Sample Serum Urine
Table 11. Precision of Duplicate Measurements of Serum and Urine Chromium Chromium concentrations, pg Cr per 100 ml N ~ of, Std dev of samples Range Mean duplicate analyses 20 4-124 44.7 h3.0 20 4-196 36.5 k2.9
the regression line (m)was 0.901 with a standard error of estimate (S) of 8.2 pg per 100 ml and a correlation coefficient (R)of 0.963. A similar comparison of 8 urine samples was made giving m = 1.043, S = 5.8 pg per 100 ml, and R = 0.923. Gas chromatography offers a potential advantage of greater sensitivity over atomic absorption. In the present study, the limit of sensitivity for the detection of chromium was 0.03 picogram injected onto the column of the gas chromatograph. This amount, which gave a peak height of 5 % above the base line, is equivalent to 0,001 pg of chromium per 100 ml of final benzene solution. In comparison, according to Feldman and Purdy (23) the limit of sensitivity of atomic absorption is 0.6 pg of chromium per 100 ml in methyl isobutyl ketone solution. In order to validate the method further, an experiment was carried out in which 4 rabbits were injected subcutaneously with 200 mg of chromium as an aqueous solution of Na2Cr207. Two control rabbits, not treated with Na2Cr2O7were also used in this study. Blood was obtained from all rabbits at regular intervals and all urine was collected. Chromium determinations were performed on all samples in duplicate. The serum chromium level of 4 pg per 100 ml prior to treatment rose to 43 pg per 100 ml immediately following the injection and gradu-
(23) F. J. Feldman and W. C . Purdy, Anal. Chim. Acta, 33, 273 (1965).
Rel. std. dev., 6.7 7.9
ally fell to 12 pg per 100 ml after four days. The total chromium excreted in the urine was 300 pg per 24 hours during the first day and dropped to 102,47, and 10 pg per 24 hours during the second, third, and fourth days, respectively. The chromium values determined in this experiment included both chromium(V1) and chromium(III), since the method included treatment of the acid digest with sodium sulfite to quantitatively convert all chromium(V1) to chromium(II1). The reproducibility of the method was evaluated by performing duplicate analyses on the serum and urine samples and this precision is summarized in Table 11. ACKNOWLEDGMENT
The assistance of W. Mertz and J. T. Piechocki in performing the atomic absorption measurements, and the technical assistance of D. S . Lindberg and L. G. Schrader is acknowledged and appreciated. RECEIVED for review August 1,1969. Accepted November 24, 1969. Supported by U. S. Atomic Energy Commission Grant AT-(404-3461, American Cancer Society Grant E374B, American Cancer Society Institutional Grant ACS-IN62H, and by Public Health Service Research Grant (National Cancer Institute) CA-98783-02.
Determination of Relative Rates by Differential Thermal Analysis 1,ynn J. Taylor and Sandra W. Watson Okemos Research Laboratory, Owens-Illinois, Inc., Okemos, Mich. 48864
PREVIOUS STUDIES (1-4) have demonstrated that differential thermal analysis (DTA) can be employed for the determination of rate constants and activation energies. We report an extension of these methods which makes it possible to determine the relative rates of reaction of different reactive compositions under comparable conditions. According to the treatment of Borchardt and Daniels ( I ) , the expression for the reaction rate corresponding to a point on the DTA thermogram is
( 1 ) H. J. Borchardt and F. Daniels, J. Am. Chem. Soc., 79, 41
(1957).
(2) H. J. Borchardt, J. Inorg. Nucl. Chem., 12, 252 (1960). (3) G. 0. Pilovan. I. D. Ryabchikov, and 0. S. Novikova. Nature.
212, 1229 (i966).
(4) A. V. Santoro, E. J. Barrett. and H. W. Hoyer, J. Am. Chem. Soc.. 89, 4545 (1967).
where n is the number of moles of reactant present at time t , no is the number of moles of reactant initially present, K is a heat-transfer coefficient characteristic of the apparatus, A is the total area under the curve, C, is the sample heat capacity, and AT is the differential temperature. At this point, the quantity of reactant remaining is
where a is the area swept out by the curve between the start of the reaction and time t . Ordinarily, the first term within the brackets in Equation 1 is much smaller than the second ( I , 2 ) ; we have been able to verify this by examination of experimental data obtained from an epoxy-amine reaction. If we neglect the first term, Equation l reduces to
_ -dn_ -_ _noAT dt
A
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Table I. Measured Activation Energies and Relative Rates Reactions of Aromatic Amines and Epoxy Resin E, Relative rate Amine (Kcal./Mole) at 150 “C rn-Phenylenediamine 23.6 1.48 Benzidine 23.4 1.11 4,4’-Methylenedianiline 22.9 1 .oo 4,4’-Sulfonyldianiline 13.7 0.16 4,4’-Methylenebis 13.0 0.125 (2-chloroaniline)
AT
I
II
A
Table 11. Measured Reactivity of rn-Phenylenediamine, Relative to That of 4,4’-Methylenedianiline, in Reactions with Epoxy Resin at 150 “C Heating rate (Tjmin.) a/A Relative rate
7
12
TEMPERATURE
10 10 10
(ORTIME)
20 20 20
Figure 1. Typical DTA curves, showing quantities measured a = shaded area; A = total area under curve. TI may be selected arbitrarily. T z is the corresponding temperature, at which the a / A ratio is equal to that at TI
Application of Equation 3 to data obtained at early stages of the reaction yields a direct measurement of the initial reaction rate (2). In order to compare the rates of two similar reactions, X and Y,DTA curves for the two reactions are obtained under identical conditions (same heating rate, etc.). From each curve, a point early in the reaction is selected; it is convenient to select corresponding points from the two curves, such that the area ratio a / A is small and equal in the two cases (see Figure 1). If we denote by ATx the measured differential temperature obtained from the curve of X a n d by ATy the measured differential temperature at a corresponding point of the curve of Y,application of Equation 1 gives Ax AY
(4)
where the derivatives are initial reaction rates and the subscripts 1 and 2 are added to indicate that the reaction rates and differential temperatures apply to different sample temperatures (TI for reaction X , and TZfor reaction Y ) . The activation energy for one of the reactions (Y)is now measured by the method of Piloyan et al. (3, 4 ) ; the activation energy obtained can be used to calculate the initial rate of reaction Y which would be observed at temperature T I , provided the effect of temperature changes on sample volume (or concentration) can be neglected.
Substitution of Equation 5 into 4 gives /dnv\
0.16
0.19 0.22 0.05 0.16
0.22
1.54 1.40 1.47 1.41 1.51 1.48
rather than initial reaction rates. In that event we are not necessarily restricted to the early stages of the reaction, but one must assume that the two reactions obey rate expressions of the same form. In such cases it is possible to derive an equation corresponding to Equation 6 in which a ratio of rate constants replaces the ratio of initial rates. EXPERIMENTAL Apparatus. All measurements were performed in the “DSC Cell” of the DuPont 900 Differential Thermal Analyzer. The sample was in the form of a thin coating on the bottom on an aluminum sample pan; the Borchardt-Daniels assumption ( I ) that thermal gradients within the sample are negligible should be valid under these experimental conditions. Reagents. A purified grade of the diglycidyl ether of Bisphenol A (Dow Epoxy Resin D.E.R. 332LC) was employed without further purification. Aromatic amines were purified by recrystallization. Procedure. Equivalent quantities of the epoxy resin and amine were employed; it was assumed that each primary amino group would react with two epoxide groups. The reactants were dissolved in a volatile solvent (methylene chloride); an aliquot of the solution was transferred to the sample holder and the solvent removed in vacuo. The resulting solvent-free reaction mixture was then subjected to differential thermal analysis in a nitrogen atmosphere with an empty sample pan as reference. Analyses were performed with the sample and reference pans reversed, to obtain a record in which the horizontal (temperature) axis was linear in time. From one experimental curve (reaction X ) a point (TI)was selected, such that the a / A ratio was between 0.05 and 0.25. The actual a / A ratio was then determined with the aid of a planimeter. From another experimental curve (reaction Y ) the corresponding point (TJ having the same a / A ratio was determined by trial and error. The relative rates were then calculated from Equation 6. Activation energies were determined by the Piloyan method (3) using data obtained at high heating rates (20-30 ‘Cjmin.) in separate experiments. RESULTS AND DISCUSSION
In the case of reactions occurring in solution, the foregoing treatment can be re-formulated in terms of rate constants 298
Measured activation energies and relative rates are recorded in Table I. Each relative rate is an average of at least five determinations at different a / A ratios and/or different heating rates.
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Measured rate ratios are insensitive to the choice of heating rate and a / A ratio, as the data of Table I1 demonstrate. Changes in the a / A ratio or heating rate will lead to changes in the temperature (TI) at which the relative rates are determined. All results can be corrected to the same temperature, provided the activation energies of all reactions have been measured. In the present instance, such corrections led to changes of 1 or less in measured rate ratios. The method outlined here involves a number of assumptions and approximations, including the assumptions enumer-
x
ated by Borchardt and Daniels ( I ) . Since we are determining ratios of reaction rates, however, errors arising from uncertainties in the individual reaction rates will tend to offset one another. The method might not give reliable results in cases where substantial thermal gradients can arise within the sample (reactions occurring in packed powders, large unstirred samples, etc.). RECEIVED for review August 15, 1969. Accepted November 17,1969.
Coulometric Titration of Amines in Chloroform Solution Peter Wuelfing, Jr., Edward A. Fitzgerald, Jr., and Herbert H. Richtol Department of Chemistry, RensseLaer Polytechnic Institute, Troy, N . Y. 12181
MANYorganic solvents have been explored as electrochemical solvents. Among these are acetonitrile, acetic acid, ethanol, dimethylformanide, etc. Chloroform, a powerful organic solvent, has found little application in electroanalytical problems mainly because of its poor electrical properties. Chloroform has served as a solvent or part of a solvent mixture in acid-base titrations ( I ) . Fritz (2) titrated aniline in chloroform with perchloric acid in acetic acid as titrant and methyl violet as indicator. The same titration was followed by means of a glass indicator electrode and a silver wire coated with a thin layer of silver chloride as reference electrode. We have found that solutions of quaternary ammonium salts in chloroform provide a medium with sufficiently low resistance to make some electroanalytical applications feasible. One area where this particular solvent system can find potential use is in one-electron oxidation processes associated with radical cations. Biphenyl radical anions (3) have successfully been employed as coulometric titrants of reducible organic compounds. The oxidation of the species dissolved in the chloroform is accomplished by the coulometric generation of bromine from tetraethylammoniumbromide (TEAB). At low conversion rates, it is possible to measure the absorptivity of the highly colored radical cations generated in the reaction. In some of the cases this coulometric technique is the only method available for determining this quantity. Coulometric titrations were also attempted, employing potentiometric and spectrophotometric end points, with the results being less precise than the absorptivity measurements. An advantage of this system is that amine radical cations are quite stable in chloroform, and water only slowly bleaches their intense color. Thus, no extra special precautions have to be taken. Some aspects of the results in chloroform are compared to those in 90% glacial acetic acid. EXPERIMENTAL Chemicals. Diphenylparaphenylenediamine (DPPD), tetramethylparaphenylenediamine (TMPD), parahydroxy(1) G. A. Harlow and D. H. Morman, ANAL.CHEM.,38, 485R
(1966).
(2) J. S. Fritz, ibid.,22, 1028 (1950). (3) D. L. Maricle, ibid., 35, 683 (1963).
diphenylamine (HDPA), tetraphenylparaphenylenediamine (TPPD), and dimethyldiphenylparaphenylenediamine (DMDPPD) were obtained commercially and recrystallized at least three times and treated with decolorizing carbon prior to use. Fisher Reagent-Grade chloroform was washed several times with concentrated sulfuric acid, then with dilute sodium hydroxide solution, then ice water, dried over sodium carbonate, stored in a completely filled brown bottle, and distilled shortly before use (4). Baker and Adamson glacial acetic acid was heated with chromium trioxide (1-2 by weight) and then distilled. Baker grade tetraethylammonium bromide (TEAB) was washed with reagent grade acetone. Fisher Reagent Grade sodium bromide was used directly. Apparatus. A Beckman DK-2A recording spectrophotometer was used to qualitatively record ultraviolet and visible spectra. Absorbance measurements were made on a Beckman D U spectrophotometer. The electrochemical cell consisted of a beaker into which two platinum electrodes were placed. The anode, a foil 2 x 2.25 cm, was open to the bulk solution. The cathode, a spiral wire 2 cm long X 0.25 cm diameter, was enclosed in a glass compartment making contact with the solution in a second glass compartment through a fine porosity frit which in turn made contact with the bulk solution through a second frit. The solution in the larger compartment between the two frits was the same as the bulk solution, 0.5M TEAB in chloroform. The solution in the inner compartment was 0.2MHCl in water to ensure that the resistance of the cell was low enough to allow proper operation of the current source, which was the Sargent Model IV coulometric current source. Resistance measurements were made with an Industrial Instrument Conductivity Bridge, Model RC 16B2. Absorptivity Determinations-Chloroform. A sample of amine, representing a great excess of the amount to be oxidized to the radical-cation, was dissolved in 100 ml of 0.1M TEAB in chloroform. A specified number of microequivalents of current were passed through the stirred solution. A 3-ml aliquot was removed by pipet and the absorbance measured cs. a blank consisting of unreacted solution. This experiment was repeated on fresh solutions for various microequivalent conversions and a Beer’s law plot of absorbance m. concentration was obtained for the various radical-cations. The total conversion to radical-cation was less than 1 % in all cases. (4) K. B. Wiberg, “Laboratory Techniques in Organic Chemistry,” McGraw-Hill, New York, N. Y., 1960, p 250.
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