. The remainder of the hole was filled with pure graphite. The slug was fitted into a steel die and compressed in a hydraulic press at 6000 psi. The pressure was held for 5 minutes and then slowly released. The formed electrode was removed from the slug by gentle
(17) J. W. Guthie, “Mass Spectrometric Analysis of Solids,” A. J. Ahearn, Ed., Elsevier Publishing Co., N. Y. 1966, Section 2c, p 117. (18) R. Brown and W. A. Wolstenholme, A. S. T. M. E-14 Meeting on Mass Spectrometery, San Francisco (1963), Paper No. 75.
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