2846
D. M.SPEROS AND R. L. WOODHOUSE
Realization of Quantitative Differential Thermal Analysis. 11.
A Solid-Gas Reaction by D. M. Speros and R. L. Woodhouse Lighting Research Laboratory, General Electric Company, Nela Park, Cleveland, Ohio 44112 (Received January 22, 1968)
The method of quantitative differentialthermal analysis reported previously1 has been applied to the study of the reaction CaCOa(s) CaO(s) COz(g) in both directions. It is shown that the method yields thermodynamic and kinetic results in agreement with those of the best past investigations. The treatment of the kinetic data leads to fundamental questionson the theory of heterogeneous reactions.
+
Introduction In part I of this paperla a description of the principles, apparatus, and procedure was given for the realization of accurate ( f1%) quantitative differential thermal analysis (QDTA). As a first proof that QDTA had been accomplished, the solid-liquid transitions of a number of substances were measured thermodynamically and kinetically covering the temperature range 232-961'. While the study of fusions of part I represents the simplest possible task, the present study of a solid-gas reaction is more complex, since in addition to the exchange of heat with the surroundings there is also an exchange of mass. The reaction chosen is one of the oldest known and, thermodynamically a t least, one of the best known
CaCOs(c) :_ICaO(c)
+ C02(g)
(1)
This reaction was studied in both directions; i.e., both the decomposition of CaC03 and its formation from CaO and COZwere examined.
Apparatus and Principles of Operation The apparatus is essentially the same as that described in part I of this paper.la Rigorous proof of the temperature and thermal balance principles was also given in part I. A less rigorous but more easily understood description of these principles is as follows; see Figure 1. The auxiliary heater, H, essentially surrounds the sample, S, and at all times the temperature of the surface of the heater, T1,is monitored and compared with that of the surroundings, T z ,by means of the differential thermocouple, C. TZmay be constant or varying; usually it is made to increase linearly with time by appropriately regulating the input to the furnace, F. For an endothermic process, T I is kept equal to Tz before, during, and after the process by appropriately regulating the power to the heater, H. In order to accomplish the equality T I = Tt during the endothermic process, an amount of electrical energy, AQ, The Journal of Physical Chemistry
must be expended. Since T I = Tz,none of this energy is lost to the surroundings, all of it being absorbed by the sample. Hence AQ = AH, where AH is the change in heat content or enthalpy of the process. In usual practice TI= Tz AT; however, AT is kept constant before, during, and after the process or is varying in a known manner (base-line drift). For an exothermic process, the input to the auxiliary heater, H, is so regulated that T I = T 2 AT, where AT is kept constant before, during, and after the process. In order to maintain the above equality during the exothermic process, the input to the heater must be re-A& then is precisely duced by an amount -AQ. what is required in order to compensate for the heat evolution by the sample during the process. This is equal to -AH; hence -AQ = - A H . The increase or decrease of electrical energy input is accomplished electronically (or by hand switching for slow processes) so that a t each instant the rate of energy input is plotted as dH/dt vs. t (or T , since usually T = A t ) , where t is time. Thus dH/dt denotes the rate of heat evolution or absorption by the sample. In part I of this paper it was proven that this rate corresponded precisely to the rate of the simple processes involved there, and hence the kinetics of these processes could be followed.
+
+
Experimental Procedure For both the endothermic and the exothermic experiments, the sample-reference assembly was placed in a vertical quartz tube, with approximately a 3-cm inside diameter, which was inserted into the tube furnace, F (Figure l ) . The upper end of the quartz tube was connected to a gas system which made possible the flow of pure, dry nitrogen through the tube at the rate of 2 l./min. At the lower end of the tube (outside the furnace), a side outlet conducted the flowing nitrogen to a calibrated flowmeter. The flowmeter was (1) (a) D. M. Speros and R. L. Woodhouse, J . Phys. Chem., 67, 2164 (1963); (b) D. M. Speroa and R. L. Woodhouse, Nature, 197, 1261 (1963).
REALIZATION OF QUANTITATIVE DIFFERENTIAL THERMAL ANALYSIS
2,547
1 ,I n
Figure I. Schematic representation of the instrumental assembly: F, furnace; 11, auxiliary heater; S,sample; C, differential thermocouple; TI, surface temperature of anxilisry heater; T,,temperature of surroundings.
partly "choked" so that the pressure in the system was slightly above atmospheric (about 800 torr). The thermocouple arid heater leads were taken out of the tube at its lower eud through insulated, gas-tight seals. The furnace used was 30 em in length, with a uniform temperature zoue of approximately 20 cm. The sample-reference assembly was placed in the middle of this zone, arid radial temperature uniformity in the region of the assembly was accomplished by inserting a 10 cm long platilium sleeve between the furnace and the quartz tube. The flow of the nitrogen in the uniformtemperature zone was made turbulent by appropriate ceramic baffles. The CaCOa used was Baker Analyzed reagent grade with less thari a 0.14% strontium content. The sample containers used in the asembly were simple cylinders, 4 mm in diameter and 16 mm in length, made of pure platinum. (a) Endothermic Experimmls. The sample weight used was in the vicinity of 100 mg, but control experiments were performed with larger or lesser amounts. The heating rate was in the vicinity of 2.4 deg/min, but rates as high as 10 deg/min and as low as 1 deg/min were also applied in control experiments. After each run, the resultiug CaO in the platinum container was placed, under a strong flow of nitrogen, in a weighing bottle which was then hermetically sealed in the flow and subsequently was weighed. The theoretical weight of CaO was obtained, for the amount of CaC03 decomposed, within the error of the semimicro analytical balance used. (b) Exothermic Experimmk. The CaO samples used were produced by the decomposition of CaCOs in the endothermic experiments described above; hence the usual sample weight was in the vicinity of 50 mg. After weighing the weighing bottle, the platinum container with the CaO sample was placed in the samplerefereuce assembly under a strong flow of nitrogen. Control runs of this procedure proved that no detectable increase in weight occurred.
Figure 2. Typical QI)TA record for the dissociation of CaCO,(s).
The exothermic experimeuts took place a t a constant temperature; the system was brought to the desired temperature and was allowed to come to a steady state producing a "fore-period" base line. Then a. flow of C02 (99.99% pure) gas, a t the usual rate of 34 ml/min, was inserted into the uitrogeri fliiw hy means o f a side tube, complete mixing being ensured. At the desired time, the flow of CO, was stopped arid a short "after-period'' base line mas obtaiued. The system was then rapidly brought t o room temperature, the sample container was removed uuder the precautions described above, and the amount of reactioii was determined by the increase in weight of the sample.
Results and Discussion ( I ) Thermodynamics. (a) The ISnrlolhermic Procesa (Decomposition of &COS). Figure 2 shows tho actual record of a typical endothermic experiment. The ordinate gives the rate of heat iuput, dH/dt. arid the ahscissa gives the temperature in degrees ccnt,igrade (lower scale) and the time in minutes (upper scale). Therefore, the area enclosed by the recorded curve and the drawn interpolntiug base line gives the chnrige in heat content, A H . The values of AH fouiid in these experiments, after referral to a given temperature,l agreed with those necepted in moderri critical compilntio~is..~~' Thus for the case shown in Figure 2, the heat-coutent chauge of the reaction at 770" was found to be 4O.SO kcal/mol. This is compared with AHno = 40.55 kcal/m~l,calculated from the data in ref 3, and with AHno = 40.85 kcal/ mol, calculated from the data in ref 4. However, little assurance can be derived from this agreement; it is seen that, under the experimerital conditions described above, CaCOJ began decomposiug at approximately 630" but that the decomposition was not completed (2) A paper on the procedure for accomplishing this referral and its theoretical justification is in press: Proceedings. 2nd International Conference on Thermal Analysis. Worehester. Mass.. Aug 1968. (3) 0. Kuhaseheaski and E. L. Evans. ".\fetnllumgienl Thermoehemistry." Pergamon Press he.. New York. N. Y., 195R. (4) K. K. Kelley. U. S. Bureau of .Mines Bulletin 584. U. 8. Government Printing Office. Washington. D. C.. 1960.
Volume 72,Ntrmber 8 Aupual 19F8
D. AI. SPEROS AND R. I,. WOODHOUSE
2343 Table I:
r\mnt
I>etcrminst.ion of the Heat of the Reaction CaO(c)
of
cao.
0.06275 0.05717 o.o4925 0.04!)25 0.04!)'25 0.04025
,\mn, of
co, *l,sorbEd. 0,00579 0.00719 o .w 2 8 0.00587
0.006R3 0.00F75
II
+ CO&)
Temp 01 reaotion. OK
722.3 742.5 781.6 784.1 816.0 821.6
-
CaCOdc) -AHIS.'
Ileat of pmocss, H I .
-AH=. kd/mol
keal/rnol
22.70 28.61 17.25 22.92 26.76 27.04
41.22 41.81 42.37 41.05 41.19 42.12
41.87 42.51 43.17 41.85 42.09 43.02
& I a n AH,* = 42.42 kenl/mol; range, 41.8.753.17 kenl/mol, AH,, = 42.49 kcal/rnol (Kelley'); AHl% = 42.85 f 1.21 keal/mol (Kitbaschewski and Evnnsl).
until a temperature of approximately Y20" had been reached about SO min later. If the fore- and afterperiod base lines were absolutely collinear, the interpolating base line could be drawn unambiguously and AH could be determined with little uncertainty. However, this is rarely the case over such large temperature (and time) intervals, some base-line "drift" always being nbserved. This is compounded by the fact that the decomposition reaction is initially so gradual that it is difficult to determine precisely its beginning. Thus it is pnssible to draw a number of interpolating base lines, all of which appear reasonably correct but which yield AH values diffcriug by a few per cent. The above are limitations of differential thermal analysis in geueral and are limitations, therefore, of QDTh. However, one of the rcasnus for the choice of this reaction was to illustrate these limit a t'ions. These limitatinns can be avoided5 by bringing the CaC03 s:rmple to a temperature higher than 630' in a flow of Sr into which Cor is inject,ed and then switching ~ f the f COS. This was not done in the experiment nf Figure 2 i u order t o nbtain the kinetics of the n o r d thermal decomposition of CaC03 (see below). (b) The ISzolhermic Process (Formutim of CaC03). Figures 3 and 4 show the actual records of typical exothermic experiments. Figure 3 shows the process taking place a t approximately 5FO"; Figure 4 shows the process taking place at approximately 470". At points A, CO, is admitted into the system aud at points B the flow of CO, is stopped. Table I summarizes the results obtained. It is seen that the mean value of AH found in this work agrees with the values in the ~ o m p i l a t i n i i s . ~The ~ ~ range of values covers approximately 1.6% of the mean. This is above the usual uncertainty ( + 1%) but it is duc almost entirely to weighing error, siuce the amount of Cor absorbed was only around F mg (Table I, second column). This uncertainty prevented the intended redetermination of hhe heat capacity data from measurements of the AH of the reaction at a series of different temperatures. The temperature of reaction (Table I, third column) was determined to the first decimal figure by means of an "adjustable-zero, adjustablerange recorder"
*
The J o u m l oJ Phvaiur( Chemialry
Figwe 4. QIITA record for the formntion of CaCO,(s) from CeO(8) and CO&) at 470".
(AZAR) and thermocouples which were calibrated by melting a series of high-purity metals in the same sample-reference assembly. Figures 3 and 4 show instrumental noise. This was partly due to the high sensitivity; it should be noted that the total heat effect recorded in these figures amounts to only about .5 cal (Table I, fourth column). (2) Kinetics. (a) G'eneral. In part I it was proven that for the simple processes involved there, the equation
N ~ Sapplicable rigorously, where dH/dt is the rate of heat absorption by the sample, Ho is the heat absorbed by the entire process involving N mol, and dz/dl is the
(6) Also. A. E. Newkirk. private communication, 1967.
2849
REALIZATION OF'QUANTITATIVE DIFFERENTIAL THERMAL ANALYSIS rate of the process in moles per unit time. dH/dt was given directly by the ordinate of the QDTA record (such as that of Figure 2) a t any time t or temperature T , and, therefore, the determination of the rate of the process was a simple matter. For a homogeneous process, the kinetic rate law is applicable dx dt
- =
k ( a - x)"
(3)
If eq 2 were to apply, then x = (N/Ho)H, where H is the heat absorbed up to time t and a = (N/Ho)Ho. Substitution in eq 3 gives dH - = kAH1-"(Ho dt
- H)"
(4)
where AH = H o / N , the enthalpy change per mole of the process. Solving eq 4 for the specific rate constant k and equating k to the Arrhenius equation
A relation similar to eq 5 was derived earliers for homogeneous reactions in a different way. Equation 3 a,nd relations derived from it have been applied extensively also to heterogeneous reactions.' This, however, immediately leads to difficulties such as the following. 1. It is necessary to define the concepts of the concentration of reacting solids and the reaction order. Gomess has stated that these terms generally have no significance in solid-state reactions. 2. It is necessary to define the concept of activation energy. Hauffeg states that the activation energy has no physical meaning if the mechanism of the reactions is unknown. 3. The term reaction rate is no longer unambiguous, since it may refer to the rate of product formation or that of interfacie migration, 4. There is no known fundamental reason why the rate should be dependent on the amount of product already formed, or reactant remaining, as stated in eq 3, since the bulk of the product and the reactant are not involved in the reaction, which proceeds a t the interface, except perhaps as diffusion barriers. (b) T h e Endothermic Process. I n view of these difficulties, the application of eq 5 to the results of Figure 2 is not, appropriate theoretically.6 Nevertheless, it is applied in a purely empirical sense. Thus this application simply examines whether the decomposition of CaCOa, as measured in this experiment, follows an exponential law. The results of this application give reasonable agreement with the best literature values, as will be seen below. Equation 5 was applied to the data of Figure 2 over the entire temperature range of the reaction (900-
-1 !O
'077
(OIC')
Figure 5. Arrhenius plot of the data on Figure 2 for three values of n. AE = 44 kcal/mol, for n = 0.2.
1090°K). For a value of n = 0.20 in eq 5, a straight line was obtained on the Arrhenius plot of Figure 5 over this entire temperature range. The slope of this line is 44 kcal/mol. Ingraham and Marier'O made a thorough literature search on past kinetic studies of the thermal decomposition of CaC03. They state that the activation energies determined by various investigators vary from a low of about 35 kcal/mol to a high of 230 kcal/mol but that the majority of the values reported lie in the range of 37-53 kcal/mol. The slope of the line in Figure 5 is within this range. However, it is compared with the value of 40.6 kcal/mol obtained by Ingraham and Marier'O by a combination of thermogravimetric determinations and measurements of the (6) H. J. Borchardt and F. Daniels, J. Amer. Chem. Soc., 79, 41 (1967). (7) H. B. Jonassen and A. Weissberger, "Technique of Inorganic
Chemistry," Vol. I, Interscience Publishers, New York, N. y., 1963, p 247. (8) W. Comes, Nature, 192,865 (1961). (9) K. Hauffe, "Reactionen in und an Festen Stoffen," Springer-Verlag, Berlin, 1955, p 639. (10) T. R. Ingraham and P. Marier, Can. J . Chem. Eng., 41, 170 (1963).
Volume 78, Number 8 August 1068
2850 rate of the CaO-CaCOs interface migration in compacts of powdered CaC03. The difference of about 3 kcal/mol between the value found in this work and that found by Ingraham and Alarier may be due to the difference in the ease of diff usion of C02 away from the reacting sample. Ingraham and Marier contained their samples in a wire mesh, while in this work the samples were contained in long, narrow (4 mm in diameter X 16 mm in length) cylindrical containers of platinum foil. The agreement between this work and past work may be fortuitous, since it depends on the validity of the rate law used, eq 5 . This will be discussed further below. (c) The Exothermic Process. In Figure 3, depicting the reaction at 560", the "reaction rate" decays very slowly from the beginning of CO2 injection until the flow of COa is stopped. At a lower temperature, namely 470", Figure 4 shows that the rate dH/dt decays quite rapidly at first. After lO-l5% of the CaO is allowed to react, the rate falls abruptly, then decays again until the C02injection is stopped. If a t any time the reaction becomes diffusion limited, then its behavior should resemble that predicted by the parabolic diffusion law. Thus, in the unidirectional case, the velocity, dl/dt, of the reaction should be inversely proportional to the first power of the distance, I , through which the gas must diffuse in order to react. In the case of QDTA, and with the same reservations as given in the endothermic case, specifically the applicability of eq 2, this would be equivalent to writing dH - B (6) dt H where B is a constant, since the distance traversed by the reaction should be proportional to the heat evolved. I n more complex geometries, it may be written that the rate is inversely proportional to some power of H, such as y.11 Then a plot of In (dH/dt) os. In H should be a straight line with a slope of -y. Figure 6 shows a number of plots of In (dH/dt) vs. In H, each curve representing CaC03 formation from CaO and GO2 at different temperatures between 420 and 480". During the early part of the reaction, the lines are curved as expected; however, as the reaction progresses further, it becomes diffusion limited, as shown by the straight lines with the given values of y. It was interesting to note that the rate and total amount of GOz absorbed by a given sample of CaO became progressively less with a repetition of the absorption-decomposition process normally involved in these experiments. It is thought that this may be due to the progressive sintering of the particles of CaO, while the samples were being heated to 820" in order to decompose the CaCOs formed, but a systematic investigation of this effect was not performed. The Journal of Physical Chemistry
D. M. SPEROS AND R. L. WOODHOUSE 1.161
I
l
l
1
I
I
I
/
I
H-
Figure 6. Plots of data from QDTA records such as on Figures 3 and 4 utilizing the equation dHldt = B/Hy.
The sudden drop of the rate of CO2 absorption seen on Figure 4 was observed on several occasions. It is thought that the cause for this is trivial, the drop in dH/dt being coincident with the CaO sample completely filling its container radially owing to the expansion upon the absorption of C02. (d) Conclusions on the Kinetic Results. It was shown that the decomposition of CaCOa follows an exponential law and that the slope of the resulting Arrhenius plot is in reasonable agreement with past work. The reaction between CaO and GO2 follows a parabolic law during the latter half of the reaction time. The validity of these results depends on the validity of eq 2 and 5 . Equation 2. Its use led to precise results in part I and to results that agree with past kinetic investigations in this paper. Additional workI2 indicates that it is obeyed in complex, multistage reactions. Pending proof of this, it appears that QDTA is of about the same usefulness in kinetic investigations as thermogravimetry and other methods that determine rates from the number of gram equivalents of products formed or reactants expended. Equation 6. This is a t present without theoretical justification and must be considered as yet another empirical equation in solid-state chemistry. However, it has been successful in past work' and, as was seen, in this work. In addition, it is applicable also in a present investigation12 of the reaction
+
2CaHPOd(s) -+ C ~ Z P Z O ~ ( SHzO(g) ) Furthermore, it can be shown that approximations (expansions) of eq 5 (or 4) and approximations (ex(11) W. E. Garner, "Chemistry of the Solid State," Butterworth and Co. Ltd., London, 1955, p 355. (12) Proceedings, 6th International Symposium on the Reactivity of Solids, Soheneotady, N. Y., Aug 1968.
2851
PHOTOLYSIS OF ALCOHOLB ADSORBED ON ALUMINA pansions) of another empirical equation of wide applicability in solid-state chemistry, the Elovich equation13 dH - = Kle-KaH dt where K1 and K 2 are constants and H has the same significance as in eq 5, give results in acceptable agreement over rather wide ranges of H and n. Equation 5 then is of rather general applicability,
and effort to discover whether it has physical significance is clearly worthwhile. Acknowledgments. The authors are indebted to many colleagues in this laboratory and at the General Electric Research and Development Center for critical reading of the manuscript, but especially to Drs. A. E. Newkirk and E. L. Simons, whose comments greatly benefited this paper. (13) J. H. DeBoer, Proceedings, 4th International Symposium on the Reactivity of Solids, Amsterdam, 1961, p 222.
Photolysis of Alcohols Adsorbed on Alumina as Studied by Electron Spin Resonance by Yoshio Ono and Tominaga Keii .Department of Applied Chemistry, Tokyo Jnstitute of Technology, Meguro, Tokyo, Japan
(Received January 26, 1968)
Alcohols adsorbed on alumina were irradiated with a high-pressure ultraviolet lamp a t liquid-nitrogen temperature and the irradiation products and their thermal stability were studied with esr technique. When adsorbed methanol was irradiated, a triplet signal was observed a t liquid-nitrogen temperature and was assigned to A10CH2, which is the decomposition product of the surface complex AlOCHs. From the change of the line shape, it has been concluded that the rotation of the radical around the C-0 axis becomes free over -140". The radical was completely stable below -90". It decayed according to the first-order kinetics with an activation energy of 2 kcal/mol above -goo, but it was still observed even at rpom temperature. The irradiation of chemisorbed ethanol gave the quintet signal which was ascribed to AIOCIICHs formed by the decomposition of the surface ethoxide. This radical was observed up to -60'. All the radicals formed by the irradiation reacted with oxygen at liquid-nitrogen temperature to form peroxy radicals.
Introduction Some free radicals stabilized on solid surfaces have been investigated recently. Kazanskiil observed the esr spectra of the methyl radical formed by the photolysis of methyl iodide and the ethyl radical formed by the radiolysis of ethane on silica gel and found that these radicals are stable up to 200-250°K on the surface of silica gel. li'ujita and Turkevich2 found the methyl radical formed by the photolysis of methyl iodide on Vycor glass to be completely stable for 2 weeks, even at room temperature. Then they studied the reactivity toward various gases, such as oxygen, methane, and hydrogen. All of' the radicals mentioned above were produced by the decomposition of physically adsorbed molecules. However, it is expected that molecules in different adsorbed states give different free radicals : that is, decomposition of the chemisorbed molecules on a surface would give other kinds of radicals than those which would be given by the decomposition of physi-
cally adsorbed molecules. On the contrary, from the knowledge of the produced species by the decoinposition of adsorbed molecules, one could obtain some information about the adsorbed states of the molecules. In fact, Kazanskii has reported that in the case of the radiolysis of adsorbed methanol, the ratio of products (hydrogen, formaldehyde, glycol, carbon monoxide, and ethane) differs with the surface coverage of metha n ~ l . He ~ has also reported that a similar phenomenon occurred in the case of the radiolysis of adsorbed cyclohexanea4 (1) V. B. Kazanskii and G . B. Pariiskii, Kinet. Katal., 2, 607 (1961); Zh. Strukt. Khim., 4, 364 (1903). (2) J. Turkevich and Y. Fujita, Discussions Faraday Soc., 42, 181 (1966). (3) V. I. Vladimirova, G . M. Zhabrova, B. M. Kadenasti, V. B. Kazanskii, and 0.B. Pariiskii, Dokl. Akad. Nauk S S S R , 164, 361 (1965). (4) V. I. Vladimirova, G . M. Zhabrova, B. M. Kadenasti, V. B. Kazanskii, and G . B. Pariiskii, ibid., 148, 101 (1963).
Volume 78, Number 8 Auguet 1968
