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  • 1 Departament of Chemistry, Inorganic Technology and Fuels, Silesian University of Technology, Krzywoustego 6, 44-100, Gliwice, Poland
  • | 2 Institute for Chemical Processing of Coal, Zamkowa 1, 41-803, Zabrze, Poland
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Abstract

For dehydration of CaC2O4·H2O and thermal dissociation of CaCO3 carried out in Mettler Toledo TGA/SDTA-851e/STARe thermobalance similar experimental conditions was applied: 9–10 heating rates, q = 0.2, 0.5, 1, 2, 3, 6, 12, 24, 30, and 36 K min−1, for sample mass 10 mg, in nitrogen atmosphere (100 ml min−1) and in Al2O3 crucibles (70 μl). There were analyzed changes of typical TGA quantities, i.e., T, TG and DTG in the form of the relative rate of reaction/process intended to be analyzed on-line by formula (). For comparative purposes, the relationship between experimental and equilibrium conversion degrees was used (for ). It was found that the solid phase decomposition proceeds in quasi-equilibrium state and enthalpy of reaction is easily “obscured” by activation energy. For small stoichiometric coefficients on gas phase side (here: ν = 1) discussed decomposition processes have typical features of phenomena analyzable by known thermokinetic methods.

Abstract

For dehydration of CaC2O4·H2O and thermal dissociation of CaCO3 carried out in Mettler Toledo TGA/SDTA-851e/STARe thermobalance similar experimental conditions was applied: 9–10 heating rates, q = 0.2, 0.5, 1, 2, 3, 6, 12, 24, 30, and 36 K min−1, for sample mass 10 mg, in nitrogen atmosphere (100 ml min−1) and in Al2O3 crucibles (70 μl). There were analyzed changes of typical TGA quantities, i.e., T, TG and DTG in the form of the relative rate of reaction/process intended to be analyzed on-line by formula (10). For comparative purposes, the relationship between experimental and equilibrium conversion degrees was used (for ). It was found that the solid phase decomposition proceeds in quasi-equilibrium state and enthalpy of reaction is easily “obscured” by activation energy. For small stoichiometric coefficients on gas phase side (here: ν = 1) discussed decomposition processes have typical features of phenomena analyzable by known thermokinetic methods.

Introduction

In the discussion on thermokinetic analysis of reaction/process of thermal decomposition of compounds undergoing destruction with observable weight loss:
1
(where the stoichiometric coefficient ν is sum of coefficients for gaseous products) an important problem is description of thermodynamic conditions under which experiments are carried out. Classic ‘single kinetic triplet’ f(α) or g(α)-E-A applies to thermokinetic conditions, not necessarily equilibrium. In all conditions, due to temperature (T) and pressure (P), appropriate laws determine equilibrium degree of conversion according to:
  1. (1)modified van ‘t Hoff's isobar for thermal dissociation of chemical compounds in solid state [15],
  2. (2)van Laar–Planck's isotherm [6, 7].
Reaction course in accordance with these laws causes that its determinant are thermodynamic quantities expressed by:
2
instead of ‘single kinetic triplet’.

It is proved that reaction enthalpy (ΔrH)—as an average quantity—is independent of temperature (T) and pressure (P), when P < 3 MPa [8].

In practice, in TGA analysis, the most commonly used is experimental degree of conversion (α) at a given temperature, which must be lower than equilibrium one (αeq) [911], but not always so.

A combination of both rights with regard to conditions (T, P) can be carried out using the basic relations for constant thermodynamic equilibrium of reaction:
3
where constant K for reaction (1) is expressed in the following manner:
4
In Eq. 4 one substitutes in accordance with Refs. [14]:
5
Using the similar procedure in Eq. 3 one obtains:
6

Identical results were presented in works [6, 7].

Finally, formula (6) is expressed as follows:
7

According to Eq. 7 intensive collection of gaseous products producing vacuum () moves equilibrium line αeq over the course deriving from isobaric conditions (4) together with (5).

It is common to carry out studies on thermal processes just in discussed way—the example is presented in Fig. 1 quoted from [12].

Fig. 1
Fig. 1

Seven experimental alpha (α)–temperature (T) curves for decomposition of calcium carbonate in nitrogen, obtained at different heating rates: 1, 3, 5, 7, 5, 10, 15, and 25 K min−1 (data acc. [12]) on the background of equilibrium relationship (23)

Citation: Journal of Thermal Analysis and Calorimetry J Therm Anal Calorim 107, 3; 10.1007/s10973-011-1909-7

Scope of the work

Basing on the analysis of thermal decomposition of two model chemical compounds (CaC2O4·H2O and CaCO3), often used as test substances, in inert atmosphere in dynamic conditions at different heating rates (q), own assessment of thermodynamic conditions of decomposition using the relative rate of reaction/process has been presented.

Basing on three-parametric equation [5], the relative rate of reaction/process was proposed for dynamic conditions [13], which results from considerations on the equilibrium course of chemical reaction of solid phase dissociation, when . It means that the term versus T should be constant, i.e., r = req = const. (r in K).

Therefore there was the study carried out, in which it was assumed that relationships r versus T will be analyzed without any data selection procedure in order to analyze graphic images obtained in dynamic conditions, electronically recording the course of thermal dissociation of selected two chemical compounds in the relation: mass versus temperature.

Assumptions

Assuming in Eq. 7 after differentiation towards temperature one obtains:
8
This result can be presented (by analogy), using equilibrium relative rate of reaction/process in the following way:
9

Equation 9 represents straight line parallel to temperature axis (T), limited by perpendicular at the point with coordinates [0, Teq] (e.g., see Fig. 3 in [14]).

It was assumed that experimental data can be directly measured by TGA [13, 15]:
10
where mi is initial mass (mg), DTG (mg K−1) and TG (mg).
The relative rate of reaction/process is linear relationship of correlated coefficients a1 and a2 [13]:
11
Coefficients a1 and a2 originate from equations:
(A) [5]:
12
or
(B) [16]:
13

Further considerations follow from comparison of temperature of maximum reaction rate Tm determined experimentally and calculated by formula (14).

According to Ref. [13] temperature of flex point (Tfp) in version [7] (formula (1–8) is identified with the Tm:
14
Another relationship is of thermodynamic-correlation nature and interconnects a1 and a2 by temperature Tr [16]:
15

According to Ref. [14], temperature Tr is represented by slope of straight lines (11) and (9). To some extent this is the analogue of isokinetic temperature, because (in theory) r = const. Analysis of experimental data consists in determination of linear relationships (11), while the relative rate of reaction/process is determined by formula (10). Next, formulas in forms (14) and (15) were used.

Each analysis of compounds (CaC2O4·H2O and CaCO3) was preceded by determination of activation energy according to modified Kissinger law in version [17]:
16
to confirm whether own data are within the range of data presented in literature.

The considerations were carried out in three areas: thermokinetic, thermodynamic, and relative rate. This approach follows from the fact that such considerations prevail in such order in literature.

The basic element of analysed thermoanalytical results consists in evaluation, whether the relative rate of reaction/process r calculated according to Eq. 10 versus T presents relationship (9), of which graphical image is rectangle area bounded by temperature Teq, or linear relationship (11) with a negative slope, expressed by coefficient a2.

Calcium oxalate monohydrate

Thermokinetics

Thermal decomposition of CaC2O4·H2O, especially at the initial stage of the process (dehydration) is still featured in both newer literature [1823] and own works [13, 17, 24]. An example of single kinetic triplet according to Ref. [21] is expressed as:
ea
and according to Ref. [17]:
eb
and from own results according to Eq. 16 was obtained:
17
i.e., E = 89.05 kJ mol−1, lnA = 15.845 (A in s−1).

Thermodynamics

Equation 9 is plotted on the basis of thermodynamic data for standard conditions:

  • T = 298.15 K and P ≈ 0.1 MPa for dehydration according to Ref. [18]:

  • ΔH = 36.4 kJ mol−1, (according to Ref. [25] enthalpy of vaporization of water in 298.15 K is 44.0 kJ mol−1)

  • ΔG = 2.2 kJ mol−1,

  • ΔCp = −10.2 J (K mol)−1—originates from summing up values: 298Cp, Table 1 in [18] and entropy in these conditions:

  • ΔS = 0.1147 kJ (K mol)−1 (acc. [26]: ΔS = 0.156 kJ (K mol)−1)

From these data, equilibrium temperature Teq (also called temperature of inversion) was determined iteratively from Gibbs–Helmholtz equation and Kirchhoff's law: when and
18
next: Teq = 317.4 K
which is to all intents and purposes consistent with the formula:
ec

From the calculations follows the average enthalpy of reaction in the temperature range of 298–318 K: ΔrH = 36.3 kJ mol−1. Figure 2 shows relationship between degree of conversion and temperature for ten heating rates, and Fig. 3—between the relative rate of reaction/process and temperature according to Eq. 10, giving the coefficient of determination (r2) with equilibrium line (9) limited by straight line Teq = 318 K (45 °C) for selected heating rates (q = 0.2, 3, and 30 K min−1).

Fig. 2
Fig. 2

Ten experimental alpha (α)–temperature (T) curves for dehydration of calcium oxalate monohydrate in nitrogen, obtained at different heating rates: 0.2, 0.5, 1, 2, 3, 6, 12, 18, 24, and 30 K min−1

Citation: Journal of Thermal Analysis and Calorimetry J Therm Anal Calorim 107, 3; 10.1007/s10973-011-1909-7

Fig. 3
Fig. 3

Relationship between the relative rate of reaction (r) and temperature (T) for dehydration of calcium oxalate monohydrate (3 of the 10 heating rates). Marked linear relationships (11) concerns selected experimental points

Citation: Journal of Thermal Analysis and Calorimetry J Therm Anal Calorim 107, 3; 10.1007/s10973-011-1909-7

Equilibrium relationship is as follows:
19
According to Eqs. 9 and 19 one obtains:
20

Equation 19 was determined on the basis of thermodynamic data [18] in standard conditions, T = 298 K, and thus, referring to Eq. 5, equilibrium conversion degree (for ν = 1) in natural way concerns this reference condition. Under these considerations, Eq. 19 should be regarded as acceptable estimation, assuming that in considered temperature range thermodynamic quantities are close to standard ones.

The difference can be attributed to slightly differing values of entropy. The issue, what may be surprising here, is the fact that this is thermodynamic or maximum value at given temperature and at atmospheric pressure P = 0.1 MPa. This does not mean that at T = 298 K, the decomposition occurs and is detectable, because in the way here may be conditions of kinetic nature, e.g., very slow evaporation or atmospheric equilibrium. For this reaction, ΔrH ≈ 36 kJ/mol is determined by the activation energy E = 80 kJ/mol (or higher) and by the heat of vaporization of water, more than 40 kJ/mol.

In turns, Fig. 4 shows experimental results that show straight lines (11). From Fig. 4 follows that each straight line (11) together with (20) intersect at a wide temperature range and not only at determined temperature Tr = 390.2 K. With the exception of q = 0.2 and 1 K min−1, each straight line (for q = 0.5, 2, 3, 6, 12, 18, 24, and 30 K min−1) intersects at higher temperature, i.e., 399 K.

Fig. 4
Fig. 4

Graphical presentation of linear relation r = a1a2T for dehydration of calcium oxalate monohydrate

Citation: Journal of Thermal Analysis and Calorimetry J Therm Anal Calorim 107, 3; 10.1007/s10973-011-1909-7

Relative rate

Table 1 presents calculated coefficients of Eq. 11 and temperature of maximum reaction rate Tm determined experimentally and calculated by Eq. 14Fig. 5 compares the two temperatures toward q.

Table 1

The results of calculations for dehydration of CaC2O4·H2O

Entryq/K min−1a1/Ka2Tm/K acc. to Eq. 14Tma/K
10.2255758 631.7388.8391.2
20.5140231 325.7406.7401.6
31 104803 233.3419.9412.9
42 48539 95.8455.2419.9
53 41190 77.4471.8430.3
66 31565 53.5510.3441.9
712 26579 40.9549.3454.8
818 24246 34.8580.6462.1
924 22163 29.8609.7467.8
1030 21049 27.1631.0472.8

Experimental value

Fig. 5
Fig. 5

Relationship between the temperature of the maximal rate of reaction (Tm) and heating rate (q) for dehydration of calcium oxalate monohydrate

Citation: Journal of Thermal Analysis and Calorimetry J Therm Anal Calorim 107, 3; 10.1007/s10973-011-1909-7

According to Fig. 2 experimental degrees of conversion α satisfy inequality αeq > α for all heating rates q, and according to Kissinger law (as well as in version (16)) temperatures of maximum reaction rate Tm increase with increasing heating rate q. However, from Fig. 3 follows that virtually all the points showing the relative rate of reaction r in terms of temperature are outside the rectangle (20). It demonstrates relative dynamic reaction course for small heating rates (according to Table 1) for q = 0.2, 0.5, 1 K min−1, moderated course (q = 1 and 3 K min−1) and close to equilibrium, when a2 < 100 for high heating rates (q ≥ 6 K min−1). Relativity of dynamics here means a reference to temperature, as well to maximum thermal rate (dα/dT) obtained at low heating rates (q), as to temperature ranges, in which conversion degree achieve the end of reaction (α → 1).

However, courses similar to the parallel (a2 = small) are greater in value than the expression req = ΔrH/νR = 4366.13 K and closer to the ratio E/R ≅ 10000 K.

Characteristic temperatures in these analyses are of very important control meaning, namely: Teq and Tm, Tf as well as Tr, which are determined experimentally. For large heating rates, thermal dissociation approaches to quasi-equilibrium with a large temperature shift of the final reaction temperature Tf in relation to Teq (Tf > Teq). Instead, for small heating rates high values of coefficient a2 are observed, what means that even for the lowest heating rate, often regarded as a pseudo-isothermal (q = 0.2 K min−1), occurs the largest deformation of the equilibrium distribution according to Eq. 7 by factor (Eq. 13), which gradually reaches value of 1 for a2 = 0 [16].

According to Fig. 5 and Table 1 the lower coefficient a2, the differences between fixed temperature Tm calculated by Eq. 14 become very large—only for large values of a2, so for very small heating rates formula (14) leads to values compatible with experiment.

Establishing the meaning of temperature Tr, for the data set in Table 1, Eq. 15 was determined:
21
what leads to Tr = 390.2 K.

Again, one may also note that constant term in Eq. 21 is much higher than the one resulting from enthalpy (req = 4366.13 K)—the same observation is included in Ref. [16].

Calcium carbonate (calcite)

Thermokinetics

Calcium carbonate was within the frame of the project described in the report [12]—the results were analyzed and discussed further in subsequent works [2729], and then in Ref. [16] in terms of significance of Eqs. (1213). Results of studies on thermal dissociation of CaCO3 discussed at the ICTAC Conference [12, 2729], also summarized in Tables 1 and 2 in Ref. [16], were used applying Kissinger law in version (16).

It was obtained:

  1. for decomposition in nitrogen: E = 201.0 kJ mol−1, ln A = 13.46 (A in s−1) (r2 = 0.9865, sl = 0.00001), according to Ref. [12] similar values was obtained by H. O. Desseyn: ln A = 13.58 (A in s−1) and E = 199 kJ mol−1, but only in this one case),
  2. for decomposition in vacuum: E = 111.9 kJ mol−1, ln A = 6.05 (A in s−1) (r2 = 0.9435, sl = 0.00122)—in Ref. [12] several pairs are similar.
Next, own data analyzed according to Eq. 16 lead to equation:
22

Relationship between conversion degree and temperature at variable heating rates and on the background of equilibrium conversion degree is presented in Fig. 6.

Fig. 6
Fig. 6

Nine experimental alpha (α)–temperature (T) curves for decomposition of calcium carbonate in nitrogen, obtained at different heating rates: 0.2; 0.5; 1; 3; 6; 12; 24; 30 and 36 K min−1

Citation: Journal of Thermal Analysis and Calorimetry J Therm Anal Calorim 107, 3; 10.1007/s10973-011-1909-7

Thermodynamics

Equilibrium relationship for calcite was taken from Ref. [16] (ΔrH = 174.9 kJ mol−1):
23
that is:
24

Compared to the ICTAC data presented in Fig. 1, results of these studies (Fig. 6) point to an even greater shift of experimental curves of conversion degree α to the left in relation to the equilibrium curve (7) for , i.e. αeq < α.

Relative rate

In Ref. [16], it was found that a2 coefficients are: for decomposition in nitrogen a2 = 208 → 63 and for heating rate q = 1–25 K min−1 (Table 1 in Ref. [16]), but they are much lower in case of decomposition in vacuum: a2 = 661–317, q = 1.8 to 10 K min−1 (Table 2 in Ref. [16]).

Figure 7 presents—similarly as in Fig. 3—relationships of the relative rate of reaction/process according to Eq. 10, giving determination coefficient (r2) together with the equilibrium line (23) limited by Teq = 1162.7 K. Table 2 compiles determined coefficients of linear relationship (11) and temperature Tm (experimental) calculated by Eq. 14.

Fig. 7
Fig. 7

Relationship between the relative rate of reaction (r) and temperature (T) for decomposition of calcium carbonate. Marked relationships (11) concerns selected experimental points, for which (r2) reached the highest value (even for r2 = 0.2232, sl = 0.05, together with increase of q: r2 → 1)

Citation: Journal of Thermal Analysis and Calorimetry J Therm Anal Calorim 107, 3; 10.1007/s10973-011-1909-7

Table 2

The results of calculations for thermal dissociation of CaCO3

Entryq/K min−1a1/Ka2Tm/K acc. to Eq. (14)Tma/K
10.256644 34.91064.7876.7
20.550285 26.01087.3902.7
31 53636 29.01109.5925.7
43 82805 59.31140.1964.0
56 113190 88.71142.0996.0
612 96902 71.11202.61019.7
724 92751 65.11248.81048.5
830 89552 61.61270.21063.8
936 89622 61.01282.41068.2

Experimental value

In Fig. 7 was indicated temperature Tr following from Eq. 25, because it relates to small values of a2 and thus exposes range closer to equilibrium. Figure 8 presents again data from Fig. 7, where straight lines (11) present experimental results.

Fig. 8
Fig. 8

Graphical presentation of linear relation r = a1a2T for decomposition of calcium carbonate

Citation: Journal of Thermal Analysis and Calorimetry J Therm Anal Calorim 107, 3; 10.1007/s10973-011-1909-7

Coefficients a1 and a2 satisfy linear relationship (Fig. 9):
25
which determines Tr = 1043.4 K. Previous analyses given in Ref. [16] set different coefficients of relationship (11):
26
Fig. 9
Fig. 9

Relation between coefficients: a1 versus a2 for decomposition of calcium carbonate

Citation: Journal of Thermal Analysis and Calorimetry J Therm Anal Calorim 107, 3; 10.1007/s10973-011-1909-7

From Fig. 8 follows that each straight line (11) together with (24) intersect at a wide temperature range, and not only at determined temperature Tr. We note again that constant term in Eq. 25 is higher than the one resulting from enthalpy (req = 21039.6 K).

Referring to Table 2, it was again established that for small values of a2 experimental temperature Tm is much lower than the one calculated by Eq. 14. Observed thermal dissociation of CaCO3 can be defined as proceeding under quasi-equilibrium conditions in relation to anticipated range of characteristic temperature according to Eq. 7 for . Maybe this is the reason of observing more chaotic arrangement of points of Fig. 8 in comparison to Fig. 4. Approximately, when a2 → 0, then Eq. 13 simplifies to relationship known as temperature criterion [24, 30]: ln α = const. − E/RT, then ΔrHE.

Discussion

The results of investigations on thermal dissociation of two chemical substances frequently used as test compounds (standards) in thermal analysis:

  1. dehydration of CaC2O4·H2O,
  2. thermal decomposition of CaCO3 (calcite).

The investigations were carried out under identical test conditions. Previously, trial and error method was used for selection of experimental conditions—mainly heating rates, nitrogen flow, crucibles—in order to a2 ratio was greater than 100. According to Tables 1 and 2 in case of calcite, it was manage to get it completely, but for dehydration of oxalate—only in a large extent.

Observing the experimental conversion degrees α toward temperature profile T, one may conclude that both compounds behave differently in relation to the equilibrium curves:

  1. dehydration proceeds under curve resulting from relationship (19), α < αeq,
  2. thermal dissociation of carbonate proceeds above relationship (22), α > αeq.

In detailed studies, the relative rate of reaction/process was explicitly determined from experimental data according to the formula (10), i.e., using T, TG, DTG, and mi—deliberately it was not used the option of smoothing by Savitzky–Golay method [31], which very useful for studies of complex organic mixtures such as coal tar pitches [15].

In the range of 0 < α < 0.05–0.1 one always must take into account the occurrence of oscillations arising from expression appearing in formula (10) by the ratio −DTG/TG ∝ dα/αdT, i.e., one is close to an indeterminate form 0/0 and using filters of type [31] does not help much here.

What is puzzling, however, is how are observed such differences between temperatures of maximum reaction rate, determined experimentally and calculated by Eq. 14. Substituting empirical relationship (15) to the formula (14) yields:
27
For a2 = 0 (and small values):
28
when a2 is large, then according to Ref. [16]
29
what, on the basis of this studies, means approaching to compliance of both temperatures Tm and Teq.

Returning to the Eq. 28 is easy to notice that one obtains this formula, if both Eq. 8 and condition dαeq/dT = 0 are used, thus this is the maximum occurring far beyond the scale where αeq ⋙ 1 (compare with Ref. [32]). For these reasons, the differences [ΔrH/2νR − (Tm)exp] must be very large, and they decreases, when a2 = large.

Thus, one may note that the quasi-equilibrium conditions prevent accurate determination of enthalpy of reaction ΔrH, because dynamic conditions directly dictate relationships dominated by activation energy E. Thermal analyses of complex organic compounds in the form of salts containing anion halogens (Cl, Br and J), as described by Błażejowski et al. [3, 4, 3336], behave differently due to the formation of a significant volume of gas (ν ≥ 2). These compounds are characterized by thermal decomposition, combined with the total volatilization of gaseous products. From this comparison, one may even get the feeling that the presence of solid phase (ν = 1) inhibits the process of destruction and it is necessary helping it through physical occurrence (vacuum, intense collection of gaseous products, volatilization).

Conclusions

  1. 1.On the basis of dehydration of calcium oxalate monohydrate and thermal dissociation of calcium carbonate (calcite) in specially selected conditions, it was found that the reactions proceed in a quasi-equilibrium conditions in relation to modified van ‘t Hoff's isobars expressed by Eq. 7 when . In the case of CaCO3 were observed small values of coefficient a2 (maximum a2 = 88.65), and the experimental curves of conversion degree toward temperature profile satisfy the relation α > αeq, what means an intense collection of gaseous product from reaction zone and, in consequence, Teq > Tf. In the case of dehydration of CaC2O4·H2O were observed very intensive courses for small heating rates q = 0.2 to 1 K min−1, what also translates to deformation equilibrium curve (7) by significant factor (Eq. 13), but at higher heating rates also importance of a2 decreases. The reference to equilibrium decomposition is consistent with expectations, because α<αeq.
  2. 2.Quasi-equilibrium conditions prevent precise determination of enthalpy of reaction (ΔrH), because dynamic conditions impose relationships dominated by activation energy (E). Despite the very significant correlation between coefficients a1 and a2 (see Refs. [3740]), the constant term in Eq. 15 is however greater than the expression (ΔrH/νR). For two reaction analysed in current paper it was not obtained values of a2 = 0 and at the same time Tf = Teq. Temperature Tr, which is an analogue of isokinetic temperature according to Arrhenius law (here: r = req = const.), may be determined by correlation—Figs. 4 and 8 indicate that the effect of convergence in one point (for one coordinate) is blurred. It should, however, be borne in mind that similar situation also concerns isokinetic temperature in isokinetic/compensation effect—for example in Ref. [41].
  3. 3.Formula (14)—characteristic for the model of relative rate of reaction/process (12, 13) and (11) becomes less important, when a2 = 0 or a2 = small for calculation of Tm.
  4. 4.In the case of dehydration of CaC2O4·H2O at low heating rates q = 0.2–1 K min−1 is observed high dynamics of decomposition determined by coefficient a2. It disappears at higher heating rates, approaching values close to but higher than req = 4366.13 K (formula (20)), but significantly shifted above equilibrium temperature above TfTeq. This effect is related to phase transformation of the reaction product—water that goes into the gas phase with a variable rate depending on the time and temperature. At lower temperature, but during the very long time (q = 0.2 K min−1), there are more favorable conditions for the evacuation of water from solid surface. In a very short time (high heating rate q ≥ 6 K min−1) high temperatures are necessary.
  5. 5.Formula (10) is very simple and enables on-line analysis, and in particular its linear relationship with temperature (11) becomes clearer with increasing heating rate q.

Experimental methodology

Thermal decomposition of calcium oxalate monohydrate CaC2O4·H2O (Aldrich, Cat. No. 28,984-1) and calcium carbonate CaCO3 (Mettler—Test Sample) was carried out using Mettler Toledo TGA/SDTA-851e/STARe, for weight samples of 10 mg, in atmosphere of nitrogen (100 ml min−1), in Al2O3 crucible (70 μl), for 10 heating rates: q = 0.2; 0.5; 1; 2; 3; 6; 12; 18; 24 and 30 K min−1 (in the case of CaC2O4·H2O) and for 9 heating rates: q = 0.2; 0.5; 1; 3; 6; 12; 24; 30 and 36 K min−1 (in case of CaCO3).

Temperatures indicated in the text by T relate to temperature of the reacting sample.

In relation to ICTAC research [12, 2729] the scope of research was broadened on both lower (q = 0.2 K min−1—it is treated as pseudo-isothermal conditions) and higher heating rates (q = 36 K min−1).

List of symbols

Variables
α

Conversion degree, 0 ≤ α ≤ 1

αeq

Equilibrium conversion degree, 0 ≤ αeq ≤ 1, P = const

αeq

Equilibrium conversion degree, 0 ≤ αeq ≤ 1, T, P = var

a0, a1 and a2

Coefficients of three-parametric equation, acc. to Eq. 12

A

Pre-exponential factor in Arrhenius equation, s−1

ΔCp

Heat capacity of reaction, J (K mol)−1

E

Activation energy, J mol−1

f(α) and g(α)

Kinetic functions toward conversion degree α

ΔrH

Average reaction enthalpy, J mol−1

ΔG

Free enthalpy, J mol−1

ΔS

Entropy, J (K mol)−1

K

Thermodynamic equilibrium constant

mi

Initial mass of sample, mg

P

Pressure, Pa

Standard pressure,

q

Heating rate, K min−1

r

Relative rate of reaction/process, K

R

Universal gas constant, R = 8,314 J (K mol)−1

T

Temperature, K

Tr

Temperature–slope in Eq. 15, K

Teq

Equilibrium temperature for αeq = 1, , K

ν

Stoichiometric coefficient

Statistical symbols
r2

Determination coefficient for linear function, 0 ≤ r2 ≤ 1

sl

Significance level

Subscripts
298

Standard state

α

Equilibrium conversion degree

eq

Equilibrium state

exp

Experimental

f

Final state

fp

Flex point

i

Initial state

m

Point of the maximal rate of reaction/process

r

Reaction

We feel grateful to Dr. Wojciech Balcerowiak from ICSO “Blachownia” (Kędzierzyn-Koźle, Poland) for providing the results of the investigations for a series of chemical compounds and thermal decomposition of calcium carbonate and calcium oxalate monohydrate.

References

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  • 7. Mianowski, A. Consequences of Holba-Šesták equation. J Therm Anal Calorim. 2009;96:507513. .

  • 8. Szarawara J , Piotrowski J. Theoretical foundations of chemical technology. Warszawa: WN; 2010. p. 151156. (in Polish).

  • 9. Šesták J . Heat, Thermal analysis and society. Czech Republic: Nucleus HK; 2004. p. 210.

  • 10. Holba, P, Šesták, J. Kinetics with regard to the equilibrium processes studied by nonisothermal technique. Z für Phys Chemie Neue Folge. 1972;80:120. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 11. Czarnecki, J, Šesták, J. Practical thermogravimetry. J Therm Anal Calorim. 2000;60:759778. .

  • 12. Brown, ME, Maciejewski, M, Vyazovkin, S, Nomen, R, Sempere, J, Burnham, A, Opfermann, J, Strey, R, Anderson, HL, Kemmler, A, Keuleers, R, Janssens, J, Desseyn, HO, Chao-Rui, L, Tang, TB, Roduit, B, Málek, J, Mitsuhashi, T. Computational aspects of kinetic analysis: Part A: the ICTAC kinetics project-data, methods and results. Thermochim Acta. 2000;355:125143. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 13. Mianowski, A. Analysis of the thermokinetics under dynamic conditions by relative rate of thermal decomposition. J Therm Anal Calorim. 2001;63:765776. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 14. Mianowski, A, Bigda, R. Thermodynamic interpretation of three-parametric equation: Part II: the relative rate of reaction. J Therm Anal Calorim. 2003;74:433442. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 15. Mianowski, A, Robak, Z, Bigda, R, Łabojko, G. Relative rate of reaction/process under dynamic conditions as the effect of TG/DTG curves transformation in thermal analysis. Przemysł Chemiczny. 2010;89:780785. (in Polish).

    • Search Google Scholar
    • Export Citation
  • 16. Mianowski, A, Baraniec, I. Three-parametric equation in evaluation of thermal dissociation of reference compound. J Therm Anal Calorim. 2009;96:179187. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 17. Mianowski, A, Bigda, R. The Kissinger law and isokinetic effect: Part II: experimental analysis. J Therm Anal Calorim. 2004;75:355372. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 18. Rak, J, Skurski, P, Gutowski, M, Błażejowski, J. Thermodynamics of the thermal decomposition of calcium oxalate monohydrate examined theoretically. J Therm Anal. 1995;43:239246. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 19. Kutaish, N, Aggarwal, P, Dollimore, D. Thermal analysis of calcium oxalate samples obtained by various preparative routes. Thermochim Acta. 1997;297:131137. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 20. Gao, Z, Amasaki, I, Nakada, M. A description of kinetics of thermal decomposition of calcium oxalate monohydrate by means of the accommodated Rn model. Thermochim Acta. 2002;385:95103. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 21. Liqing, L, Donghua, C. Application of iso-temperature method of multiple rate to kinetic analysis. J Therm Anal Calorim. 2004;78:283293. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 22. Frost, RL, Weier, ML. 2004 Thermal treatment of whewellite—thermal analysis and Raman spectroscopic study. Thermochim Acta. 409:7985. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 23. Vlaev, L, Nedelchev, N, Gyurova, K, Zagorcheva, M. A comparative study of non-isothermal kinetics of decomposition of calcium oxalate monohydrate. J Anal Appl Pyrolysis. 2008;81:253262. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 24. Mianowski, A, Radko, T. The possibility of identification of activation energy by means of the temperature criterion. Thermochim Acta. 1994;247:389405. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 25. Barin, I. Thermochemical data of pure substances, Vol. 1. Weinheim: VCH Verlagsgesellschaft; 1989 649650.

  • 26. Latimer, WM, Schutz, PW, JFG Hicks Jr. The heat capacity and entropy of calcium oxalate from 19 to 300° absolute. The entropy and free energy of oxalate ion. J Am Chem Soc. 1933;55:971975. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 27. Maciejewski, M. Computational aspects of kinetic analysis: part B: the ICTAC Kinetics Project—the decomposition kinetics of calcium carbonate revisited, or some tips on survival in the kinetic minefield. Thermochim Acta. 2000;355:145154. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 28. Burnham, AK. Computational aspects of kinetic analysis: part D: the ICTAC kinetics project-multi-thermal-history model-fitting methods and their relation to isoconversional methods. Thermochim Acta. 2000;355:165170. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 29. Roduit, B. Computational aspects of kinetic analysis: part E: the ICTAC kinetics Project—numerical techniques and kinetics of solid state processes. Thermochim Acta. 2000;355:171180. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 30. Ortega, A. The incorrectness of the temperature criterion. Thermochim Acta. 1996;276:189198. .

  • 31. Savitzky, A, Golay, MJE. Smoothing and differentiation of data by simplified least-squares procedures. Anal Chem. 1964;36:16271639. .

  • 32. Mianowski, A. The Kissinger law and isokinetic effect. J Therm Anal Calorim. 2003;74:953973. .

  • 33. Błażejowski, J. Thermal properties of amine hydrochlorides. Part I. Thermolysis of primary n-alkylammonium chlorides. Thermochim Acta. 1983;68:233260. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 34. Łubkowski, J, Błażejowski, J. Thermal properties and thermochemistry of alkanaminium bromides. Thermochim Acta. 1990;157:259277. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 35. Thanh, HV, Gruzdiewa, L, Rak, J, Błażejowski, J. Thermal behaviour and thermochemistry of hexachlorozirconates of mononitrogen aromatic bases. Thermochim Acta. 1993;230:269292. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 36. Janiak, T, Rak, J, Błażejowski, J. Thermal features and thermochemistry of hexachlorohafnates of nitrogen aromatic bases. Theoretical studies on the geometry and thermochemistry of HfCl6 2−. J Therm Anal. 1995;43:231237. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 37. Mianowski, A, Siudyga, T. Thermal analysis of polyolefin and liquid paraffin mixtures. J Therm Anal Calorim. 2003;74:623630. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 38. Mianowski, A, Błażewicz, S, Robak, Z. Analysis of the carbonization and formation of coal tar pitch mesophase under dynamic conditions. Carbon. 2003;41:24132424. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 39. Mianowski, A, Bigda, R, Zymla, V. Study on kinetics of combustion of brick-shaped carbonaceous materials. J Therm Anal Calorim. 2006;84:563574. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 40. Mianowski, A, Siudyga, T. Influence of sample preparation on thermal decomposition of wasted polyolefins-oil mixtures. J Therm Anal Calorim. 2008;92:543552. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 41. Owczarek M , Mianowski A. The influence of oxygen upon reactivity of chars in the presence of steam. In: Chemical technology at the turn of century. Gliwice: SKKTChem, Silesian University of Technology; 2000. p. 535538.

    • Search Google Scholar
    • Export Citation
  • 1. Kowalewska, E, Błażejowski, J. Thermochemical properties of H2SnCl6 complexes. Part I. Thermal behaviour of primary n-alkylammonium hexachlorostannates. Thermochim Acta. 1986;101:271289. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 2. Janiak, T, Błażejowski, J. Thermal features, thermochemistry and kinetics of the thermal dissociation of hexachlorostannates of aromatic mono-amines. Thermochim Acta. 1989;156:2743. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 3. Janiak, T, Błażejowski, J. Thermal features, thermolysis and thermochemistry of hexachlorostannates of some mononitrogen aromatic bases. Thermochim Acta. 1990;157:137154. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 4. Dokurno, P, Łubkowski, J, Błażejowski, J. Thermal properties, thermolysis and thermochemistry of alkanaminium iodides. Thermochim Acta. 1990;165:3148. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 5. Mianowski, A. Thermal dissociation in dynamic conditions by modeling thermogravimetric curves using the logarithm of conversion degree. J Therm Anal Calorim. 2000;59:747762. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 6. Mianowski, A, Bigda, R. Thermodynamic interpretation of three-parametric equation; Part I. New from of equation. J Therm Anal Calorim. 2003;74:423432. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 7. Mianowski, A. Consequences of Holba-Šesták equation. J Therm Anal Calorim. 2009;96:507513. .

  • 8. Szarawara J , Piotrowski J. Theoretical foundations of chemical technology. Warszawa: WN; 2010. p. 151156. (in Polish).

  • 9. Šesták J . Heat, Thermal analysis and society. Czech Republic: Nucleus HK; 2004. p. 210.

  • 10. Holba, P, Šesták, J. Kinetics with regard to the equilibrium processes studied by nonisothermal technique. Z für Phys Chemie Neue Folge. 1972;80:120. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 11. Czarnecki, J, Šesták, J. Practical thermogravimetry. J Therm Anal Calorim. 2000;60:759778. .

  • 12. Brown, ME, Maciejewski, M, Vyazovkin, S, Nomen, R, Sempere, J, Burnham, A, Opfermann, J, Strey, R, Anderson, HL, Kemmler, A, Keuleers, R, Janssens, J, Desseyn, HO, Chao-Rui, L, Tang, TB, Roduit, B, Málek, J, Mitsuhashi, T. Computational aspects of kinetic analysis: Part A: the ICTAC kinetics project-data, methods and results. Thermochim Acta. 2000;355:125143. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 13. Mianowski, A. Analysis of the thermokinetics under dynamic conditions by relative rate of thermal decomposition. J Therm Anal Calorim. 2001;63:765776. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 14. Mianowski, A, Bigda, R. Thermodynamic interpretation of three-parametric equation: Part II: the relative rate of reaction. J Therm Anal Calorim. 2003;74:433442. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 15. Mianowski, A, Robak, Z, Bigda, R, Łabojko, G. Relative rate of reaction/process under dynamic conditions as the effect of TG/DTG curves transformation in thermal analysis. Przemysł Chemiczny. 2010;89:780785. (in Polish).

    • Search Google Scholar
    • Export Citation
  • 16. Mianowski, A, Baraniec, I. Three-parametric equation in evaluation of thermal dissociation of reference compound. J Therm Anal Calorim. 2009;96:179187. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 17. Mianowski, A, Bigda, R. The Kissinger law and isokinetic effect: Part II: experimental analysis. J Therm Anal Calorim. 2004;75:355372. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 18. Rak, J, Skurski, P, Gutowski, M, Błażejowski, J. Thermodynamics of the thermal decomposition of calcium oxalate monohydrate examined theoretically. J Therm Anal. 1995;43:239246. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 19. Kutaish, N, Aggarwal, P, Dollimore, D. Thermal analysis of calcium oxalate samples obtained by various preparative routes. Thermochim Acta. 1997;297:131137. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 20. Gao, Z, Amasaki, I, Nakada, M. A description of kinetics of thermal decomposition of calcium oxalate monohydrate by means of the accommodated Rn model. Thermochim Acta. 2002;385:95103. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 21. Liqing, L, Donghua, C. Application of iso-temperature method of multiple rate to kinetic analysis. J Therm Anal Calorim. 2004;78:283293. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 22. Frost, RL, Weier, ML. 2004 Thermal treatment of whewellite—thermal analysis and Raman spectroscopic study. Thermochim Acta. 409:7985. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 23. Vlaev, L, Nedelchev, N, Gyurova, K, Zagorcheva, M. A comparative study of non-isothermal kinetics of decomposition of calcium oxalate monohydrate. J Anal Appl Pyrolysis. 2008;81:253262. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 24. Mianowski, A, Radko, T. The possibility of identification of activation energy by means of the temperature criterion. Thermochim Acta. 1994;247:389405. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 25. Barin, I. Thermochemical data of pure substances, Vol. 1. Weinheim: VCH Verlagsgesellschaft; 1989 649650.

  • 26. Latimer, WM, Schutz, PW, JFG Hicks Jr. The heat capacity and entropy of calcium oxalate from 19 to 300° absolute. The entropy and free energy of oxalate ion. J Am Chem Soc. 1933;55:971975. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 27. Maciejewski, M. Computational aspects of kinetic analysis: part B: the ICTAC Kinetics Project—the decomposition kinetics of calcium carbonate revisited, or some tips on survival in the kinetic minefield. Thermochim Acta. 2000;355:145154. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 28. Burnham, AK. Computational aspects of kinetic analysis: part D: the ICTAC kinetics project-multi-thermal-history model-fitting methods and their relation to isoconversional methods. Thermochim Acta. 2000;355:165170. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 29. Roduit, B. Computational aspects of kinetic analysis: part E: the ICTAC kinetics Project—numerical techniques and kinetics of solid state processes. Thermochim Acta. 2000;355:171180. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 30. Ortega, A. The incorrectness of the temperature criterion. Thermochim Acta. 1996;276:189198. .

  • 31. Savitzky, A, Golay, MJE. Smoothing and differentiation of data by simplified least-squares procedures. Anal Chem. 1964;36:16271639. .

  • 32. Mianowski, A. The Kissinger law and isokinetic effect. J Therm Anal Calorim. 2003;74:953973. .

  • 33. Błażejowski, J. Thermal properties of amine hydrochlorides. Part I. Thermolysis of primary n-alkylammonium chlorides. Thermochim Acta. 1983;68:233260. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 34. Łubkowski, J, Błażejowski, J. Thermal properties and thermochemistry of alkanaminium bromides. Thermochim Acta. 1990;157:259277. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 35. Thanh, HV, Gruzdiewa, L, Rak, J, Błażejowski, J. Thermal behaviour and thermochemistry of hexachlorozirconates of mononitrogen aromatic bases. Thermochim Acta. 1993;230:269292. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 36. Janiak, T, Rak, J, Błażejowski, J. Thermal features and thermochemistry of hexachlorohafnates of nitrogen aromatic bases. Theoretical studies on the geometry and thermochemistry of HfCl6 2−. J Therm Anal. 1995;43:231237. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 37. Mianowski, A, Siudyga, T. Thermal analysis of polyolefin and liquid paraffin mixtures. J Therm Anal Calorim. 2003;74:623630. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 38. Mianowski, A, Błażewicz, S, Robak, Z. Analysis of the carbonization and formation of coal tar pitch mesophase under dynamic conditions. Carbon. 2003;41:24132424. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 39. Mianowski, A, Bigda, R, Zymla, V. Study on kinetics of combustion of brick-shaped carbonaceous materials. J Therm Anal Calorim. 2006;84:563574. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 40. Mianowski, A, Siudyga, T. Influence of sample preparation on thermal decomposition of wasted polyolefins-oil mixtures. J Therm Anal Calorim. 2008;92:543552. .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 41. Owczarek M , Mianowski A. The influence of oxygen upon reactivity of chars in the presence of steam. In: Chemical technology at the turn of century. Gliwice: SKKTChem, Silesian University of Technology; 2000. p. 535538.

    • Search Google Scholar
    • Export Citation

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Journal of Thermal Analysis and Calorimetry
Language English
Size A4
Year of
Foundation
1969
Volumes
per Year
4
Issues
per Year
24
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 1388-6150 (Print)
ISSN 1588-2926 (Online)

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