Estimation of Preexponential Factor from Thermal Decomposition Curve of an Unweighed Sample R. N. Rogers and L. C . Smith University of California, Los Alamos Scient@ Laboratory, P . 0 . Box 1663, Los Alamos, N . M . 87544
A METHOD OF ESTIMATING the activation energy from the differential scanning calorimeter (DSC) or differential thermal analysis (DTA) curve of a small, unweighed sample has been presented (I, 2). We describe here a n equally simple method of estimating the preexponential factor. It is required that the decomposition be first-order in the reactant, but otherwise the result is independent of sample weight, instrument calibration, or heat of reaction, providing the last is sensibly different from zero. The method is based on the following considerations: The deflection of the DSC curve from the base line is given by b = -adm/dt, where b is the deflection, -dmjdt is the rate of decomposition of the sample, and a is the heat of reaction per unit weight of the sample divided by the sensitivity factor of the instrument. If the sample decomposes according t o a first-order rate law, we can write
< '
I
300 *C
Differentiating with respect to time we have
The maximum in the curve occurs when dbjdt = 0. Substituting this in the last result and solving for A we obtain
(3)
Table I. Values of Log A from Different Sources A in sec-l Literature (3) Calcd E, DSC kcal/ from methodb log A mole Compound T,,XO PETN (pentaerythritol tetranitrate) 20.0 19.8 47.0 19.6 RDX (hexahydro-l,3,5-trinitro-s-triazine) 18.2 18.4 18.5 47.5 HMX (octahydro-1,3,5,7tetranitro-1,3,5,7-tetrazo-
cine) 18.9 18.1 19.7 52.7 Tetryl (N-rnethyl-N,2,4,6tetranitroaniline) 15.4 38.4 15.4 Using activation energies from indicated reference and 20" C/ min heating rate. b Using activation energies determined with Perkin-Elmer DSC-1B ( 1 ) and rate constants determined from weighed samples. Q
(1) R. N. Rogers and E. D. Morris, Jr., ANAL.CHEM.,38, 412 (1966). (2) G. 0. Piloyan, I. D. Ryabchikov, and 0. S. Novikova, Nature, 212, 1229 (1966). (3) E. K. Rideal and A. J. B. Robertson, Proc. Roy. SOC.(London), A195, 135 (1948). 1024
ANALYTICAL CHEMISTRY
Figurel. DT curve of RDX where B = dT/dt is the heating rate and Tux is the temperature at which b reaches its maximum. Note that only E, T,,, and B are required for the calculation of A . In Table I the values of log A determined in this way for several common explosives are compared with the corresponding values determined by a direct method with weighed samples, and with values reported in the literature. The agreement is obviously excellent. The values of A for RDX and tetryl were determined from Equation 1 at several heating rates. The results, summarized in Table 11, suggest a slight trend in the direction of decreasing A with increasing B. The source of this unexpected effect has not been identified, but it does not appear to be unduly troublesome. As a further check on the method, the effect of sample size was briefly investigated. The results of these experiments, given in Table 111, confirm that the method is independent of sample size. A significant sample size effect would strongly suggest that the decomposition reaction was not a simple firstorder reaction. Table 11. Log A Determined at Various Heating Rates Heating RDX Tetryl Log A T,,, (OK) log A rate, "C/min TmSx(OK) 2.5 49 1 18.8 5.0 505 18.5 416 15.5 10.0 515.5 18.4 486 15.4 20.0 526.5 18.2 496.3 15.4 40.0 539 18.0 508.5 15.2
~~
The method also appears usable with DTA curves even though the actual heating rate is not accurately known at the maximum with highly exothermic (or endothermic) materials. For example, the DTA curve determined on a IO-mg sample of RDX at a heating rate of 11 " C/minute is shown in Figure 1 (the procedure used to determine this curve is described in ref 4). Tmaxis 523" K! which corresponds to log A = 18.1, in excellent agreement with the data given in Table I. For E = 46000 and Tux = 500" K the relative error in A is given by 6A 6E -G47--48-A E
6Tmax Tmax
+ 6B-B
Table 111. Effect of Sample Size on Log A Sample Compound size, mg T,,, Log A RDX 0.461 527a 18.2 HMX Tetryl
PETN
(4)
The result would thus appear to be quite sensitive to errors in E and T,.,, but not very sensitive to errors in B (the last explains why the method seems to work well with DTA curves). Reasonable practical values for the expected errors in E, T,,, and B are 1 I;cal/mole, 2' K, and 5 %, respectively; the corresponding errors in A (with E = 46000, Tmax= 500" K) are a factor of 2.7, a factor of 1.2, and a factor of 1.05. Thus in practice the accuracy with which A can be determined by this method will depend primarily on the accuracy with which E is known. (4) R. N. Rogers, Microchem. J., 5,91 (1961).
1.050 0.056 0.714 0.100 0.754 0.053 0.922 0.355 0.598
527a 563.5a 563.50 4955 496.3s 506. 5b 508.5* 4855 487"
18.2 18.9 18.9 15.4 15.4 15.3 15.2 19.7 19.6
Heating rate, 20" C/min. Heating rate, 40" C/min.
T o summarize, this method, combined with the previously reported method for determining E, now makes it possible to obtain reasonably good estimates of both A and E for many materials from the DSC or DTA curves of small, unweighed samples. RECEIVED for review March 24, 1967. Accepted May 1, 1967. Work performed under the auspices of the U. S. Atomic Energy Commission.
Spectrophotometric Titration of Inorganic Cyanates in INonaqueous Solvents Fred Trusell, P. A. Argabright and W. F. McKenzie Denver Research Cente.*,Marathon Oil Co., Littleton, Colo. 80120
THEMAJORITY of analytical methods for inorganic cyanates can be grouped under three major headings. The cyanate is either titrated with silver nitrate, determined directly by spectrophotometry, or hydrolyzed to liberate ammonia, which is measured spectrophotometrically. End point detection techniques for titrimetry include an adsorption indicator ( I ) , amperometry (2, 3)) potentiometry (4, and conductimetry (5, 6). However, results from ( I ) are consistently low by about 5 %, while an eml)irical correction factor must be added to the titrant volume in (4). One of the direct spectrophotometric methods (7) is described in such brevity that no guide to accuracy, reproducibility, or interfering substances are offered, while the other (8) requires four successive extractions. The indirect spectrophotometric methods (9, IO) require ion exchange separations. This note describes a direct spectrophotometric titration of cyanate with cobalt(I1). (1) (2) (3) (4) (5) (6)
R. Ripan-Tilici,Z. Anal. Chem., 102,32 (1935). S. Ikeda and J. Nishida, Bunseki Kuguku, 13, 133 (1964). Ibid., 13, 433 (1964). R. Ripan-Tilici,Z. A i d . Chem., 98, 23 (1934). Ibid., 99, 415 (1934). 0. Pfundt, Angew. Chem., 46,218 (1933).
( 7 ) A. I. Finkel'shtein and G. A. Zhukova, Zauodsk. Lab., 30, 943 (1964).
(8) E. L. Martin and J. McClelland, ANAL.CHEM., 23,1519 (1951). (9) W. H. R. Shaw and J J. Bordeaux, Ibid., 27,136 (1955). (10) J. M. Kruse and M. 13. Mellon, Zbid., 25,1188 (1953).
EXPERIMENTAL
Apparatus. Absorption spectra were obtained with a Cary Model 14 recording spectrophotometer. Absorbance measurements at a fixed wavelength were made with a Beckman Model D U spectrophotometer using 1-cm cells. Reagents. Titrant solutions 0.025M in cobalt(I1) were prepared by dissolving 1.83 grams of cobalt perchlorate, hexahydrate in 200 r n l of the appropriate solvent. These solutions were then standardized against potassium cyanate. J. T. Baker reagent grade potassium cyanate used in this study was assayed by precipitation with semicarbazide (11) and found to be 99.6 A 0.4% KNCO. Procedure. Dissolve a sample containing 2.5 to 20 mg cyanate ion in 1 ml of distilled water. Then add 50 ml of the appropriate solvent. Titrate the sample incrementally with standard 0.025M cobalt(I1) perchlorate. Measure the absorbance of the solution after each addition. In the experiments described below, a portion of the solution was placed in a 1-cm cell and the absorbance measured at 645 mp. This portion was then returned to the solution and the titration was continued. By appropriately modifying the cell compartment of the spectrophotometer, this measurement could be made directly on the solution in the titration vessel at a less sensitive wavelength. The end point is located in the conventional manner from a plot of absorbance us. volume of titrant added. (11) A. B. Heagy, J. Assoc. Ofic.Agr. Chemists, 35, 377 (1952). VOL 39, NO. 8, JULY 1967
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