KINETKSOF
CALCIUM
FORMA?E PYROLYSIS
583
The Kinetics of Calcium Formate Pyrolysis in Potassium Bromide Matrix'
by K. 0. Hartman and I. C. Hisatsune Department of Chemistry, Whitmore Laboratory, The Pennsylvania State University, University P a r k , Pennsylsania I6802 (Received September 21, 1964)
~
The thermal decomposition of calcium formate dispersed in potassium bromide disks (infrared pellets) has been studied by observing the changes in optical densities with heating of several infrared absorption bands of the reactant formate and the product carbonate. The reaction was found to be first order in formate with a rate constant of k (sec.-l) = 4.4 X 1011 exp [(-52,000 f 3000)/ R T ] . Changing the matrix to potassium iodide, varyin g the initial formate concentration over a range of a factor of ten, or changing several conditions in the fabrication of the disks still gave the same kinetic results to within experimental errors. The deuterium isotope effect has also been measured.
Introduction
Experimental
Quantitative kinetic studies of solid state chemical reactions have been conducted in the past largely by therniogravimetric niethod (t.g.a.) or by measuring the pressure of evolved gas as a function of time. In neither of these techniques can the concentrations of the reactant be determined directly nor can reaction intermediates be easily detected. Also, results from these techniques are often dependent on the particle size of the reacting phase.2 In this work we used an infrared spectroscopic method similar to that of Bent and Crawford3& and Hisatsune and S ~ a r e zto~ ~study the thermal decomposition of calcium formate in the solid state. The reactant was isolated in an inert matrix and yuantitative kinetic results were obtained by directly following the concentrations of the reactant and the product. The investigation of the calcium formate pyrolysis was chosen because this reaction appeared relatively free of complications and because sonie data such as the decomposition temperature4 and the product analysis5 were available. Also, the decomposition of mixtures of calcium formate and cupric formatefi and calcium palmitate7 have been reported. In the present work the stoichiometry, the reaction order, rate constants, and the activation energy were determined. Since a number of product and reactant infrared bands were followed, we were able to test our data for internal consistency. Results froiii therniogravimetric and differential thermal analyses were found to corroborate our results.*
Chemicals. Calcium formate froni RIatheson Colenian and Bell (98.5%) was recrystallized from 20% ethanol. The crystals were transparent and most of them were light tan while some were colorless. The original powder had a light brown color. Calcium formate-d was prepared froin Fisher reagent grade calcium chloride and sodium formate-d (99%) of Nerck Sharp and Dohme of Canada, Ltd. Approximately 0.1 g. of formate-d and 0.3 g. of calcium chloride were dissolved in 3 nil. of deionized water that had been distillea from a dilute Ii31n04 solution. Small colorless crystals precipitated, which were filtered and washed with 95% ethanol. The matrix material was optical grade potassium broniide powder or potassium iodide crystal obtained
(1) Abstracted in part from a Ph.D. Thesis of K. 0. Hartman. (2) A. It. Carthew, Am. Mineralogist, 40, 107 (1955).
( 3 ) (a) H. A. Bent and B. Crawford, Jr., J . Am. Chem. Soc., 79, 1793 (1957); (bj I. C. Hisatsune and N. H. Suarez, Inorg. Chem., 3, 168
(1964). (4) V. Zapletal, J. Jedlicka, and V. Ruzicka, Chem. Listy, 50, 1409 (1956).
( 5 ) (a) F. Fischer, A. Tropsch, and A. Schellenberg, Ges. Abhandl. Kenntnis Kohle. 6,330 (1921); (b) K. A. Hofmann and K. Schurnpelt, Ber. Chem. Ges., 49, 303 (1916). (6) V. Ituzicka and E. Kalalova, C'ollection Czech. Chem. Commun., 27, 429 (1962). (7) H . Sakurni and Y. Okamoto, M e m . Inst. Sci. I n d . Res. Osaka C'niu., 17, 209 (1960). (8) F. W. Freeberg. Ph.D. thesis research in progress, Department of Chemistry, The Pennsylvania State University.
Volume 69, Siimber 2
February 1.966
K. 0 . HARTMAX AKD I. C. HISATSUXE
581
froin Harshaw Chemical Co. The calciuni carbonate was a Fisher reagent grade product. Apparatus. The oven used for niost of the work was a Teinpco Model FA-1415M built by Therniolyne Co. I n preliminary runs the oven teiiiperature was only controlled froin about f4 to f lo', but in subsequent runs a iiiodificalion in the control unit allowed us to maintain constant temperature to within 0.8'. The oven could be operated up to about 900". Oven teiiiperatures were nieasured with a chroniel-alumel therniocouple arid a Minneapolis-Honeywell potentionieter (Rubicon Inst.) Model KO.2745. The 13- and 15-1iiin. pellet dies, the niechanical grinder, and the hydraulic press that were used have been described previously. 3b A Mettler seniiiiiicro balance Model 5-6 was used to weigh samples for kinetic runs. Masses were read to 3 X g . It was found by weighing an aluniinuni foil of 0.355 g. that the average deviation was 15 X 10-6 g. and that the niaxinium deviation was 50 X g. These figures were determined by iiiaking 20 weighings over a period of 44 iiiiri. during which the room temperature varied between 25.0 and 25.5'. The balance zero was set before each weighing as was done when weighing samples for kinetic runs. A similar calibration carried out when rooin temperature varied froni 21 to 25' indicated an average deviag. tion of 50 X The spectra were recorded on a Perkin-Elmer Model 21 with a NaCl prism from 2 to 15 1.1 or on a PerkinElmer Nodel 521 dual grating instruinerit from 2.5 to 40 1.1. The frequencies could be read from the grating instrument with a precision of 0.5 cni.-' and the transmittance to ITnder the scanning conditions eniployed, the accuracy was of the order of 1.0 cni.-l and 1% in transmittance. Pellet Preparatzon. Initially, samples were prepared siniply by weighing by difference the desired aiiiount of calciuni forniate and potassium broniide. Since concentrations tts low as 0.4 ing./g., z.e., 0.4 ing. of solute/g. of matrix salt, had to be prepared, a dilution niethod was used fo- later samples. A saniple of calcium formate with a concentration of 20.63 f 0.06 iiig./g. was prepared, ground for 2 inin., and heated for 1 hr. at 110'. Portioris of this saniple were weighed with additional potassiuin bromide. The concentrations of pellets prepared in this manner were known to 1%. The concentrations of calciuni forinate studied ranged from 0.4 t o 4 .0 nig./g. The calciuni forniate and the alkali halide matrix were mixed by grinding them together in an agate vial and ball on a iiiechanical vibrator. The grinding time The .Journal of Physical Chemistry
was varied from 1 to 5 niin. Some samples were mixed by hand grinding in an agate mortar. After mixing, the powdered samples mere evacuated for at least 3 niin. in the pellet die before pressing. The pressing time was varied from 1 to 5 iiiin., and the pressure from 5.84 X lo4 to 17.5 X lo4 p.s.i. Our pressed pellets were transparent and colorless or slightly cloudy. Typically, they weighed about 0.5 g. Stoichzometry. The stoichionietry of the decomposition reaction was determined by using pellets containing known aniounts of product, calciuni carbonate, which were prepared by the dilution technique. From the spectra of hhese pellets a graph of absorbance of the 875 band us. ing. of carbonate was constructed. The absorbance of the 875-cni.-' band from the spectrum of a pellet in which the forniate was completely decomposed was then read, corrected for pellet weight loss (see Kinetics section), and conipared with the graph to determine the amount of Carbonate produced. The 875-cni.-l band was used to deterniirie the stoichiometry because it was an intense band and its band width in the product spectruni and in the reagent grade carbonate was approxiiiiately the saine. Furthermore, it is a riondegenerate mode bandg which is less likely to be affected by the environmental differences. Kinetics. The kinetic data were obtained in the following manner. The pellets were placed in the oven at a reaction temperature between 450 and 520' for the appropriate time period. They were then removed from the oven, cooled to rooin temperature, and the spectra were recorded. The pellets were usually cool to the touch within 30-40 sec. after removal froiii the oven. Such heating and quenching processes were repeated until the reaction was coiiiplete. Besides siniple observation of the change in the spectruiii with heating, the following experinients were perfornied. After various heating times, the pellets were ground under atmospheres of nitrogen or oxygen. Others were ground under benzene After such treatiiients the pellets were repressed aiid the spectra were again recorded. The effects of subsequent heating on these pellets were also investigated. When a pellet was heated, it expanded, became opaque, and had to be re-pressed in ordertorestoretransparency. This was done in early runs by breaking the pellet in half, placing the pieces in the die, and pressing a t the usual pressure. This procedure led to inhoniogeneities as evidenced by the change in optical density of solute bands with rotation of the pellet. With many re-pressings over the course of a long kinetic run, (9) K Nakarnoto, "Infrared Spectra of Inorganic and Coordination Compounds," John Wiley and Sons, Inc , New York, N Y , 1963, 13 92
KINETICSOF CALCIUM FORMATE PYROLYSIS
the opi ical density was observed to vary by as much as 30y0 with rotation of the pellet. Uniformly sanding off the pellets around the circuiiiference so that they fitted i,he die eliniinated this problem, and the optical density was independent of the orientation of the pellet in the spectroriieter beam. With this method, however, 0.5 to 1.5% of the total weight of the pellet was lost with each re-pressing. The absorbances of the observed bands were corrected for this weight loss by niultiplying the absorbance at time t by the initial weight of the pellet divided by the weight a t time t . In early runs, the absorbance readings were corrected by following the decreasing thickness of the pellet with a micrometer. The thickness could not be determined with as iiiuch sensitivity as the weight, however. A weak band at 2170 cni.-l due to cyanate impurity3b appeared in most of the heated pellets.
585
Table I : Observed Calcium Formate Frequencies (cm.-1)
7 -
-Initial-
KBI
Modea
u(G-H)
-
Ca(HC0z)z --Heated-KI KBr
2889 w 2862 w
2890 2865 u,(COZ) 1 5 8 0 ~ ~1585 up(C-H) 1397 s 1400 1387 s 1390 u,(COz) 1359 s 1361 1348 s 1351 uW(C-H) 1078 w 1077 1068 w 1066 up(C0,) 799 s 802 777 s 781
KI
-Ca(DCOz)eInitial KBr only Heated
2872 w
2875
2155
2143
1598 vs 1378 s
1600 1380
1585 1009
1350s
1354
1590 1029 1005 1348 1321 909
784 s
784
792 772
779
a LY = antisymmetric stretch; p = bending; u stretch; and o = out-ot-plane wagging.
=
1340
symmetric
Results Within the limits described in the Experiniental sectiori, variation of the pressure used to press the powder into pellets had no effect on the solute spectrum or on the decomposition rate. Increasing the grinding time, however, led to better dispersion of the solute in the matrix and, hence, to sharper absorption bands, but it did not cause a variation in the decoiiiposition kinetics. It was found that grinding the powder while it was hot (approximately 90') also gave better dispersion. Increments in grinding time beyond 3 niin. had a negligible effect on the spectrum. The following changes were observed in the spectrum of calcium formate with heating a t high teniperatures. The spectrum of the unheated pellet which consisted of crystallites of calcium formate embedded in potassium bromide matrix showed doublet structures in most of the formate bands. With short heating, the doublet structures of the calcium formate bands coalesced into singlets (Table I). The bands were still broad and remained so throughout the reaction. In soine pellets the initial spectra did not show the doublet structure but showed instead the singlet bands, which were usually observed after heating. With continued heating, the intensities of the forniate bands decreased until they finally disappeared. Another set of absorption bands, which were identified as those of calcium carbonate, appeared and grew with heating. The observed frequencies of Ca(HCO& and Ca(DC02)2 in both potassium bromide arid iodide matrices and their assigninerits are given in Table I. The frequencies are in good agreement with those reported by Harvey, et a/.,1° except for the hydrogen out-ofplane bending mode which differs by 6 cni.-l for both
doublet frequencies. The formate frequencies after heating are also listed in this table. Table I1 gives a comparison of the frequencies of the reaction product and those of calciuni carbonate in the calcite crystal structure dispersed in IiBr matrix. All of the frequencies are in good agreement except for the antisynimetric stretch band at 1440 c i n - l , which is degenerate. Table I1 : Observed Calcium Carbonate Frequencies, KBr Rlatrix (cm.-') .imignmenta
1087 1087
(R)+ 2 X (R)+ 711
Decomposition product
Reagent salt
2500 w 1790 m 1440 vs 875 s 846 w 711 m 310 m
2500 1790 1420 874 845 i10 308
711
CO
u,( VU
'P Y(
Ca-0)
See footnote of Table I. ( R ) see ref. 9.
=
Raman active fundamental,
Since formate saiiiples prepared by the dilution technique had the inost reliable coriceritrations, they were used to analyze the stoichionietry. In 19 runs, the ratio of nioles of calciuiii foriiiate to nioles of calcium carbonate formed was found to be 0.96 f 0.12 with a inaxiniuni deviation of 0.23. The ratio mas independent of initial formate concentration whirh was (10) K. B. Harvey, B. A. Morrow. and H. E. Shurvell. Can. J . C h ~ m , 41, 1181 (1963).
Volume 69, .Vumher 8
February 1966
586
K. 0. HARTMAN AND I. C. HISATSUNE
varied by a factor of eight. The over-all reaction therefore is Ca(HCO&
-+ CaC03
+ H2 + CO
Carbon monoxide trapped in the pellet was observed only twice in 40 runs. Its band was very weak and had the P- and R-branches a t about 2150 and 2180 cm.-' which were characteristic of a gas phase spectrum. It appeared after the initial heating in a kinetic run and then vanished after the next heating interval. Other absorption bands observed during the course of the reaction were 2330 (w), 1630 (w), and 2655 (vu,) cni.-'. The 1630 and 2655 cm.-' bands were due to formate ion isolated in the potassiuni bromide matrix. The 2330 cin. band was due to carbon dioxide trapped in the m a t r i ~ . ~ " KOnew bands were observed when a heated pellet was ground in oxygen or nitrogen and then repressed. In general, the absorbance of both the formate and carbonate increased regardless of whether oxygen or nitrogen was used. A new band a t 662 c m - ' was observed in the spectra of pellets that were ground under benzene and then re-pressed. This band was weak and disappeared upon heating the pellet a t 100'. By recording the spectrum a t appropriate time intervals, optical density us. heating time curves were constructed. These plots showed the continuous decrease of the formate concentration and the concomitant increase of the carbonate concentration. Two methods were used to determine the order of the decomposition reaction. In the first method, the logarithm of AO.D./At was plotted against the logarithm of 0,11.,where O.D. is the optical density of the reactant absorption band. Since the optical density is proportional to the concentration of the formate ion, the slope of this line is equal to the order of the reaction. Applying this treatment to the 784 e m - ' formate band, we obtained a reaction order of 1.0 f 0.1 in eight runs. Orders of 1.04 and 1.09 were found from a siniilar treatment on the 711 and 1440 c m - ' carbonate absorption bands. The second method was siinply ploti ing the logarithm of any formate band optical density against time and observing that this was a linear function of time for over 90% of the reaction. To evaluate the rate constants, the logarithm of the optical density of a formate band or the logarithm of the carbonate optical density a t the end of the reaction minus its v d u e a t time t was plotted against time. This was done for absorption bands which did not appreciably overlap with other bands. Such plots for different bands gave approximately the same slopes. The rate constants obtained from the various carbonate The Journal of Physical Chemistry
Table 111: Calcium Formate Decomposition Rate Constants (10-3 min.-' units) Temp.,
784 cm.-l
"C.
(HCOz-)
711 cm.-l
875 cm. -1 (COa-2)
Potassium bromide matrix
450 450 454 454 454 456 456 480 490 490 500 500 500 505 505 505 507 515 515 518 518
f1 f1 f6 f6 f6 f5 f5 f1 f1 f1 f4 f4 f4 f 10 f 10 f 10 f1 i8 f8 i6 i6
5 5 6 5 6 9 8 23 37 37 48 49 58 48 62 86 82 72 72 120 98
1 2 0 7 7 0 7
4 4 12 7 6 14 11 27 41 37 47 44 55 40 57 38 91 70 72 110 100
9 8 5 9
5.4 5.5 15 9.3 7.0 16 15
40 49 23 52 41 88 71 71 120 110
Potassium iodide matrix
491 f 1 491 f 1
42 40
43 41
44 39
Calcium f o r m a t e 4 in potassium bromide matrix 468 f 1 4.8 5 0 5.0 491 f 1 19 19 23 46 45 45 509 f 1
and formate bands are listed with the reaction temperatures in Table 111. The scatter in some of the constants that should be the same was due to two things: poor teinperature control and inhomogeneities introduced by breaking the pellets in the re-pressing process. With the elimination of these sources of error, the precision of the rate constants was improved to 10% uncertainty. The rate constants were observed to be independent of the concentration for the range studied which was from 0.4 to 4.0 mg./g. The first-order rate constants for the decomposition of calcium formate in a potassium iodide matrix a t 490' are also listed in Table 111. They are within experiinental error of those obtained in the potassium bromide matrix. In Table IV the activation energies arid frequency factors obtained from various absorption bands that were followed are summarized. The results from the 784 cni. -l formate band are the most reliable since this band had sufficient intensity and did not overlap with
KINETICS OF CALCIUM
FORMATE PYROLYSIS
587
Table IV : Experimental Activation Energy and Frequency Factor
Frequency. crn. - 1
Activation energy, kcal./mole
Frequency factor, 8ec. - 1
Potassium bromide matrix 784 ((formate) 52.0 f 3 . 0 1598 ((formate) 49.0 f 3.0 875 ((carbonate) 50.0 f 3 . 0 71 1 carbonate) 51 5 f 3 . 0 Potassium iodide matrix 784 i:formate) (52.0)" Calcium formate-d in potassium bromide 779 ((formate) 59.0 f 3.0 Thermogravimetric analysis Undiluted Ca( H C O Q ) ~ 47 f 6' Undiluted Ca(HCOz)2 56 f 6" Ca( HCOz)Z in KBr disk 56 f 6c Ca(HCO& in KBr disk (52Id
4.4 X 8.0 X 1.3 X 3.2 X
loL1 10lo 10" 10"
4 . 0 X 10" matrix 1 . 5 x 1013
6 . 0 x 1013 1 . 0 x 1013 5 . 0 X 10"
a Activation energy from 784 em.-' band in KBr matrix. Isothermal run. Temperature programmed run. Isothermal run, activation energy from 784 cm.-l band in KBr matrix.
other absorption bands. The 3 kcal./mole error was calculated on the basis of 10% error in the experimental rate constants, and activation energies calculated from diff ererit calciuni formate and calcium carbonate bands agreed within this estimated error. The rate constants and activation energies determined by the therniogravimetric analysiss are also listed in Table IV. The frequency factor for the isothernial run in KBr disk was calculated using the spectroscopically determined activation energy. The pyrolysis of calcium formate-d wasinvestigatedat three temperatures and the observed rate constants are given in Table 111. The activation energy was 59 f 3 kcal./niole.
Discussion We observed spectroscopically that two formate ions decomposed to form one carbonate ion. This stoichiometry was also confiriiied by the thermogravinietric analysis.8 Although oxalate has been reported as a niinor product,jb we did not observe its characteristic infrared bands during our pyrolysis. The other products, hydrogen arid carbon inonoxide, would easily diffuse out of the niatrix during the heating cycle and, in fact, our disks showed blistering after heating. There was also strong evidence that carbon inonoxide, which was actually observed twice, disproportionated into carbo11 dioxide and carbon in the disks. Trapped carbon dioxide was observed in all pellets, and a gray or brown color developed in the disks with heating. Siniilar color changes have been reported also by pre-
vious i~ivestigators.~~ Samples run in the differential thernial analyzer under nitrogen atniosphere also had a gray color while those decomposed under oxygen atmosphere, where the carbon nionoxide was conipletely oxidized to carbon dioxide, were white. Undoubtedly, the coloring of the pellets with heating is due to formation of dispersed carbon in the matrix. Such disproportionation of carbon nionoxide has been observed by others in the solid state deconiposition of oxalates." Glasner and Steinberg12 have measured the extent of disproportionation in rare earth oxalates under a variety of conditions and found as much as 70y0 reaction. The broadness of the infrared bands throughout the reaction and the fact that calcite was the reaction product indicated that niost of the calcium formate did not go into solid solution with the matrix salt. The sharp although weak bands a t 1630 and 2655 c 1 n - l showed, however, that a sinall aniount of formate ions did go into the matrix. These bands have been identified as solid solution bands of formate ion in potassium bromide iiiatrix on the basis of a parallel work in progress in this laboratory on the decoinposition of sodium and potassium formate in potassiuiii broniide niatrix. Since the calcium formate did not go into solid solution with the matrix to any significant extent, the matrix should not greatly affect the decaonipositiori kinetics of calcium formate. Othei cxperiiiierital observations which support this view are as follows. I n both potassiuin broniide and iodide matrices, the reaction rate constants were the same within experimental error. Arrheriius activation energies obtained froni the therniogravinietric analysis on undiluted calciuni formate are also in agreement with our spectroscopic values. The rate constants from the t.g.a., however, are higher than ours by a factor of about 30. These differences, we believe, are due to the fact that in the t.g.a. the oven teniperature rather than the saniple temperature was measured and that self-heating of the occurred during the deconiposition. The differential thernial analysis of the undiluted calcium forniate in oxygen atniosphere showed an exot heniiic peak due to CO oxidation and a large jump in the saniple teniperature. Freeberg also followed the decomposition of calcium forniate in KBr matrix by the t.g.a. nlethod.S An isothermal run a t 472' on a pellet containing 10 nig. of calciuni forniate/g. of potassiuni bromide gave a rate ~~
~~
(11) E. L. Head and C. E. Holley, Jr., J . Inorg. .\wZ. Chrm., 2 6 ,
525 (1964). (12) A. Glosner and XI. Steinberg. ibid., 2 2 , 39 (1961) (13) A. E. Newkirk, Anal. Chem., 3 2 , 1558 (1900).
588
K. 0. HARTMAN AND I. C. HISATSUNE
constant of 25 X lop3 min.-’ with an estimated error of about 30%. A temperature-programmed run on a similar pellet gave 56 f 6 kcal./mole for the reaction activation energy. These results are in good agreeniin.-’ ment with the spectroscopic values of 18 X and 52 f 3 kcal./mole, respectively, for the rate constant a t the same temperature and the activation energy. Interestingly, smoother thermogravinietric curves were obtained froni deconiposition studies with KBr disks compared to those from undiluted material. The large difference between the rate constants for the deconiposition of Ca(HC02)2and Ca(DC02)2suggests that we have a primary isotope effect with a C-H bond of the formate ion being broken in the transition state. The temperature dependence of the kinetic isotope effect can be estimated by considering the zeropoint energy effect14 kHIkD
eXp[hC(uH - v1,)/2kT]
where v is the C-H (C-D) bond stretching frequency in em.-’. Using the observed frequencies given in Table I, we have calculated the ratios of b”~, and these together with the observed ratios are listed in Table V.
782.5 f 1 764 f 1 741 f 1 Temperature dependence
-
..Ca+20 2 C H - HC02- Ca+2... The distance between the carbon atom of one formate ion and the closest oxygen atom of the next ion is 3.3 8.,and the distance between the carbon atoms of the two ions i ~ ~ 3 . 8 5 Since the C-0 distance in carbonate ion is 1.3 A., the formate ions need only move by about 1 8. toward each other and rotate slightly to form the following transition complex.
0I
...ca+o=cI ...0- ca+2... + ..pa+co3-2 ... I 1 + H,CO H..*C=O I 2
2
ca+2
H
Table V : Kinetic Isotope Effect Temp.. “K.
a simple dissociation of the formate ion into a hydrogen atoni and a C02- free radical. Sonie insight into the mechanism of the deconiposition reaction of calciuni formate can be gained by examining the crystal structure even though our spectral data show that the structure of this compound in heated pellets is not the same as the room temperature structure. The room temperature single crystal structure1* shows that there is an alternating chain illustrated schematically as follows.
ka/b Obsd.
Cslod.
1 . 8 7 f 0 35 2 00 f 0 40 2 75 f 0.55 exp[( +7000 f: 6000)/RT]
1.95 1 97 2 02 exp[ +2000/RT]
This complex can then break as shown above, inbo a carbonate ion, which is between two calcium ions, and fornialdehyde, which immediately decomposes into hydrogen gas and carbon monoxide. Fornialdehyde is known to decompose readily above about lZ0°.’9 The distance between two calcium ions in zoom teniperature structure of calciuni formate is 6.7 A . , and this in calcite. niay be compared to a distance of 6.36 The mechanism described above is similar to one of the three decomposition mechanisms proposed earlier by Hofniann and Schunipe1t.j The energetics of the above reaction scheme can be estimated and compared with experimental quantities. From the standard heats of formation and available heat capacity data, we calculate that the over-all decomposition reaction is endothermic by 14 kcal./mole. A & .
The temperature dependence of k ~ / kis ~also given in this table. The agreement between theory and experiment is reasonable in view of the approximate nature of the above equation. Ovenall and Whiffen15 have generated COZ- radical in sodium formate single crystals by yirradiation, and Brivati, et a1.,16have produced the same free radical in calcium forinate in a similar manner. Since there was the possibility that the ( 2 0 2 - radical may have been generated thentially in our pellets, we have exaniined the e.p.r. spectra of several of the heated disks. However, no signal due to free radicals was observed. This negative result together with the fact that the observed activation energy is smaller than the formate C-H bond dissociation energy, which we estimate to be about 76 kcal./mole by analogy with formaldehyde,17 suggests that the reaction rate-determining step is not The Journal of Physical Chemistry
(14) L. Melander, “Isotope Effects on Reaction Rate,” Ronald Press Co., New York. N. Y., 1962, p. 20.
(15) D. W. Ovenall and D. H. Whiffen, M o l . Phys.. 4, 135 (1960). (16) J. A . Brivati. N. Keen, AI. C. It. Symons. and P. A. Trevalian, Proc. Chem. Soc.. 66 (1961). (17) T. L. Cottrell, “The Strengths of Chemical Bonds,” 2nd Ed., Butterworth and Co., Ltd., London, 1958, p. 184. (18) I. Nitta and K. Osaki, X Sen (Osaka Cniv.). 5 , 47 (1948), cited in Strzict. Rept., 2, 556 (1948). (19) H. Newton and B. F. Dodge, J . Am. Chem. SOC.,55, 4747 (1933).
KINETICSOF CALCIUM FORMATE PYROLYSIS
This value compares favorably with an experimental value of 15.5 f 2 kcal./niole obtained by differential thermal analysis.8 From the experimental enthalpy of actival ion of 52 kcal./niole and the estimated enthalpy of decomposition of formaldehyde of +2.6 kcal./mole, we obtain an enthalpy of activation of 40.6 f 3 kcal./ mole for the reverse reaction HzCO
+ CaC03 +Ca(HC02)2
This value may be compared with 45 kcal./mole calculated from the Hirschfelder rulez0 in which the C-H bond energy in formaldehyde and the CO bond energy in the carbonate ion were taken, respectively, as 76 kcal./rn~le'~and 84 kcal./niole.21 The experimental entropy of activation for the over-all reaction is a small negative value (-7.1 f 5 cal./deg.-mole), and this is also consistent with the above reaction scheme which involves a cyclic transition complex. Another evidence which suggests that formaldehyde may be involved in our reaction is the observation niade by Toyoda.22 He has identified formaldehyde as one of the products of calcium formate pyrolysis carried out a t reduced pressure.
Summary The thermal decomposition of calcium formate has been studied in the solid state by observing the changes
589
in the infrared absorption bands of calcium formate dispersed in KBr matrix. The changes in concentrations of both the reactant and product were followed spectroscopically, and the reaction rate constants, activation energy, kinetic isotope effect, and stoichiometry were determined. Our spectroscopic kinetic results were found to be in good agreement with those from thermogravimetric analysis. Coniparison of these data suggests that our spectroscopic method gave good experimental precision. Furthermore, our technique enables checks for internal consistency of the data and also affords opportunities of observing possible reaction intermediates. The present infrared pellet method should be of general utility in the study of solid state chemical reactions.
Acknowledgments. We are pleased to acknowledge the financial assistance from the Xational Science Foundation in the form of a research grant, SSFG17346. We are indebted to F. E. Freeberg for the theriiiogravinietric and differential thermal analyses data. (20) A. A. Frost and R. G. Pearson, "Kinetics and Mechanism," 2nd Ed., John Wiley and Sons, Inc., New York, N. Y . , 1962, p. 107. (21) L. Pauling, "The Nature of Chemical Bond." 3rd Ed., Cornell IJniversity Press, Ithaca, N. Y . , 1960, p. 85. (22) R. Toyoda, BuEl. Inst. Chem. Res. Kyoto Univ., 2 0 , 11 (1950).
Volume 69, S u m b e r 2
February 1965
