Thermogravimetry of Tungsten Trioxide SIR: The thermogram for tungsten trioxide recently reported by Carey, Raby, and Banks ( I ) is unique in showing that this substance, although stable to -650" C., apparently suffers a twostage weight loss above this temperature as shown in Figure I d . No explanation was offered for this behavior, nor were the experimental conditions given. In contrast, a thermogram obtained by us for tungstic acid, Figure lB, does not show a weight loss between 700" and 1000" C., nor do thermograms reported by others for tungsten trioxide. I t therefore seems desirable to comment further on the dynamic thermogravimetry of tungsten t'rioxide and the importance of reporting experimental conditions with dynamic thermograms. Dynamic t'hermogravimetric data are seldom in exact agreement with isothermal therniogravimetric data, but the differences should show trends which are reasonable and explicable in terms of the differences in experimental conditions. The resulk &ported by Carey, Raby, and I3anks, however, show inconsistencies in both drying temperature and rate of weight loss. The dynamic thermogram (Figure 1 A ) shows that their sample, ". . , became anhydrous a t " I n contrast, for their second series of experiments, "It was necessary, too, to dry t'he tungsten trioxide a t 500" C. for 1 hour in an oxygen atmosphere to guarantee perfect dryness." If a sample of tungsten trioxide can be rendered anhydrous a t about 100" C. in a dynamic thermogravimet,ric run, then this same sample can be dried isothermally a t 100" C., and an isothermal t,emperature of 500 " C. should not be necessary. The inconsistencies in rate of weight loss are more complex. The second reported series of experiments was designed to study t,he relations between volatility and stoichiometry. These experiments were performed in platinum boats and, as summarized in t'heir Figure 2 , show t'hat the rate of weight loss from both sources increases in a smooth and continuous manner from 700" to 1300" C. The thermogram (Figure 1-4))on the other hand, indicates a more complicated behavior, showing (if one assumes a linear heating rate) first a constant rate of weight loss bet'ween 700" and 1000" C., then a range of temperature, 1000" to 1150" C., in which the rate of weight loss is zero, and finally a second region of constant rate of weight loss above 1150" C. The I'lateau over the range 1000" to 1150" C. is not unreasonable in light of their 146
ANALYTICAL CHEMiSTRY
isothermal weight loss experiments (which show a rate of -0.02% per hour a t 1000" C. and ~ 0 . 2 %per hour a t 1150" C.) because a t heating rates commonly used in dynamic thermogravimetry (150" to 300" C. per hour) the accumulated weight loss over this 150" range might be only 0.1%. This small change could easily be obscured by the apparent weight gain of the sample in that region ( 9 ) . On the other hand, the almost 1.5y0 weight loss shown on the thermogram between 650" and 1000" C. implies a rate of weight loss much greater than those calculated from the isothermal experiments which range from only 0.002% to 0.027, per hour in this temperature interval. This loss is not only incompatible with the rate data of their Figure 2 , but is also in disagreement with other dynamic thermograms of tungsten trioxide. * i s an example, the thermogram for tungstic acid, H2t1'O4,obtained by us, Figure lB, shows that decomposition
FURNACE. TEMPERATURE, "C Figure 1 . Thermograms for tungsten trioxide and tungstic acid A.
B.
Tungsten trioxide. Constructed from Figure 1 o f reference 1 Tungstic acid. Baker and Adamson, HpWO4. The sample, 2 . 8 6 7 4 grams in a n open 3-0 porcelain crucible, was heated in ambient air a t 300°/hr. W e i g h t loss = 6.98% corrected for apparent weight gain. Theory for H z W 0 4 = 7.21%
started slightly above room temperature, and that constant weight was attained a t -650" C.; the tungsten trioxide thus obtained is stable and shows no further change in weight on being heated from 650" to 1017" C. The thermogram was obtained on a Chevenard thermobalance whose performance has been reported elsewhere (9). In its high temperature region the thermogram is in agreement with the results of Duval (2) who has shown dynamic thermograms of a number of organotungstate precipitates used for analysis. Many of these compounds decomposed to produce tungsten trioxide a t temperatures below 700" C., and their thermograms displayed a smooth plateau of constant weight in the region 700" to 1000" C. for the tungsten trioxide so formed. Only after recognizing their limitations can the results of dynamic thermogravimetry be related to the ignition temperatures generally recommended for the gravimetric determination of tungsten as tungsten trioxide. A s we have already emphasized elsewhere (8), the appearance of a plateau for a compound on a dynamic thermogram does not necessarily imply that the compound is isothermally stable. either in a thermodynamic or practical sense, a t all or any temperatures that lie on that plateau. The temperature limits between which it extends apply only to the particular conditions of that pyrolysis, and may also depend upon whether it is the material initially loaded into the crucible or whether it is formed in the container by decomposition of a precursor. Thus, in Figure lB, the plateau for tungsten trioxide begins a t 650" C. only because, under the conditions of our experiment, dehydration of its precursor, tungstic acid, was not complete until the furnace had reached that temperature. Under different conditions, or with a different precursor,-e.g., the organotungstate precipitates studied by Duval-the plateau would have begun a t a different temperature. The temperature a t the end of a plateau on a dynamic thermogram is also a function of the experimental conditions and therefore cannot be used to set an upper limit to the isothermal stability of the compound that it represents ( 8 ) . Indeed, it is invariably higher than the maximum safe temperature for isothermal ignition. The extension of the tungsten trioxide plateau in Figure 1B to 1017" C. means only that the rate of weight loss up to that temperature was too slow to produce a
detectable cumulative weight loss during the 70 minutes required to heat the saml~lefrom 650" to 1020" C. I t offers no assurance that prolonged heat'ing a t 1000" C. (or even a t lower temperatures) would not produce a detectable weight loss. There is, however, independent evidence that tungsten trioxide is pract'ically nonvolatile in dry atmospheres at. 1000" C., and five additional references are worth citing in this regard. Millner and Neugebauer (6) observed that 0.5 gram of tungsten trioxide, heated a t 1000" C. in a vacuum of 0.001 mm. for 58 hours, lost only a trace in weight'. ,\lso, K e b b , Korton, and Wagner (IO) noted that the volatilization of tungsten oxides u p to 1000" C. was insignificant so that oxidation of tungsten could be followed by measuring t,he weight gain of specimens. By contrast, in atmospheres from which water was not rigorously excluded weight losses were observed a t 1000" C. Thus Meyer, Oosteroni, and Van Oeveren ( 5 ) report'ed that moist tungsten trioxide lost weight when heated rapidly to high temperatures, but they did not observe this loss if the sample was dried at' 300" to 400" C. before ignition a t 1000" C. Hillebrand, Lundell, Bright, and Hoffman (4)recommend the ignition range 750" to 850" C. in ambient air as high enough to ensure complete dehydration and low enough to avoid significant losses by volatilization. Finally, there
is abundant evidence, recently reviewed and summarized by Glemser and Wendlandt ( S ) , that water vapor will transport tungsten trioxide in the range of interest here, 650" to 1000" C., probably as NOz(OH)n. The cumulative effect of all the reported observations is to suggest, but not to prove, that the discrepancies in the results of different chemists in drying tungsten trioxide to constant weight, and the 650" to 1000" C. weight loss observed by Carey, Raby, and Banks, may be due to the varying water content of the atmosphere. If in the latter case, the thermogram was obtained in a closed or nearly closed system, it is possible to ascribe the weight loss in the region 650" to 1000" C. to the reaction R O 1 HzO = JTOz(OH)z,which ceased when all the water had been combined as vaporized W02(OH)2and deposited in a cooler part of the system as HzWOa. The indicated amount of water lost below 200" C. in Figure 1-4 is about 40y0 more than enough to account for this weight loss. Considerable additional experimental work is certainly necessary to show whether this proposed explanation is sound. This example has been discussed in some detail in an attempt to emphasize the value of reporting procedural data with thermograms, particularly if they are complex. I n many instances authors may not wish to discuss all features of a published thermogram
+
because such feature< may not be germane to the main argument, but the important procedural data could eaiily be included at a cost of no more than a few lines of type. TTe have suggested elsewhere ( 7 ) the kinds of information which would be most useful. LITERATURE CITED
(1) Carey, M . A., Raby, B. A , , Banks, C. Y.,AXAL.CHEM.36, 1166 (1964). (2) Duval, C., "Inorganic Thermogravimetric Analysis," chap. 58, Elsevier, Amsterdam, 1953. ( 3 ) Glemser, O., Wendlandt, H. ( i . , "Advances in hyrganic Chemistry and Radiochemistry, H. J. Emeleus and A. G. Sharpe, eds., Val, 5 , pp. 215-258, Academic Press, New York, 1963. (4) Hillebrand, W. F., Lundell, G . E. F., Bright, H. A , , Hoffman, J. I., "Applied ' Inorganic A4nalysis," 2nd ed., p. 690, Wiley, New York, 1953. ( 5 ) Meyer, G., Oosterom, J . F., Van Oeveren, W. J., Rec. Trav. Cham. 78, 417 (1959). ( 6 ) Mllner, 'T., Keugebauer, J., LYature 163,601-2 (1949). ( 7 ) Newkirk, A . E., Simons, E . L., Talanta 10, 1199 (1963). (8) Simons, E . L., Newkirk, A . E., Zbid., 11, 549-571 (1964). (9) Simons. E. L.. Newkirk. A . E.. ' Aliferis, 'I.j ANN:. CHEM. 29, 48-54 (1957). (10) Webb, W. W., Norton, J. T., Wagner, C., J . Electrochem. SOC.103, 107 (1956). A . E. NEWKIRK E. L. S ~ ~ o z s General Electric Research Laboratory Schenectady, K.Y.
Ana lysis by Differentia I Kinetics Mixed Higher Stoichiometries in a Second Order Homocompetitive System SIR: Differential Rat,e Analysis (DRX), which utilizes the different rates of reaction of organic compounds x i t h a particular reagent, has been used in recent years, especially by Siggia and his coworkers (2, 5, 6 ) . to effect analyses of binary mixtures of closely similar compounds which had previously proved difficult. Where second order kinetics pertain, most systems described have the following charact,eristics: The stoichiometry of the reaction of each component with the reagent is 1:1 (or perhaps 2 : 1). 'I'he total initial molecular concentrat,ion of the mixture is readily measurable via the functional group-e.g., determination of the hydroxyl content in a mixture of monohydric alcohols gives the total molecular concentration. Assuming secaond order kinetics, a conventional plot, of log
(: 7:) __
us. t can
be made over the whole reaction timei.e., including the initial regime when both components are reacting with the reagent. In this correspondence, a second order system is investigated in which: Each component has a different (high) stoichiometry with the reagent; the total initial molecular concentration cannot be measured via a total functional group determination; and the conventional second order kinetic plot cannot be made to cover the early regime when both components are reacting. X nonempirical procedure, avoiding calibration curves and the need for exact reproduction of bath temperature, is employed. THEORY
Consider a reaction in which one mole of polyfunctional compound reacts with J moles of reagent, and which nevertheless exhibits second order kinetics. if
initially there are a. moles of reactant and h moles of reagent, then where x is the number of moles of compound which has reacted a t time t , and k is a rate constant we have:
kt
( h - Jz)
2.303
= ___
Hence a plot of log ( h a - ? )
us. t
~
should give a straight line with an intercept at t
=
0 of log
(9 >
,
S o w consider the initial concentration of a moles to be composed of almoles of component .1 and a2 moles of component B-Le., a = ai a2-and the stoichiometries of the reactions (mole. of reagent to moles of component) to be J 1 and J n for the two component3 .t and B , reslxctively. h - Jx. In Equation 1, ~is the ratio
+
a - x
VOL. 37, NO. 1 , JANUARY 1965
e
147
