Determination of Density Distribution Functions of the Apparent Activation Energies for Nonisothermal Decomposition Proc
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THE decomposition reaction of sodium bicarbonate is represented by the equation 2NaHCO3 ! Na2 CO3ðsÞ þ CO2ðgÞ " þ H2 OðlÞ
½1
in the range 355 to 485 K. The decomposition is both time and temperature dependent.[1] This decomposition process has been investigated from time to time because of its numerous uses in different types of industries.[2–10] A typical example would be its use as a dentifrice. The published information discusses the decomposition temperature and the enthalpy of the reaction. An apparent activation energy of 85.8 kJmol-1 has been reported for the reaction based upon the mechanism of a contracting sphere.[6] The apparent activation energy (Ea) varies with the differences in the grain size of the investigated substance. BOJAN JANKOVIC´, Assistant Professor, is with the Faculty of Physical Chemistry, University of Belgrade, 11001 Belgrade, Serbia and Montenegro. Contact e-mail: bojanjan@ffh.bg.ac.yu Manuscript submitted August 1, 2007. Article published online December 13, 2007. METALLURGICAL AND MATERIALS TRANSACTIONS B
In our previous article of the sodium bicarbonate decomposition process under nitrogen atmosphere in nonisothermal conditions, the kinetic scheme of this process was established.[11] It was concluded that the decomposition process of NaHCO3 using nitrogen is a multistep mechanism and can be described by the two-parameter autocatalytic Sˇesta´k–Berggren (SB) reaction model.[11] Using the isoconversional (model-free) method, the complex behavior of the Ea on the degree of conversion (a) was established. Using Ma´lekÕs procedure, it was concluded that the nonisothermal decomposition of NaHCO3 can be described by the following kinetic triplet: Ea = 92.1 kJmol-1, A=2.52 · 1010 min-1 and f(a)=a0.21(1 – a)1.08 (where M = 0.21 and N = 1.08 represent the mean values of SB kinetic parameters).[11] It was concluded that the increasing value of the kinetic parameter M indicates a more important role of the crystallized phase on the overall kinetics. On the other hand, a higher value of the kinetic parameter N (N > 1) indicates increasing complexity of the investigated process. However, the temptation to equate parameters M and N with a definite crystallization mechanism should be VOLUME 39B, FEBRUARY 2008—75
avoided, and too much physical significance should not be attached to the numerical values of what is essentially a phenomenological convenience. In particular, this warning applies to processes exhibiting a complex behavior, as in the case of nonisothermal decomposition of NaHCO3. In our previous article,[11] it was concluded that the complexity of the investigated decomposition process was probably connected with secondary nucleation of Na2CO3 for a £ 0.25 and with the overlapping of crystals in the process of growing for the conversions a ‡ 0.85. In this article, the new procedure for the determination of the density distribution functions of the apparent activation energies (ddfEas) (distributions of reactivity) at four different heating rates, for the nonisothermal decomposition proc
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