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Standard enthalpy, entropy and Gibbs free energy of formation of «A» type carbonate phosphocalcium hydroxyapatites
Accepted Manuscript Standard enthalpy, entropy and Gibbs free energy of formation of « A » type carbonate phosphocalcium hydroxyapatites Sonia Jebri, Ismail Khattech, Mohamed Jemal PII: DOI: Reference:
S0021-9614(16)30343-3 http://dx.doi.org/10.1016/j.jct.2016.10.035 YJCHT 4865
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J. Chem. Thermodynamics
Received Date: Revised Date: Accepted Date:
11 April 2016 7 October 2016 22 October 2016
Please cite this article as: S. Jebri, I. Khattech, M. Jemal, Standard enthalpy, entropy and Gibbs free energy of formation of « A » type carbonate phosphocalcium hydroxyapatites, J. Chem. Thermodynamics (2016), doi: http:// dx.doi.org/10.1016/j.jct.2016.10.035
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Standard enthalpy, entropy and Gibbs free energy of formation of «A» type carbonate phosphocalcium hydroxyapatites Sonia Jebri1
Ismail Khattech2*
Mohamed Jemal2
1
Research Centre and Water Technology, Natural Water Treatment Laboratory, Borj Cédria BP 273, 8020 Soliman, Tunisia; 2 Université de Tunis El Manar, Faculty of Science, Chemistry Department, Materials Cristal Chemistry and Applied Thermodynamics Laboratory LR15SE01, 2092 Tunis, Tunisia; *Corresponding author: Ismail Khattech. E-mail adresses: [email protected]. Tel.: +216 98 208 884. Journal of Chemical Thermodynamics ABSTRACT «
A» type carbonate phosphocalcium hydroxyapatites having the general formula Ca10(PO 4)6(OH)(2-2x)(CO3)x with
0≤x≤1, were prepared by solid gas reaction in the temperature range of 700-1000°C. The obtained materials were characterized by X-ray diffraction and infrared spectroscopy. The carbonate content has been determined by CH-N analysis. The heat of solution of these products was measured at T = 298 K in 9 wt% nitric acid solution using an isoperibol calorimeter. A thermochemical cycle was proposed and complementary experiences were performed in order to access to the standard enthalpies of formation of these phosphates. The results were compared to those previously obtained on apatites containing strontium and barium and show a decrease with the carbonate amount introduced in the lattice. This quantity becomes more negative as the ratio of substitution increases. Estimation of the entropy of formation allowed the determination of standard Gibbs free energy of formation of these compounds. The study showed that the substitution of hydroxyl by carbonate ions contributes to the stabilisation of the apatite structure. Keywords:
Carbonate hydroxyapatites
formation
Entropy of formation
Isoperibol calorimeter
Heat of solution Enthalpy
of
Gibbs free energy of formation
1. Introduction Apatites are a large class of mineral compounds with the general formula M10(XO4)6Y2, where M is generally a divalent cation (Ca2+, Sr2+, Ba2+, Pb2+, etc), XO4 is a trivalent or tetravalent anion (PO 43-, VO43-, AsO43-, SiO44-, etc) and Y can be a halide, hydroxyl or carbonate group. They form the major part of sedimentary phosphates ores. Due to a chemical composition close to that of the mineral part of calcified tissues [1,2], phosphocalcium hydroxyapatite, Ca10(PO4)6(OH)2, has proved to be an attractive material for biological applications and medical purposes [3,4]. It is commonly used as a bone substitute [5-7] despite the presence of carbonate in the bony apatite [8,9]. Hydroxyapatite crystallizes in P63/m space group with OH groups located on six fold helicoidal axis. Incorporation of carbonate ion in hydroxyapatite can occur in two different sites replacing either OH- or PO43-, leading to «A» or «B» type carbonate apatite respectively [10,11]. The physico-chemical properties of these
1
materials are highly affected by the carbonate localization and the chemical composition. In this context, many studies have been devoted to synthesis, structural analyses and thermal stability of carbonated and noncarbonated hydroxyapatites [12-24]. For non-carbonated apatites, a recent paper recapitulates an overview of the available thermodynamic data [25]. Indeed these studies show a decrease in stability versus the size of alkaline earth cations substituting Ca2+ in the apatitic edifice such as Sr2+ or Ba2+. For carbonated compounds, the stability is reduced by the incorporation of CO32-ions in PO4 3- sites [15], while such substitution in OH- sites seams to increase the stability of apatites containing strontium and barium [12,13]. The present paper is a continuation of two previous ones performed on the solid solutions M10(PO4)6(OH)(22x)(CO3)x,
with 0≤x≤1 and M = Sr2+ and Ba2+ [12,13] and deals with synthesis, characterization and
thermochemical study of similar carbonate phosphocalcium hydroxyapatites.
2. Synthesis «
A» type carbonate apatites (A-CO3-Hap) were prepared in tow steps. The first one consists in synthesizing
phosphocalcium hydroxyapatite Ca10(PO4)6(OH)2 by double decomposition in aqueous medium. Experiments consist in adding, drop by drop, during 90 minutes, a solution of diammonium hydrogen phosphate (0.31 M) into a boiling solution of calcium nitrate (0.12 M) [26]. The precipitation pH has been adjusted to about 11 by adding ammonia solution (28 wt%). The obtained precipitate was washed and dried during 12 hours at 70°C, then ignited at 800°C for 24 hours under wet Argon atmosphere (PH2O = 0.47105 Pa). The synthesis can be schematized by the following reaction: 10 ( ) + 6 ( ) + 8 → ( ) () + 20 + 6 The purity and crystallinity of the obtained samples were checked by X-ray diffraction and IR spectroscopy. The second synthesis step consists in heating calcium hydroxyapatite in CO2 gas flow. Various amounts of carbonate were introduced in the lattice by varying the time of gas flowing (from half an hour to ten days) and the temperature of synthesis (from 700 to 1000°C). Carbonatation occurred according to the following reaction: ( ) () () + () → ( ) ()( ) ( ) () + () The reagents used are of analytical quality. The chemical formula, provenance and mass fraction purity of each compound used for the synthesis and during the calorimetric study are reported in Table 1. Table 1
3. Characterization Control of purity of the synthesized products was achieved by X-ray diffraction and infrared spectroscopy. Determination of carbonate amount was performed by C-H-N analysis.
2
3.1. IR spectroscopy Infrared experiments were performed on pellets obtained by mixing 1.5 mg of the product in 300 mg of KBr for IR spectroscopy. The spectra were recorded between 400 and 4000 cm-1 using a Perkin-Elmer 7700 FT-IR spectrometer. They exhibit the characteristic absorbance bands of carbonate groups substituting hydroxyl ions in the tunnel, which appear at 879, 1460 and 1549 cm-1, confirming the formation of A-CO3-Hap [10]. Superposition of spectrum of apatites having the compositions 0.394, 0.578 and 0.840 mol of carbonate per unit cell is given in Fig. 1. They show that the higher the carbonate content, the higher is the intensity of the corresponding bands. One can also notice a decrease of absorbance band of hydroxyl (3572 cm-1) when carbonate is introduced in the lattice. Fig. 1 3.2. X-ray diffraction X-ray diffraction patterns have been recorded on the samples with a D8 ADVANCE Bruker diffractometer using copper radiations (Kα1 = 1.5406 Å; Kα2 = 1.5445 Å). Fig. 2 shows examples of well-crystallized phases of carbonated and non-carbonated hydroxyapatites. The lattice parameters of the structure were refined by ‘‘ERACEL’’ program and reported in Table 2. One can notice an increase of “a” parameter and a slight variation of “c” when introducing carbonate. Fig. 2 Table 2 Fig. 3 shows the variation of the lattice parameters versus the rate of carbonate substitution ‘x’. Because of the slight variation of ‘‘c’’, the variation of ‘‘a’’ induces a similar variation of the lattice volume. Fig. 3
3.3. Elemental analysis of Carbon The carbonate content of the preheated powders was measured by C-H-N analysis (JOBIN YVON HORIBA); the lower limit of detection was less than 0.01 wt%. About 40 mg of the sample was heated at 1800°C under O2 gas flow. The CO2 emitted during the combustion was quantified by infrared analysis. The results are given by Table 2. The density of the studied compounds was determined according to the following equation: /( ! ) =
#$% & '
(1)
Where Z is the formula units per unit cell (Z=1), Mw is the molar weight and V is the unit cell volume. N is the Avogadro’s constant. The results with the corresponding uncertainties are reported in Table 2.
3
4. Thermochemical study 4.1. Calorimeter device The device is an isoperibol calorimeter. It has been previously described in detail [12,13,15,27]. The energy evolved during a process induces a variation of the temperature of the reactional medium, which is measured using a thermistance probe connected to a Wheatstone bridge provided with a recorder and a DC supplier. Experiment started by searching a quasi equilibrium state corresponding to a recorded baseline which slightly deviates from the horizontal line. The chemical calibration process results in a “d” shift on the recorder followed by a line parallel to the previous baseline. The device was calibrated by a key reaction [12]. Experiments consist in dissolving various amounts of trihydroxymethyl aminomethane (HOCH2)3CNH2 or ‘‘THAM’’ in 350 ml of 0.1 mol kg-1 hydrochloric aqueous solution. The energy (Ei) corresponding to an amount (mi ) was calculated taking into account the mass of the solid and the key value for the standard enthalpy of dissolution of THAM picked from literature (-29.74 kJ mol1
) [28]. The calculated energy ‘E’ was plotted versus the shift ‘d’ (mm) recorded between the two baselines.
Statistical treatment [29] showed that ‘E’ can be expressed as: E = C.d, where ‘C’ is the mean calibration coefficient calculated as: /(( !! ) =
∑* +* *,
= 0.3202 ± 0.0024
(2)
The reliability of the device was tested by measuring the solution enthalpy of potassium chloride (KCl) in water at T = 298.15 K. The resulting molar dissolution enthalpy (17.57 ± 0.11 kJ mol-1) is in a good agreement with the literature data (17.584 ± 0.017 kJ mol-1) [30]. 4.2. Enthalpy of solution Dissolution of the apatites at T = 298.15 K was carried out in 350 cm3 of 9 wt% nitric acid solution in which carbon dioxide was continuously bubbled to avoid the retention of CO2 produced by the reaction. Different amounts of the apatites were dissolved under stirring, and the molar dissolution enthalpies can be determined according to a mathematical treatment in which the statistical weight (ω i) of an experimental result depends on the corresponding variance. This procedure leads to derive the dissolution enthalpy as: △ 23 =
∑4* .△5* 6* ∑4* 6*,
= 7 /(( )
(3)
Where (ωi) is the reciprocal of the variance of ∆Hi (ωi =1/σ∆Hi2), and (∆Hi) is the energy resulting from dissolving mi (mg). This calculation is detailed in references [31,32]. However, neglecting the uncertainties on the abscissa, (ω i) can be taken as equal to the reciprocal of the square of the error, since the latter is proportional to the square root of the variance. Application of this formula has been preceded by a statistical treatment on the results obtained with the same device. This has shown that the intercept of the line giving (∆Hi) as a function of (mi) is statistically negligible [32]. ∆Hi was calculated by the product ∆Hi = C.di where (C) is the calibration coefficient. The expanded uncertainty on ∆Hi, εi or U(∆Hi) was calculated by the following relationship developed by Guedens et al. [33]: 9(:5* )
8
:5*
; =8
9(<) <
; +8
=()
;
(4)
4
In which the expanded uncertainty U(C)=0.0024 J mm-1, (U(C)/C)=7.5.10-3 [12] and the standard uncertainty u(d)=1mm. The results are reported in Table 3. ∆solH is the proportionality factor between the energy released and the weight ‘m’ (yi=A.mi), one can calculate the error on ‘A’ (or ∆solH) taking into account the propagation of error. This leads to: > (7) = ∑C ?
@A
@6*
@A
B > (!C ) + ∑C ?@D B > (EC )
(5)
*
Neglecting the error on (mi) and taking into account the ‘A’ expression, in Eq. (3), one can derive the variance on A, σ2(A), as: > (7) =
∑*
6,* G , F (D* )
(6)
σ2(yi ) represents the dispersion of (yi ) values around the mean value, EIH . This supposes several measurement of (yi ) or ∆Hi for the same mass (mi). Assuming (yi ) value, reported in Table 3, as the mean of two values differing from yi by εi, this leads to σ2(yi)=2εi2 and allows to calculate σ2(A) for each series of measurements. The expanded uncertainty on ‘A’ factor was calculated by the product U(A)=t.σ(A) where ‘t’ is the Student factor for (N-1) degrees of freedom and ‘N’ the number of dissolution experiments of each apatite compound. The right column of Table 3 reports the molar dissolution enthalpies of these products together with their expanded uncertainties. The molar enthalpy of dissolution of all the compounds does not depend on the mass of the solid ‘m’. Indeed, the drawing of this quantity as a function of ‘m’ (not reported) leads to horizontal lines with slopes lying in the limit intervals [-0.0007, 0.0068]-[-0.0603, 0.0690]. Fig. 4 shows the variation of the standard enthalpy of solution of the studied compounds versus the rate of CO32- per unit cell. Table 3 Fig. 4 4.3. Enthalpy of formation Direct measurement of the standard enthalpy of formation of such compounds is impossible. However, this quantity can be calculated through a thermochemical cycle involving a succession of steps for which the “sum” corresponds to the enthalpy of formation of the compound. The following sequence of processes has been considered: 10( ) + 6 + () + (2 − ) → ( ) ()( ) ( ) () + 20 (1) K () + 2 → ( ) + () + L (1 − ) K() () + 2 → ( ) + 2 L
3 ( ) () + 18 → 9 ( ) + 6
(2) (3) (4)
() + (1 − ) () () + 3 ( ) () → ( ) ()( ) ( ) () In addition to the dissolution reaction of the apatite already mentioned (step 1), this scheme includes the dissolution of x moles of calcium carbonate (step 2), (1-x) moles of calcium hydroxide (step 3) and 3 moles of tricalcium phosphate (step 4). Their corresponding enthalpies were measured in the same solvent under similar conditions as for the apatites. The results are shown in Tables 4, 5 and 6. Table 7 gathers both dissolution and formation enthalpies of the reactants. The latter were picked from literature.
5
Table 4 Table 5 Table 6 Table 7 Combining the measurement results with those of literature enables to express the enthalpy of formation as: NO ° QR , 7 − − TU V/(W( !XY ) = −N23 ° QR , 7 − − TUV − 160 − 13697.7
(7)
Values of the standard enthalpy of formation are reported in the second column of Table 8 and Fig. 5. Uncertainty on this quantity was determined tacking into account the uncertainties on ∆solH°(T0, A-CO3-Hap), ∆solH° of entities involved in complementary reactions and the carbonate composition ‘x’ [33]. The formation enthalpy determined for the non-carbonated calcium hydroxyapatite (-13361 kJ mol-1) differs from the literature ones (-13312 [15] and -13305 kJ mol-1 [18]) by only 0.37 to 0.42%. For the sake of comparison, Fig. 5 reports also the results obtained previously with the other A-Carbonate apatites [12,13]. The plot of ∆fH°(T0) versus the carbonate content for the solid solution M10(PO 4)6(OH)(22x)(CO3)x
exhibit different shape. For strontium and barium carbonate apatites, one can notice a regular decrease
in the enthalpy of formation (more negative) when the amount of carbonate increases, while for calcium apatites, a minimum was observed at about 0.6 mole of carbonate content. Table 8 Fig. 5 4.4. Verification of the calorimetric results The dissolution process of CaCO3, Ca3(PO 4)2 and Ca(OH)2 were combined with other dissolution, dilution, and formation processes in order to get the formation reaction. The corresponding enthalpy of formation calculated by considering the measured molar enthalpy of solution was compared to the theoretical value of literature. For calcium carbonate, the following succession has been selected because of the availability of data of the involved compounds and entities: ( ) (23) + 71.7 (23) + () → () + 2 ( ; 35.35 ) 3C] ( ) . 4 () + ^XY_`ab → ( ) (23) + 4 (23) () + () + 4 () + 5 () → ( ) . 4 () (c) + () → ()
(1) (2) (3) (4)
2 ( ; 35.35 ) 3C] → () + () + 3 () + 70.7 3C]
(5)
67.7 3C] + ^XY_`ab → 67.7 (23)
(6)
3 3C] → 3 () + ()
(7)
3 () + (c) + () → () 2 The subscript “sol” means “in solution”.
In this succession, step (1) is the reverse of the dissolution. Step (2) and (6) correspond to dissolution of (Ca(NO3)2, 4H2O)
(sd)
and dilution of H2O respectively, the corresponding enthalpies were determined in the
same condition as for calcite. Steps (3), (4), (5) and (7) correspond to the formation reactions. Their enthalpies were picked from the literature and gethered in Table 9. Combining these values leads to: -1201.0 kJ mol-1 for
6
the standard formation enthalpy of calcite at 25°C. This value differs from that of literature (-1207.6 kJ mol-1) [34] by only 0.54%. For tricalcium phosphate, the following sequence of processes has been considered: 3 ( ) (23) + 2 (23) + 212 (23) → ( ) () + 6 ( ; 35.35 ) 3C]
3 ( ) . 4 () + ^XY_`ab → 3 ( ) (23) + 12 (23) 3 () + 3 () + 12 () + 15 () → 3 ( ) . 4 ()
6 ( ; 35.35 ) 3C] → 3 () + 3 () + 9 () + 212 3C] 2 ( ; 0.756 ) 3C] + ^XY_`ab → 2 (23) + 1.512 (23) 2 () + 3 () + 4 () + 1.512 3C] → 2 ( ; 0.756 ) 3C] 198.588 3C] + ^XY_`ab → 198.588 (23)
12 3C] → 12 () + 6 ()
(1) (2) (3) (4) (5) (6) (7) (8)
3 () + 2 () + 4 () → ( ) ()
Combining the measurement results (step 1) with those of literature (step 2 to 8) leads to: -4096.9 kJ mol-1 as standard formation enthalpy of tricalcium phosphate at 25°C. This value differs from that of literature (-4120.8 kJ mol-1 [34]) by only 0.58%. For calcium hydroxide the following sequence of processes has been considered: ( ) (23) + 72.7 (23) → () () + 2 ( ; 35.35 ) 3C] ( ) . 4 () + ^XY_`ab → ( ) (23) + 4 (23) () + () + 4 () + 5 () → ( ) . 4 ()
2 ( ; 35.35 ) 3C] → () + () + 3 () + 70.7 3C] 68.7 3C] + ^XY_`ab → 68.7 (23)
2 3C] → 2 () + ()
(1) (2) (3) (4) (5) (6)
() + () + () → () ()
Combining the measurement results (∆solH (Ca(OH)2) = -82.92 kJ mol-1) (step 1) with those of literature (step 2 to 6) leads to: -1030.9 kJ mol-1 as standard formation enthalpy of calcium hydroxide at 25°C. This value differs from that of literature (-985.2 kJ mol-1 [34]) by 4.63%. This could result from the trapping of few amounts of water and CO2 in Ca(OH)2. According to this cycle, and taking into account the litteraure value of the enthaly of formation of Ca(OH)2, the calculated value of the dissolution enthalpy of this product is (-128.6 kJ mol-1). In this case one can express the enthalpy of formation of the apatite as: NO ° QR , 7 − − TU V/(W( !XY ) = −N23 ° QR , 7 − − TUV − 114.3 − 13743.4
(8) -1
The formation enthalpy determined for the non-carbonated calcium hydroxyapatite is (-13407 kJ mol ). The difference from the literature ones moves from ≈ 0.40% to ≈ 0.75%. Moreover, the values of ∆fH° of the apatites, calculated tacking into account the literature data lies in the definition intervals of our experimental values as it is shown in Fig. 6. Table 9 Fig. 6
7
4.5. Enthalpy of mixing of the limit products M10(PO4)6(OH)(2-2x)(CO3)x can be considered as a solid solution obtained by mixing M10(PO4)6CO3 and M10(PO4)6(OH)2 according to the following scheme: d ( ) ( ) + (1 − ) d ( ) () → d ( ) ()( ) ( ) The molar enthalpy of mixing can be determined from the solution enthalpies of the reactants and product as follows: N6C ° ()/(W( !XY ) = −N23 ° () + N23 ° ( = 1) + (1 − ) N23 °( = 0)
(9)
This quantity can also be deduced from Fig. 5 by considering the difference between the enthalpy of formation of the solid solution for a given composition and that deduced from the straight line joining the points corresponding to the limit products. Fig. 7 shows the results for calcium and barium compounds. For strontium Fig. 5 shows a linear variation over ‘x’ and so the mixing enthalpy is null in the all composition range. Fig. 7 Neglecting the entropy factor, the negative values of this data shows that, for calcium and barium compounds, whatever the carbonate composition, the solid solution M10(PO4)6(OH)(2-2x)(CO3)x is more stable than the corresponding stoichiometric mixture of the end members. 4.6. Estimation of standard entropy and Gibbs free energy of formation Direct measurement of the standard entropy is almost impossible. However, an approach was developed to better estimating this quantity. This approach consists in searching a reaction which involves the compound considered with other compounds whose entropies of formation are known. A-CO3-Hap can be obtained combining Ca3(PO 4)2, CaCO3 and Ca(OH)2 according to the following reaction : 3 ( ) () + () + (1 − ) () () → ( ) ()( ) ( ) () , with 0 ≤ x ≤ 1. The entropy of this reaction can be written as : Nc ^ ° QR , 7 − − TU V/(( e !XY ) = ^ ° QR , 7 − − TU V − ^ °(R , ) − (1 − )^ ° (R , () ) − 3 ^ ° (R, ( ) )
(10)
Neglecting the value of the entropy of reaction, the standard entropy of the apatite at 298 K can be expressed as : ^ ° QR , 7 − − TU V/(( e !XY ) = ^ ° (R , ) + (1 − )^ ° (R , () ) + 3 ^ ° (R , ( ) )
(11)
Taking into account the literature data [34] (Table 7, column 5), the standard entropy of the apatite can be calculated according to the following equation: ^ ° QR , 7 − − TU V/(( e !XY ) = 790.55 + 8.3
(12)
The entropy of formation of A-CO3-Hap corresponds to the following reaction:
10 () + 6 () + ?13 + B 2 ( ) + (1 − ) () + (c) → ( ) ()( ) ( ) () 2
with 0 ≤ x ≤ 1, can be expressed as :
NO ^ ° QR , 7 − − TU V/(( e !XY ) = ^ ° QR , 7 − − TU V − 10 ^ ° (R , ) − 6 ^ ° (R , ) − (13 + )^ ° (R , ) − (1 − ) ^ ° (R , ) − ^ ° (R , )
(13)
Considering Eq. (12) and the literature data given by Table 7, one can derive the formation entropy as :
8
NO ^ ° QR , 7 − − TU V/(( e !XY ) = −2664.5 + 30.57
(14)
If we assume the entropy of formation to equal this limit, one can deduce the expression of standard Gibbs free energy of formation as : NO f ° QR , 7 − − TUV/(W( !XY ) = NO ° QR , 7 − − TU V − 298.15 10 NO ^ ° QR , 7 − − TU V
(15)
Table 8 gathers the calculated values of the entropy, standard molar entropies and Gibbs free energy of formation of the studied compounds. Variations of the two later quantities versus the carbonate content are shown in Fig. 8 and 9. One can notice that the replacement of two hydroxyl groups by one carbonate contributes to an increase of the standard entropy of formation. The Gibbs free energy of formation of A-CO3-Hap decreases till the composition 0.6 mole of carbonate suggesting that incorporation of this amount of carbonate in «A» sites contributes to increase the stability of these compounds. For B-type carbonate apatites, having the general formula Ca(10-x+u)(PO4)(6-x)(CO3)x(OH)(2-x+2u), the stability is reduced when PO4 3- groups were replaced by carbonate ions [15]. The destabilization observed for B-CO3-Hap can be explained by the creation of vacancies in the cationic sites accompanying the PO43- substitution. This probably contributes to decrease the stability of the edifice, while the A-Carbonatation does not create such vacancies. Fig. 8 Fig. 9
5. Conclusion Calorimetric study was performed and thermochemical cycle was proposed in order to access to the enthalpy of formation of A-CO3-Hap. The results were compared to those previously obtained with strontium and barium carbonate apatites and showed that the replacement of two hydroxyl groups by one carbonate is accompanied by an energy amount the magnitude of which depends significantly on the nature of metal ‘M’. An attempt to correlate this dependence to the difference between the enthalpies of formation of MCO3 and M(OH)2 failed. At the energitical point of view, this phenomenon seems to be more complex than a simple replacement of some MOH bounds by MCO3 ones. The influence of the other entities of the lattice is probably very important. For the fully carbonated apatites, the stability ranking is Ba-apatite > Ca-apatite > Sr-apatite. This could be related to structural modifications in the apatitic edifice induced by the increase of the cation and the anion size on the c-axis channel [36,37]. The method of estimating Gibbs free energy was applied for «A» type carbonate apatites. The results showed that this quantity decreases with the rate of substitution reaching a minimum at about x = 0.6. According to this study, apatite with 0.6 mol of carbonate per unit cell is the more stable of the solid solution Ca10(PO 4)6(OH)(22x)(CO3)x.
Acknowledgements
The authors are indebted to Professor Mohamed Ben Amor, Director of Natural Water
Treatment Laboratory, for accepting to support financially the carbonate analysis.
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[20] C.J. Liao, F.H. Lin, K.S. Chen, J.S. Sun, Thermal decomposition and reconstitution of hydroxyapatite in air atmosphere, Biomaterials. 20 (1999) 1807-1813. [21] S. Jebri, H. Boughzala, A. Bechrifa, M. Jemal, Rietveld structural refinement of «A » type phosphostrontium carbonate hydroxyapatites, Powder Diffraction. 28 (2013) S409-S424. [22] H. Takahashi, M. Yashima, M. Kakihana, M. Yoshimura, A differential scanning calorimeter study of the monoclinic (P21/b) ↔ hexagonal (P63/m) reversible phase transition in hydroxyapatite, Thermochim. Acta. 371 (2001) 53-56. [23] M.E. Fleet, X. Liu, Local structure of channel ions in carbonate apatite, Biomaterials. 26 (2005) 7548-7554. [24] K.D Rogers, P. Daniels, An X-ray diffraction study of the effects of heat treatment on bone mineral microstructure, Biomaterials. 23 (2002) 2577-2585. [25] C. Drouet, A comprehensive guide to experimental and predicted thermodynamic properties of phosphate apatite minerals in view of applicative purposes, J. Chem. Thermodynamics. 81 (2015) 143-159. [26] A. Bechrifa, Synthèse, caractérisation et détermination de grandeurs thermochimiques de phosphates à base de calcium et/ou de cadmium, Thesis. Tunis El Manar University, 2002. [27] A. Ben Chérifa, M. Jemal, Sur la réaction de dissolution des phosphates dans les acides: Enthalpie de dissolution du phosphate tricacique β dans l’acide nitrique, Ann. Chim. Sci. Mat. Fr. 10 (1985) 543-548. [28] J.O. Hill, G. Öjelund, I. Wadsö, Thermochemical results for “tris” as a test substance in solution calorimetry, J. Chem. Thermodyn. 1 (1969) 111-116. [29] C. Camlong-Viot, G. Morgant, Évaluations comparatives: Presentation de deux outils statistiques. Two statistical methods of comparison, Immunoanal Biol Spéc. 20 (2005) 320-328. [30] I. Wadsö, R.N. Goldberg, Standards in isothermal microcalorimetry, Pure App. Chem. (2001) 1625-1639. [31] D.E. Sands, Weighting Factors in Least Squares, J. Chem. Educ. 51 (1974) 473-474. [32] M.D. Pattengill, D.E. Sands, Statistical Significance of Linear Last-Squares Parameters, J. Chem. Educ. 56 (1979) 244-247. [33] W.J. Guedens, J. Yperman, J. Mullens, L.C. Van Poucke, Statistical Analysis of Errors: A Practical Approach of an Undergraduate Chemistry Lab, J. Chem. Educ. 70 (1993) 776-779. [34] R. Lide David, Editor, Handbook of Chemistry and Physics, 87th ed. CRC Press, 2006/2007. [35] NBS, Tables of Chemical Thermodynamics Properties, Phys. Chems. Ref. Data, Suppl. 2 (1982) 11. [36] J.C. Elliott, G. Bonel, J.C. Trombe, Space group and lattice constants of Ca10(PO4)6CO3, J. Appl. Cryst. 13 (1980) 618-621. [37] M. Nadal, J.P. Legros, G. Bonel. Mise en évidence d’un phénomène d’ordre- désordre dans le réseau des carbonate-apatites strontiques. C. R. Acad. Sci (Paris) 272 (1971) 45-48.
11
Standard enthalpy, entropy and Gibbs free energy of formation of « A» type carbonate phosphocalcium hydroxyapatites
Sonia Jebri1
Ismail Khattech2*
Mohamed Jemal2
1
Research Centre and Water Technology, Natural Water Treatment Laboratory, Borj Cédria BP 273, 8020 Soliman, Tunisia; 2
Université de Tunis El Manar, Faculty of Science, Chemistry Department, Materials Cristal Chemistry and Applied Thermodynamics Laboratory LR15SE01, 2092 Tunis, Tunisia; *Corresponding author: Ismail Khattech. E-mail adresses: [email protected]. Tel.: +216 98 208 884. Journal of Chemical Thermodynamics
List of figures Fig. 1. Infrared spectra of A-CO3-Hap with x = 0.394, 0.578, 0.840 compared to that of pure hydroxyapatite (x = 0).
Fig. 2. X-ray diffraction patterns of A-CO3-Hap with x = 0.394, 0.578, 0.840 and 0 (hydroxyapatite).
Fig. 3. Variation of ‘a’ parameter and the lattice volume ‘V’ versus the carbonate content ‘x’.
Fig. 4. Standard enthalpy of solution at temperature T = 298.15 K and pressure p = 0.1 MPa measured for ACO3-Hap in 9 wt% HNO3 versus the rate of CO32- ions per unit cell.
12
Fig. 5. Comparative results of the standard formation enthalpy at temperature T = 298.15 K and pressure p = 0.1 MPa of carbonate hydroxyapatites M10(PO 4)6(OH)(2-2x)(CO3)x, where M = Ca, Sr and Ba: (♦) Calcium apatites; (■) Strontium apatites; (▲) Barium apatites.
Fig. 6. Enthalpy of formation of A-CO3-Hap at temperature T = 298.15 K and pressure p = 0.1 MPa: (♦) Experimental data; (■) Determined based on the calculated enthalpy of dissolution of Ca(OH)2.
Fig. 7. Variation of the mixing enthalpy of the solid solution versus ‘x’, determined from the solution enthalpies at temperature T = 298.15 K and pressure p = 0.1 MPa : (♦) Calcium apatites; (▲) Barium apatites.
Fig. 8. Variation of standard entropy of formation at temperature T = 298.15 K and pressure p = 0.1 MPa of ACO3-Hap versus the CO32- content.
Fig. 9. Variation of standard Gibbs free energy of formation at temperature T = 298.15 K and pressure p = 0.1 MPa of A-CO3-Hap versus the CO32- content.
13
Fig. 1. Infrared spectra of A-CO3-Hap with x = 0.394, 0.578, 0.840 compared to that of pure hydroxyapatite (x = 0).
7000
7000
1 1 2
6000 5000 yt is 4000 n te3000 n I 2000
x=0
0 0 1
1000
2 0 2
0 1 22 0 1
0 11 0 1 2
20
30
2 2 2
0 1 3 1 33 1 10 3 12
0 10
5000 y its 4000 n et 3000 n I 2000
2 1 10 0 3
2 0 0
2?
40
7000
50
5000
3 1 2
0 2 14 2 4 0 2 1 30 0 1 3 4
1000
0 11 02 1
0 5
15
25
20 1
01 2
2?
35
20 2
01 20 2 1
1 002 11
15
25
0 1 3
3 2 2 1 2 2 1 2 2 4 1 1 00 3 3 3 30 1 1 10 42 3 1 40 2
45
3 2 1 2 2 2 0 2 44 10 0 2 1 2 1 0 11 3 3 3 3 4 3 11 02
103
35
2?
55
45
7000
55
x=0.840
1 1 2
6000 5000
020 001
00 1
5
x=0.578
2 0 2
20 0
0
2 1 10 0 3
tyi 4000 s n et 3000 In 2000
x=0.394 121 003
1000
60
112
6000
11 2
6000
2 1 1 0 0 3
4000 ty si n et3000 n I2000
2 0 0 0 0 1
1000
01 0 21 1
0 5
15
25
2 0 1
0 1 2
2?
2 0 2
0 1 3
35
3 2 21 22 1 21 23 00 4 0 1 3 30 3 1424 0 1 1 3 1 2
45
Fig. 2. X-ray diffraction patterns of A-CO3-Hap with x = 0.394, 0.578, 0.840 and 0 (hydroxyapatite).
15
55
9,54 9,52 9,5
a/Å
9,48 9,46 9,44 9,42 9,4 0
0,1
0,2
0,3
0,4
0,5 x
0,6
0,7
0,8
0,9
1
0,6
0,7
0,8
0,9
1
540 the carbonate content ‘x’.
538
V /Å3
536 534 532 530 528 0
0,1
0,2
0,3
0,4
0,5
x
Fig. 3. Variation of ‘a’ parameter and the lattice volume ‘V’ versus the carbonate content ‘x’.
Fig. 4. Standard enthalpy of solution at temperature T = 298.15 K and pressure p = 0.1 MPa measured for A-CO3-Hap in 9 wt% HNO3 versus the rate of CO32- ions per unit cell.
Fig. 5. Comparative results of the standard formation enthalpy at temperature T = 298.15 K and pressure p = 0.1 MPa of carbonate hydroxyapatites M10(PO4)6(OH)(2-2x)(CO3)x, where M = Ca, Sr and Ba: (♦) Calcium apatites; (■) Strontium apatites; (▲) Barium apatites.
Fig. 6. Enthalpy of formation of A-CO3-Hap at temperature T = 298.15 K and pressure p = 0.1 MPa: (♦) Experimental data; (■) Determined based on the calculated enthalpy of dissolution of Ca(OH)2.
Fig. 7. Variation of the mixing enthalpy of the solid solution versus ‘x’, determined from the solution enthalpies at temperature T = 298.15 K and pressure p = 0.1 MPa : (♦) Calcium apatites; (▲) Barium apatites.
Fig. 8. Variation of standard entropy of formation at temperature T = 298.15 K and pressure p = 0.1 MPa of A-CO3-Hap versus the CO32- content.
Fig. 9. Variation of standard Gibbs free energy of formation at temperature T = 298.15 K and pressure p = 0.1 MPa of A-CO3 -Hap versus the CO32- content.
Standard enthalpy, entropy and Gibbs free energy of formation of «A» type carbonate phosphocalcium hydroxyapatites
Sonia Jebri1
Ismail Khattech2*
Mohamed Jemal2
1
Research Centre and Water Technology, Natural Water Treatment Laboratory, Borj Cédria BP 273, 8020 Soliman, Tunisia; 2
Université de Tunis El Manar, Faculty of Science, Chemistry Department, Materials Cristal Chemistry and Applied Thermodynamics Laboratory LR15SE01, 2092 Tunis, Tunisia; *Corresponding author: Ismail Khattech. E-mail adresses: [email protected]. Tel.: +216 98 208 884. Journal of Chemical Thermodynamics
List of Tables Table 1 Provenance and mass fraction purity of the compounds used in synthesis and calorimetric study a.
Table 2 Percentages of carbon weight, carbonate composition per unit cell ‘x’, lattice parameters, molar weight Mw and density ρ of A-CO3-Hap at temperature T = 298.15 K and pressure p = 0.1 MPa a.
Table 3 Mass m, “d” shift recorded between the baselines, measured enthalpy ∆Hi and standard molar enthalpies of solution ∆solH° measured for A-CO3-Hap in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa a.
Table 4 Mass m, “d” shift recorded between the baselines and enthalpy of dissolution ∆Hi with expanded uncertainty measured for CaCO 3 in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa (level of confidence = 0.95) a.
23
Table 5 Mass m, “d” shift recorded between the baselines and enthalpy of dissolution ∆Hi with expanded uncertainty measured for Ca(OH)2 in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa (level of confidence = 0.95) a.
Table 6 Mass m, “d” shift recorded between the baselines and enthalpy of dissolution ∆Hi with expanded uncertainty measured for Ca3(PO4)2 in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa (level of confidence = 0.95) a.
Table 7 Standard molar enthalpies of solution ∆solH°, formation enthalpy ∆fH° and entropies S° of entities involved in complementary reactions at temperature T = 298.15 K and pressure p = 0.1 MPa a.
Table 8 Standard enthalpies of formation ∆fH°, entropies S°, standard entropies and Gibbs free energies of formation ∆fS° and ∆fG° of A-CO3-Hap at temperature T = 298.15 K and pressure p = 0.1 MPa a. Table 9 Standard enthalpies of solution ∆solH° and formation ∆fH°, of the chemical products and entities at temperature T = 298.15 K and pressure p = 0.1 MPa.
24
Table 1 Provenance and mass fraction purity of the compounds used in synthesis and calorimetric study a . Compound
Source
Mass fraction purity
Ca(NO3)2.4H2O
Merck
0.990
(NH4)2HPO4
Fluka
0.999
(NH3; 2.43 H2O)
Fluka
0.999
Ar
Air Liquide
0.999
CO2
Air Liquide
0.999
(HOCH2)3CNH2
Acros
0.990
KCl
Merck
0.995
(HNO3; 1.88 H2O)
Fluka
0.999
CaCO3
Fluka
0.990
Ca(OH)2
Aldrich
0.990
Ca3(PO4)2 b
Synthesis
0.990
a
No further purification was made.
b
Control of purity of tricalcium phosphate was achieved by IR spectroscopy and X-ray diffraction.
25
Table 2 Percentages of carbon weight, carbonate composition per unit cell ‘x’, lattice parameters, molar weight Mw and density ρ of A-CO3-Hap at temperature T = 298.15 K and pressure p = 0.1 MPa a.
Mw /g mol-1
ρ /g cm-3
528.8 ± 0.2
1004.8
3.155
6.880 ± 0.002
529.0± 0.3
1010.3
3.171
9.439 ± 0.003
6.888 ± 0.005
531.6± 0.5
1015.1
3.174
0.474
9.464 ± 0.002
6.888 ± 0.001
534.3 ± 0.2
1018.1
3.164
0.681
0.578
9.468 ± 0.002
6.885 ± 0.001
534.5 ± 0.2
1019.9
3.168
0.823
0.701
9.470 ± 0.001
6.889 ± 0.001
535.0 ± 0.1
1023.0
3.175
0.982
0.840
9.481 ± 0.002
6.887 ± 0.001
536.1 ± 0.2
1026.7
3.180
1.066
0.913
9.511 ± 0.002
6.875 ± 0.001
538.5 ± 0.2
1028.6
3.173
1.173
1
9.527 ± 0.002
6.868 ± 0.002
539.8 ± 0.3
1030.8
3.172
wt% C
x
b
0
0
9.414 ± 0.002
6.890 ± 0.001
0.252
0.212
9.423 ± 0.003
0.466
0.394
0.559
a
a /Å
b
c /Å
b
V /Å3
Standard uncertainties u are u(wt% C)=0.050 u(x) = 0.050, u(T) = 0.01 K, u(p) = 10 kPa, u(MW) = 1.3 g mol-1
and u(ρ) = 0.004 g cm-3. b
Lattice parameters with standard uncertainties.
26
Table 3 Mass m, “d” shift recorded between the baselines, measured enthalpy ∆Hi and standard molar enthalpies of solution ∆solH° measured for A-CO3-Hap in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa a. Chemical formula
Ca10(PO4)6(OH)2
Ca10(PO4)6(OH)1.576(CO3)0.212
Ca10(PO4)6(OH)1.212(CO3)0.394
m/
d/
-∆Hi /
b
-∆solH°/
b
mg
mm
J
J
kJ mol-1
kJ mol-1
128.3
132.0
42.26
0.45
336.2
5.2
142.7
147.5
47.23
0.48
101.8
103.5
33.14
0.41
70.1
74.0
23.69
0.37
93.3
99.5
31.86
0.40
82.6
86.0
27.54
0.38
134.4
145.0
46.43
0.48
83.4
68.5
21.93
0.36
267.5
4.3
120.3
100.0
32.02
0.40
100.9
83.0
26.57
0.38
93.8
76.5
24.49
0.37
132.5
110.0
35.22
0.42
125.6
104.0
33.30
0.41
138.2
114.5
36.66
0.42
77.9
65.0
20.81
0.36
79.0
58.0
18.57
0.35
233.7
5.0
66.9
48.0
15.37
0.34
46.2
32.5
10.41
0.33
88.0
64.0
20.49
0.35
85.2
60.0
19.21
0.35
112.3
84.0
26.89
0.38
U(∆Hi) /
U(∆solH°) /
27
Ca10(PO4)6(OH)1.052(CO3)0.474
Ca10(PO4)6(OH)0.844(CO3)0.578
Ca10(PO4)6(OH)0.598(CO3)0.701
53.7
39.0
12.49
0.33
142.2
99.2
31.76
0.40
141.3
99.0
31.70
0.40
80.7
60.0
19.21
0.35
70.2
50.0
16.01
0.34
102.3
72.0
23.05
0.36
92.1
65.0
20.81
0.36
121.4
85.5
27.38
0.38
154.0
111.5
35.70
0.42
95.4
67.0
21.45
0.36
68.3
48.0
15.37
0.34
78.4
57.0
18.25
0.35
74.5
54.0
17.29
0.35
90.4
67.5
21.61
0.36
155.6
115.5
36.98
0.43
96.6
70.0
22.41
0.36
101.2
76.0
24.33
0.37
122.1
90.5
28.98
0.39
52.6
38.0
12.17
0.33
129.9
92.0
29.46
0.39
88.3
64.5
20.65
0.36
100.9
72.0
23.05
0.37
81.5
61.0
19.53
0.35
96.5
75.5
24.17
0.37
71.7
55.0
17.61
0.35
64.1
50.0
16.01
0.34
31.0
23.5
07.52
0.32
231.8
3.7
238.8
3.7
252.8
5.2
28
Ca10(PO4)6(OH)0.320(CO3)0.840
Ca10(PO4)6(OH)0.174(CO3)0.913
Ca10(PO4)6(CO3)1
51.8
41.5
13.29
0.33
147.3
113.0
36.18
0.42
99.1
77.0
24.65
0.37
85.2
83.5
26.73
0.38
96.1
96.5
30.90
0.40
107.9
106.5
34.10
0.41
121.1
117.5
37.62
0.43
126.5
126.0
40.34
0.44
69.0
67.5
21.61
0.36
78.1
76.0
24.33
0.37
135.2
130.0
41.62
0.45
78.1
77.5
24.81
0.37
57.9
58.0
18.57
0.35
86.3
88.0
28.18
0.38
100.9
101.5
32.50
0.40
67.9
66.5
21.29
0.36
109.9
109.0
34.90
0.42
124.1
121.5
38.90
0.44
136.2
136.0
43.55
0.46
121.0
133.5
42.74
0.46
63.0
69.0
22.09
0.36
72.5
80.0
25.61
0.37
111.4
122.5
39.22
0.44
105.4
117.0
37.46
0.43
77.9
85.5
27.38
0.38
82.4
92.5
29.62
0.39
100.4
109.5
35.06
0.42
322.4
4.8
327.9
5.1
364.0
5.4
29
a
Standard uncertainties u are u(T) = 0.01 K, u(p) = 10 kPa, u(m) = 0.1 mg and u(d) = 1 mm, u(wt% HNO3) =
0.1%. b
U(∆Hi ) and U(∆solH°) are expanded uncertainty with 0.95 level of confidence.
30
Table 4 Mass m, “d” shift recorded between the baselines and enthalpy of dissolution ∆Hi with expanded uncertainty measured for CaCO3 in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa (level of confidence = 0.95) a .
m /mg
d /mm
-∆Hi /J
U(∆Hi) /J
82.3
50.0
16.01
0.34
157.1
99.5
31.86
0.40
105.6
65.0
20.81
0.36
122.9
79.5
25.45
0.37
200.9
129.0
41.30
0.45
144.4
95.0
30.42
0.39
96.4
64.5
20.65
0.36
166.8
105.5
33.78
0.41
101.5
63.0
20.17
0.35
158.2
102.5
32.82
0.40
75.4
49.0
15.69
0.34
209.4
136.0
43.55
0.46
135.8
87.0
27.86
0.38
a
Standard uncertainties u are u(T) = 0.01 K, u(p) = 10 kPa, u(m) = 0.1 mg and u(d) = 1 mm, u(wt% HNO3) =
0.1%.
31
Table 5 Mass m, “d” shift recorded between the baselines and enthalpy of dissolution ∆Hi with expanded uncertainty measured for Ca(OH)2 in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa (level of confidence = 0.95) a .
m /mg
d /mm
-∆Hi /J
U(∆Hi) /J
19.0
66.5
22.09
0.36
26.1
90.0
28.82
0.39
33.9
117.5
37.62
0.43
45.2
159.5
51.07
0.50
40.3
143.0
45.79
0.47
16.2
56.5
18.73
0.35
49.1
170.5
54.59
0.52
a
Standard uncertainties u are u(T) = 0.01 K, u(p) = 10 kPa, u(m) = 0.1 mg and u(d) = 1 mm, u(wt% HNO3) =
0.1%.
32
Table 6 Mass m, “d” shift recorded between the baselines and enthalpy of dissolution ∆Hi with expanded uncertainty measured for Ca3(PO4)2 in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa (level of confidence = 0.95) a.
m /mg
d /mm
-∆Hi /J
U(∆Hi) /J
93.0
85.0
27.21
0.38
106.6
97.5
31.22
0.40
68.4
60.0
19.21
0.35
125.3
111.5
35.70
0.42
141.9
126.5
40.50
0.44
157.3
140.5
44.99
0.47
a
Standard uncertainties u are u(T) = 0.01 K, u(p) = 10 kPa, u(m) = 0.1 mg and u(d) = 1 mm, u(wt% HNO3) =
0.1%.
33
Table 7 Standard molar enthalpies of solution ∆solH°, formation enthalpy ∆fH° and entropies S° of entities involved in complementary reactions at temperature T = 298.15 K and pressure p = 0.1 MPa a. Compound
U(∆solH) /
∆fH° /
S° /
kJ mol-1
kJ mol-1
kJ mol-1
J K-1 mol-1
CaCO3
-20.54
0.24
-1207.6
91.62
[34]
Ca(OH)2
-82.92
1.29
-985.2
83.30
[34]
Ca3(PO4)2
-89.07
1.64
-4120.8
235.75
[34]
Ca(crystal)
41.55
[34]
P(white, crystal)
41.05
[34]
C(graphite)
5.73
[34]
H2(gaz)
130.39
[34]
O2(gaz)
204.84
[34]
b
∆solH° /
Reference
Element
a
Standard uncertainties u are u(T) = 0.01 K and u(p) = 10 kPa.
b
Present work with expanded uncertainty U(∆solH) (level of confidence = 0.95).
34
Table 8 Standard enthalpies of formation ∆fH°, entropies S°, standard entropies and Gibbs free energies of formation ∆fS° and ∆fG° of A-CO3-Hap at temperature T = 298.15 K and pressure p = 0.1 MPa a. Chemical Formula
-∆fH° /
S° /
-∆fS° /
-∆fG° /
kJ mol-1
J K-1 mol-1
J K-1 mol-1
kJ mol-1
Ca10(PO4)6(OH)2
13361
790.5
2664.5
12567
Ca10(PO4)6(OH)1.576(CO3)0.212
13464
792.3
2658.1
12672
Ca10(PO4)6(OH)1.212(CO3)0.394
13527
793.8
2652.5
12736
Ca10(PO4)6(OH)1.052(CO3)0.474
13542
794.5
2650.0
12752
Ca10(PO4)6(OH)0.844(CO3)0.578
13551
795.3
2646.9
12762
Ca10(PO4)6(OH)0.598(CO3)0.701
13557
796.4
2643.1
12769
Ca10(PO4)6(OH)0.320(CO3)0.840
13510
797.5
2638.9
12723
Ca10(PO4)6(OH)0.174(CO3)0.913
13516
798.1
2636.7
12730
Ca10(PO4)6(CO3)1
13494
798.9
2634.0
12709
a
Standard uncertainties u are u(T) = 0.01 K and u(p) = 10 kPa, the combined expanded uncertainties Uc are
Uc(∆fH°) = 78 kJ mol-1, Uc(S°) = 0.8 J K-1 mol-1, Uc(∆fS°) = 3.0 J K-1 mol-1, Uc(∆fG°) = 78 kJ mol-1 with 0.95 level of confidence.
35
Highlights
•
A-type carbonate hydroxyapatites with 0≤x≤1 were prepared and characterized by DRX, IR spectroscopy and CHN analysis.
•
The heat of solution was measured in 9 wt% HNO3 using an isoperibol calorimeter.
•
The standard enthalpy of formation was determined by thermochemical cycle.
•
Gibbs free energy has been deduced by estimating standard entropy of formation.
•
Carbonatation increases the stability till x = 0.6 mole.
Table 9 Standard enthalpies of solution ∆solH° and formation ∆fH°, of the chemical products and entities at temperature T = 298.15 K and pressure p = 0.1 MPa. Compound
∆solH° /kJ mol-1
Reference
∆fH° /kJ mol-1
Reference
36
Ca(NO3)2. 4H2O
33.3
[35]
-2132.3
[35]
CO2 (g)
-
-
-393.51
[34]
H2Oliq
0
[35]
-285.83
[34]
{HNO3; 35.35H2O}
-
-
-206.8
[35]
{H3PO4;0.756H2O}
-7.87
[35]
-1271.8
[35]
37
S0021-9614(16)30343-3 http://dx.doi.org/10.1016/j.jct.2016.10.035 YJCHT 4865
To appear in:
J. Chem. Thermodynamics
Received Date: Revised Date: Accepted Date:
11 April 2016 7 October 2016 22 October 2016
Please cite this article as: S. Jebri, I. Khattech, M. Jemal, Standard enthalpy, entropy and Gibbs free energy of formation of « A » type carbonate phosphocalcium hydroxyapatites, J. Chem. Thermodynamics (2016), doi: http:// dx.doi.org/10.1016/j.jct.2016.10.035
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Standard enthalpy, entropy and Gibbs free energy of formation of «A» type carbonate phosphocalcium hydroxyapatites Sonia Jebri1
Ismail Khattech2*
Mohamed Jemal2
1
Research Centre and Water Technology, Natural Water Treatment Laboratory, Borj Cédria BP 273, 8020 Soliman, Tunisia; 2 Université de Tunis El Manar, Faculty of Science, Chemistry Department, Materials Cristal Chemistry and Applied Thermodynamics Laboratory LR15SE01, 2092 Tunis, Tunisia; *Corresponding author: Ismail Khattech. E-mail adresses: [email protected]. Tel.: +216 98 208 884. Journal of Chemical Thermodynamics ABSTRACT «
A» type carbonate phosphocalcium hydroxyapatites having the general formula Ca10(PO 4)6(OH)(2-2x)(CO3)x with
0≤x≤1, were prepared by solid gas reaction in the temperature range of 700-1000°C. The obtained materials were characterized by X-ray diffraction and infrared spectroscopy. The carbonate content has been determined by CH-N analysis. The heat of solution of these products was measured at T = 298 K in 9 wt% nitric acid solution using an isoperibol calorimeter. A thermochemical cycle was proposed and complementary experiences were performed in order to access to the standard enthalpies of formation of these phosphates. The results were compared to those previously obtained on apatites containing strontium and barium and show a decrease with the carbonate amount introduced in the lattice. This quantity becomes more negative as the ratio of substitution increases. Estimation of the entropy of formation allowed the determination of standard Gibbs free energy of formation of these compounds. The study showed that the substitution of hydroxyl by carbonate ions contributes to the stabilisation of the apatite structure. Keywords:
Carbonate hydroxyapatites
formation
Entropy of formation
Isoperibol calorimeter
Heat of solution Enthalpy
of
Gibbs free energy of formation
1. Introduction Apatites are a large class of mineral compounds with the general formula M10(XO4)6Y2, where M is generally a divalent cation (Ca2+, Sr2+, Ba2+, Pb2+, etc), XO4 is a trivalent or tetravalent anion (PO 43-, VO43-, AsO43-, SiO44-, etc) and Y can be a halide, hydroxyl or carbonate group. They form the major part of sedimentary phosphates ores. Due to a chemical composition close to that of the mineral part of calcified tissues [1,2], phosphocalcium hydroxyapatite, Ca10(PO4)6(OH)2, has proved to be an attractive material for biological applications and medical purposes [3,4]. It is commonly used as a bone substitute [5-7] despite the presence of carbonate in the bony apatite [8,9]. Hydroxyapatite crystallizes in P63/m space group with OH groups located on six fold helicoidal axis. Incorporation of carbonate ion in hydroxyapatite can occur in two different sites replacing either OH- or PO43-, leading to «A» or «B» type carbonate apatite respectively [10,11]. The physico-chemical properties of these
1
materials are highly affected by the carbonate localization and the chemical composition. In this context, many studies have been devoted to synthesis, structural analyses and thermal stability of carbonated and noncarbonated hydroxyapatites [12-24]. For non-carbonated apatites, a recent paper recapitulates an overview of the available thermodynamic data [25]. Indeed these studies show a decrease in stability versus the size of alkaline earth cations substituting Ca2+ in the apatitic edifice such as Sr2+ or Ba2+. For carbonated compounds, the stability is reduced by the incorporation of CO32-ions in PO4 3- sites [15], while such substitution in OH- sites seams to increase the stability of apatites containing strontium and barium [12,13]. The present paper is a continuation of two previous ones performed on the solid solutions M10(PO4)6(OH)(22x)(CO3)x,
with 0≤x≤1 and M = Sr2+ and Ba2+ [12,13] and deals with synthesis, characterization and
thermochemical study of similar carbonate phosphocalcium hydroxyapatites.
2. Synthesis «
A» type carbonate apatites (A-CO3-Hap) were prepared in tow steps. The first one consists in synthesizing
phosphocalcium hydroxyapatite Ca10(PO4)6(OH)2 by double decomposition in aqueous medium. Experiments consist in adding, drop by drop, during 90 minutes, a solution of diammonium hydrogen phosphate (0.31 M) into a boiling solution of calcium nitrate (0.12 M) [26]. The precipitation pH has been adjusted to about 11 by adding ammonia solution (28 wt%). The obtained precipitate was washed and dried during 12 hours at 70°C, then ignited at 800°C for 24 hours under wet Argon atmosphere (PH2O = 0.47105 Pa). The synthesis can be schematized by the following reaction: 10 ( ) + 6 ( ) + 8 → ( ) () + 20 + 6 The purity and crystallinity of the obtained samples were checked by X-ray diffraction and IR spectroscopy. The second synthesis step consists in heating calcium hydroxyapatite in CO2 gas flow. Various amounts of carbonate were introduced in the lattice by varying the time of gas flowing (from half an hour to ten days) and the temperature of synthesis (from 700 to 1000°C). Carbonatation occurred according to the following reaction: ( ) () () + () → ( ) ()( ) ( ) () + () The reagents used are of analytical quality. The chemical formula, provenance and mass fraction purity of each compound used for the synthesis and during the calorimetric study are reported in Table 1. Table 1
3. Characterization Control of purity of the synthesized products was achieved by X-ray diffraction and infrared spectroscopy. Determination of carbonate amount was performed by C-H-N analysis.
2
3.1. IR spectroscopy Infrared experiments were performed on pellets obtained by mixing 1.5 mg of the product in 300 mg of KBr for IR spectroscopy. The spectra were recorded between 400 and 4000 cm-1 using a Perkin-Elmer 7700 FT-IR spectrometer. They exhibit the characteristic absorbance bands of carbonate groups substituting hydroxyl ions in the tunnel, which appear at 879, 1460 and 1549 cm-1, confirming the formation of A-CO3-Hap [10]. Superposition of spectrum of apatites having the compositions 0.394, 0.578 and 0.840 mol of carbonate per unit cell is given in Fig. 1. They show that the higher the carbonate content, the higher is the intensity of the corresponding bands. One can also notice a decrease of absorbance band of hydroxyl (3572 cm-1) when carbonate is introduced in the lattice. Fig. 1 3.2. X-ray diffraction X-ray diffraction patterns have been recorded on the samples with a D8 ADVANCE Bruker diffractometer using copper radiations (Kα1 = 1.5406 Å; Kα2 = 1.5445 Å). Fig. 2 shows examples of well-crystallized phases of carbonated and non-carbonated hydroxyapatites. The lattice parameters of the structure were refined by ‘‘ERACEL’’ program and reported in Table 2. One can notice an increase of “a” parameter and a slight variation of “c” when introducing carbonate. Fig. 2 Table 2 Fig. 3 shows the variation of the lattice parameters versus the rate of carbonate substitution ‘x’. Because of the slight variation of ‘‘c’’, the variation of ‘‘a’’ induces a similar variation of the lattice volume. Fig. 3
3.3. Elemental analysis of Carbon The carbonate content of the preheated powders was measured by C-H-N analysis (JOBIN YVON HORIBA); the lower limit of detection was less than 0.01 wt%. About 40 mg of the sample was heated at 1800°C under O2 gas flow. The CO2 emitted during the combustion was quantified by infrared analysis. The results are given by Table 2. The density of the studied compounds was determined according to the following equation: /( ! ) =
#$% & '
(1)
Where Z is the formula units per unit cell (Z=1), Mw is the molar weight and V is the unit cell volume. N is the Avogadro’s constant. The results with the corresponding uncertainties are reported in Table 2.
3
4. Thermochemical study 4.1. Calorimeter device The device is an isoperibol calorimeter. It has been previously described in detail [12,13,15,27]. The energy evolved during a process induces a variation of the temperature of the reactional medium, which is measured using a thermistance probe connected to a Wheatstone bridge provided with a recorder and a DC supplier. Experiment started by searching a quasi equilibrium state corresponding to a recorded baseline which slightly deviates from the horizontal line. The chemical calibration process results in a “d” shift on the recorder followed by a line parallel to the previous baseline. The device was calibrated by a key reaction [12]. Experiments consist in dissolving various amounts of trihydroxymethyl aminomethane (HOCH2)3CNH2 or ‘‘THAM’’ in 350 ml of 0.1 mol kg-1 hydrochloric aqueous solution. The energy (Ei) corresponding to an amount (mi ) was calculated taking into account the mass of the solid and the key value for the standard enthalpy of dissolution of THAM picked from literature (-29.74 kJ mol1
) [28]. The calculated energy ‘E’ was plotted versus the shift ‘d’ (mm) recorded between the two baselines.
Statistical treatment [29] showed that ‘E’ can be expressed as: E = C.d, where ‘C’ is the mean calibration coefficient calculated as: /(( !! ) =
∑* +* *,
= 0.3202 ± 0.0024
(2)
The reliability of the device was tested by measuring the solution enthalpy of potassium chloride (KCl) in water at T = 298.15 K. The resulting molar dissolution enthalpy (17.57 ± 0.11 kJ mol-1) is in a good agreement with the literature data (17.584 ± 0.017 kJ mol-1) [30]. 4.2. Enthalpy of solution Dissolution of the apatites at T = 298.15 K was carried out in 350 cm3 of 9 wt% nitric acid solution in which carbon dioxide was continuously bubbled to avoid the retention of CO2 produced by the reaction. Different amounts of the apatites were dissolved under stirring, and the molar dissolution enthalpies can be determined according to a mathematical treatment in which the statistical weight (ω i) of an experimental result depends on the corresponding variance. This procedure leads to derive the dissolution enthalpy as: △ 23 =
∑4* .△5* 6* ∑4* 6*,
= 7 /(( )
(3)
Where (ωi) is the reciprocal of the variance of ∆Hi (ωi =1/σ∆Hi2), and (∆Hi) is the energy resulting from dissolving mi (mg). This calculation is detailed in references [31,32]. However, neglecting the uncertainties on the abscissa, (ω i) can be taken as equal to the reciprocal of the square of the error, since the latter is proportional to the square root of the variance. Application of this formula has been preceded by a statistical treatment on the results obtained with the same device. This has shown that the intercept of the line giving (∆Hi) as a function of (mi) is statistically negligible [32]. ∆Hi was calculated by the product ∆Hi = C.di where (C) is the calibration coefficient. The expanded uncertainty on ∆Hi, εi or U(∆Hi) was calculated by the following relationship developed by Guedens et al. [33]: 9(:5* )
8
:5*
; =8
9(<) <
; +8
=()
;
(4)
4
In which the expanded uncertainty U(C)=0.0024 J mm-1, (U(C)/C)=7.5.10-3 [12] and the standard uncertainty u(d)=1mm. The results are reported in Table 3. ∆solH is the proportionality factor between the energy released and the weight ‘m’ (yi=A.mi), one can calculate the error on ‘A’ (or ∆solH) taking into account the propagation of error. This leads to: > (7) = ∑C ?
@A
@6*
@A
B > (!C ) + ∑C ?@D B > (EC )
(5)
*
Neglecting the error on (mi) and taking into account the ‘A’ expression, in Eq. (3), one can derive the variance on A, σ2(A), as: > (7) =
∑*
6,* G , F (D* )
(6)
σ2(yi ) represents the dispersion of (yi ) values around the mean value, EIH . This supposes several measurement of (yi ) or ∆Hi for the same mass (mi). Assuming (yi ) value, reported in Table 3, as the mean of two values differing from yi by εi, this leads to σ2(yi)=2εi2 and allows to calculate σ2(A) for each series of measurements. The expanded uncertainty on ‘A’ factor was calculated by the product U(A)=t.σ(A) where ‘t’ is the Student factor for (N-1) degrees of freedom and ‘N’ the number of dissolution experiments of each apatite compound. The right column of Table 3 reports the molar dissolution enthalpies of these products together with their expanded uncertainties. The molar enthalpy of dissolution of all the compounds does not depend on the mass of the solid ‘m’. Indeed, the drawing of this quantity as a function of ‘m’ (not reported) leads to horizontal lines with slopes lying in the limit intervals [-0.0007, 0.0068]-[-0.0603, 0.0690]. Fig. 4 shows the variation of the standard enthalpy of solution of the studied compounds versus the rate of CO32- per unit cell. Table 3 Fig. 4 4.3. Enthalpy of formation Direct measurement of the standard enthalpy of formation of such compounds is impossible. However, this quantity can be calculated through a thermochemical cycle involving a succession of steps for which the “sum” corresponds to the enthalpy of formation of the compound. The following sequence of processes has been considered: 10( ) + 6 + () + (2 − ) → ( ) ()( ) ( ) () + 20 (1) K () + 2 → ( ) + () + L (1 − ) K() () + 2 → ( ) + 2 L
3 ( ) () + 18 → 9 ( ) + 6
(2) (3) (4)
() + (1 − ) () () + 3 ( ) () → ( ) ()( ) ( ) () In addition to the dissolution reaction of the apatite already mentioned (step 1), this scheme includes the dissolution of x moles of calcium carbonate (step 2), (1-x) moles of calcium hydroxide (step 3) and 3 moles of tricalcium phosphate (step 4). Their corresponding enthalpies were measured in the same solvent under similar conditions as for the apatites. The results are shown in Tables 4, 5 and 6. Table 7 gathers both dissolution and formation enthalpies of the reactants. The latter were picked from literature.
5
Table 4 Table 5 Table 6 Table 7 Combining the measurement results with those of literature enables to express the enthalpy of formation as: NO ° QR , 7 − − TU V/(W( !XY ) = −N23 ° QR , 7 − − TUV − 160 − 13697.7
(7)
Values of the standard enthalpy of formation are reported in the second column of Table 8 and Fig. 5. Uncertainty on this quantity was determined tacking into account the uncertainties on ∆solH°(T0, A-CO3-Hap), ∆solH° of entities involved in complementary reactions and the carbonate composition ‘x’ [33]. The formation enthalpy determined for the non-carbonated calcium hydroxyapatite (-13361 kJ mol-1) differs from the literature ones (-13312 [15] and -13305 kJ mol-1 [18]) by only 0.37 to 0.42%. For the sake of comparison, Fig. 5 reports also the results obtained previously with the other A-Carbonate apatites [12,13]. The plot of ∆fH°(T0) versus the carbonate content for the solid solution M10(PO 4)6(OH)(22x)(CO3)x
exhibit different shape. For strontium and barium carbonate apatites, one can notice a regular decrease
in the enthalpy of formation (more negative) when the amount of carbonate increases, while for calcium apatites, a minimum was observed at about 0.6 mole of carbonate content. Table 8 Fig. 5 4.4. Verification of the calorimetric results The dissolution process of CaCO3, Ca3(PO 4)2 and Ca(OH)2 were combined with other dissolution, dilution, and formation processes in order to get the formation reaction. The corresponding enthalpy of formation calculated by considering the measured molar enthalpy of solution was compared to the theoretical value of literature. For calcium carbonate, the following succession has been selected because of the availability of data of the involved compounds and entities: ( ) (23) + 71.7 (23) + () → () + 2 ( ; 35.35 ) 3C] ( ) . 4 () + ^XY_`ab → ( ) (23) + 4 (23) () + () + 4 () + 5 () → ( ) . 4 () (c) + () → ()
(1) (2) (3) (4)
2 ( ; 35.35 ) 3C] → () + () + 3 () + 70.7 3C]
(5)
67.7 3C] + ^XY_`ab → 67.7 (23)
(6)
3 3C] → 3 () + ()
(7)
3 () + (c) + () → () 2 The subscript “sol” means “in solution”.
In this succession, step (1) is the reverse of the dissolution. Step (2) and (6) correspond to dissolution of (Ca(NO3)2, 4H2O)
(sd)
and dilution of H2O respectively, the corresponding enthalpies were determined in the
same condition as for calcite. Steps (3), (4), (5) and (7) correspond to the formation reactions. Their enthalpies were picked from the literature and gethered in Table 9. Combining these values leads to: -1201.0 kJ mol-1 for
6
the standard formation enthalpy of calcite at 25°C. This value differs from that of literature (-1207.6 kJ mol-1) [34] by only 0.54%. For tricalcium phosphate, the following sequence of processes has been considered: 3 ( ) (23) + 2 (23) + 212 (23) → ( ) () + 6 ( ; 35.35 ) 3C]
3 ( ) . 4 () + ^XY_`ab → 3 ( ) (23) + 12 (23) 3 () + 3 () + 12 () + 15 () → 3 ( ) . 4 ()
6 ( ; 35.35 ) 3C] → 3 () + 3 () + 9 () + 212 3C] 2 ( ; 0.756 ) 3C] + ^XY_`ab → 2 (23) + 1.512 (23) 2 () + 3 () + 4 () + 1.512 3C] → 2 ( ; 0.756 ) 3C] 198.588 3C] + ^XY_`ab → 198.588 (23)
12 3C] → 12 () + 6 ()
(1) (2) (3) (4) (5) (6) (7) (8)
3 () + 2 () + 4 () → ( ) ()
Combining the measurement results (step 1) with those of literature (step 2 to 8) leads to: -4096.9 kJ mol-1 as standard formation enthalpy of tricalcium phosphate at 25°C. This value differs from that of literature (-4120.8 kJ mol-1 [34]) by only 0.58%. For calcium hydroxide the following sequence of processes has been considered: ( ) (23) + 72.7 (23) → () () + 2 ( ; 35.35 ) 3C] ( ) . 4 () + ^XY_`ab → ( ) (23) + 4 (23) () + () + 4 () + 5 () → ( ) . 4 ()
2 ( ; 35.35 ) 3C] → () + () + 3 () + 70.7 3C] 68.7 3C] + ^XY_`ab → 68.7 (23)
2 3C] → 2 () + ()
(1) (2) (3) (4) (5) (6)
() + () + () → () ()
Combining the measurement results (∆solH (Ca(OH)2) = -82.92 kJ mol-1) (step 1) with those of literature (step 2 to 6) leads to: -1030.9 kJ mol-1 as standard formation enthalpy of calcium hydroxide at 25°C. This value differs from that of literature (-985.2 kJ mol-1 [34]) by 4.63%. This could result from the trapping of few amounts of water and CO2 in Ca(OH)2. According to this cycle, and taking into account the litteraure value of the enthaly of formation of Ca(OH)2, the calculated value of the dissolution enthalpy of this product is (-128.6 kJ mol-1). In this case one can express the enthalpy of formation of the apatite as: NO ° QR , 7 − − TU V/(W( !XY ) = −N23 ° QR , 7 − − TUV − 114.3 − 13743.4
(8) -1
The formation enthalpy determined for the non-carbonated calcium hydroxyapatite is (-13407 kJ mol ). The difference from the literature ones moves from ≈ 0.40% to ≈ 0.75%. Moreover, the values of ∆fH° of the apatites, calculated tacking into account the literature data lies in the definition intervals of our experimental values as it is shown in Fig. 6. Table 9 Fig. 6
7
4.5. Enthalpy of mixing of the limit products M10(PO4)6(OH)(2-2x)(CO3)x can be considered as a solid solution obtained by mixing M10(PO4)6CO3 and M10(PO4)6(OH)2 according to the following scheme: d ( ) ( ) + (1 − ) d ( ) () → d ( ) ()( ) ( ) The molar enthalpy of mixing can be determined from the solution enthalpies of the reactants and product as follows: N6C ° ()/(W( !XY ) = −N23 ° () + N23 ° ( = 1) + (1 − ) N23 °( = 0)
(9)
This quantity can also be deduced from Fig. 5 by considering the difference between the enthalpy of formation of the solid solution for a given composition and that deduced from the straight line joining the points corresponding to the limit products. Fig. 7 shows the results for calcium and barium compounds. For strontium Fig. 5 shows a linear variation over ‘x’ and so the mixing enthalpy is null in the all composition range. Fig. 7 Neglecting the entropy factor, the negative values of this data shows that, for calcium and barium compounds, whatever the carbonate composition, the solid solution M10(PO4)6(OH)(2-2x)(CO3)x is more stable than the corresponding stoichiometric mixture of the end members. 4.6. Estimation of standard entropy and Gibbs free energy of formation Direct measurement of the standard entropy is almost impossible. However, an approach was developed to better estimating this quantity. This approach consists in searching a reaction which involves the compound considered with other compounds whose entropies of formation are known. A-CO3-Hap can be obtained combining Ca3(PO 4)2, CaCO3 and Ca(OH)2 according to the following reaction : 3 ( ) () + () + (1 − ) () () → ( ) ()( ) ( ) () , with 0 ≤ x ≤ 1. The entropy of this reaction can be written as : Nc ^ ° QR , 7 − − TU V/(( e !XY ) = ^ ° QR , 7 − − TU V − ^ °(R , ) − (1 − )^ ° (R , () ) − 3 ^ ° (R, ( ) )
(10)
Neglecting the value of the entropy of reaction, the standard entropy of the apatite at 298 K can be expressed as : ^ ° QR , 7 − − TU V/(( e !XY ) = ^ ° (R , ) + (1 − )^ ° (R , () ) + 3 ^ ° (R , ( ) )
(11)
Taking into account the literature data [34] (Table 7, column 5), the standard entropy of the apatite can be calculated according to the following equation: ^ ° QR , 7 − − TU V/(( e !XY ) = 790.55 + 8.3
(12)
The entropy of formation of A-CO3-Hap corresponds to the following reaction:
10 () + 6 () + ?13 + B 2 ( ) + (1 − ) () + (c) → ( ) ()( ) ( ) () 2
with 0 ≤ x ≤ 1, can be expressed as :
NO ^ ° QR , 7 − − TU V/(( e !XY ) = ^ ° QR , 7 − − TU V − 10 ^ ° (R , ) − 6 ^ ° (R , ) − (13 + )^ ° (R , ) − (1 − ) ^ ° (R , ) − ^ ° (R , )
(13)
Considering Eq. (12) and the literature data given by Table 7, one can derive the formation entropy as :
8
NO ^ ° QR , 7 − − TU V/(( e !XY ) = −2664.5 + 30.57
(14)
If we assume the entropy of formation to equal this limit, one can deduce the expression of standard Gibbs free energy of formation as : NO f ° QR , 7 − − TUV/(W( !XY ) = NO ° QR , 7 − − TU V − 298.15 10 NO ^ ° QR , 7 − − TU V
(15)
Table 8 gathers the calculated values of the entropy, standard molar entropies and Gibbs free energy of formation of the studied compounds. Variations of the two later quantities versus the carbonate content are shown in Fig. 8 and 9. One can notice that the replacement of two hydroxyl groups by one carbonate contributes to an increase of the standard entropy of formation. The Gibbs free energy of formation of A-CO3-Hap decreases till the composition 0.6 mole of carbonate suggesting that incorporation of this amount of carbonate in «A» sites contributes to increase the stability of these compounds. For B-type carbonate apatites, having the general formula Ca(10-x+u)(PO4)(6-x)(CO3)x(OH)(2-x+2u), the stability is reduced when PO4 3- groups were replaced by carbonate ions [15]. The destabilization observed for B-CO3-Hap can be explained by the creation of vacancies in the cationic sites accompanying the PO43- substitution. This probably contributes to decrease the stability of the edifice, while the A-Carbonatation does not create such vacancies. Fig. 8 Fig. 9
5. Conclusion Calorimetric study was performed and thermochemical cycle was proposed in order to access to the enthalpy of formation of A-CO3-Hap. The results were compared to those previously obtained with strontium and barium carbonate apatites and showed that the replacement of two hydroxyl groups by one carbonate is accompanied by an energy amount the magnitude of which depends significantly on the nature of metal ‘M’. An attempt to correlate this dependence to the difference between the enthalpies of formation of MCO3 and M(OH)2 failed. At the energitical point of view, this phenomenon seems to be more complex than a simple replacement of some MOH bounds by MCO3 ones. The influence of the other entities of the lattice is probably very important. For the fully carbonated apatites, the stability ranking is Ba-apatite > Ca-apatite > Sr-apatite. This could be related to structural modifications in the apatitic edifice induced by the increase of the cation and the anion size on the c-axis channel [36,37]. The method of estimating Gibbs free energy was applied for «A» type carbonate apatites. The results showed that this quantity decreases with the rate of substitution reaching a minimum at about x = 0.6. According to this study, apatite with 0.6 mol of carbonate per unit cell is the more stable of the solid solution Ca10(PO 4)6(OH)(22x)(CO3)x.
Acknowledgements
The authors are indebted to Professor Mohamed Ben Amor, Director of Natural Water
Treatment Laboratory, for accepting to support financially the carbonate analysis.
9
References [1] A. Onishi, P.S. Thomas, B.H. Stuart, J.P. Guerbois, S. Forbes, Tg-Ms characterisation of pig bone in an inert atmosphere, J. Therm. Anal. Cal. 88 (2007) 405-409. [2] T. Devièse, M.P. Colombini, M. Regert, B.H. Stuart, J.P. Guerbois, TGMS analysis of archaeological bone from burials of the late Roman period, J. Therm. Anal. Cal. 99 (2010) 811-813. [3] M. Descamps, J.C. Hornez, A. Leriche, Manufacture of hydroxyapatite beads for medical applications, J. Eur. Ceram. Soc. 29 (2009) 369-375. [4] L.L. Hench, Bioceramics: from concept to clinic, J. Am. Ceram. Soc. 74 (1991) 1487-1510. [5] V. Benezra Rosena, L.W. Hobbsa, M. Spectorb, The ultrastructure of anorganic bovine bone and selected synthetic hyroxyapatites used as bone graft substitute materials, Biomaterials. 23 (2002) 921-928. [6] C. Combes, C. Rey, Amorphous calcium phosphates: synthesis, properties and uses in biomaterials, Acta Biomater. 6 (2010) 3362-78. [7] E. Landia, G. Celottia, G. Logroscinob, A. Tampieria, Carbonated hydroxyapatite as bone substitute, J. Eur. Ceram. Soc. 23 (2003) 2931-2937. [8] H. Krzysztof, M.B. Miroslaw, B.M. Jadwiga, H. Maria, M. Wlodzimierz, P. Tomasz, P. Anna, Z. Jerzy, Natural hydroxyapatite - its behaviour during heat treatment, J. Eur. Ceram. Soc. 26 (2006) 537-542. [9] F. Peters, K. Schwarz, M. Epple, The structure of bone studied with synchrotron X-ray diffraction, X-ray absorption spectroscopy and thermal analysis, Thermochim. Acta. 361 (2000) 131-138. [10] G. Bonel, Contribution à l’étude de la carbonatation des apatites II. Synthèse et étude des propriétés physico-chimiques des apatites carbonatées de type B. III. Synthèse et étude des propriétés physico-chimiques d’apatites carbonatées dans deux types de sites. Evolution des spectres infrarouge en fonction de la composition des apatites, Ann. Chim. Sci. Mat. 7 (1972) 127-144. [11] P. Roux, G. Bonel, Sur la préparation de l’apatite carbonatée de type A à haute température par évolution sous pression de gaz carbonique, Ann. Chim. Sci. Mat. 2 (1977) 159-165. [12] S. Jebri, H. Boughzala, A. Bechrifa, M. Jemal, Structural analysis and thermochemistry of ‘‘A’’ type phosphostrontium carbonate hydroxyapatites, J. Therm. Anal. Calorim. 107 (2012) 963-972. [13] S. Jebri, A. Bechrifa, M. Jemal, Standard enthalpies of formation of ‘‘A’’ type carbonate phosphobaryum hydroxyapatites, J. Therm. Anal Calorim. 109 (2012) 1059-1067. [14] H. Zendah, I. Khattech, Standard enthalpy, entropy and Gibbs free energy of formation of “B” type carbonate fluorapatites, J. Chem. Thermodynamics. 87 (2015) 29-33. [15] F. Bel Hadj Yahia, M. Jemal, Synthesis, structural analysis and thermochemistry of B-type carbonate apatites, Thermochim. Acta. 505 (2010) 22-32. [16] I. Khattech, M. Jemal, Décomposition thermique de fluorapatites carbonates de type B «inverses», Thermochim. Acta. 118 (1987) 267-275. [17] M. Jemal, Thermochemistry and relative stability of apatite phosphates, Phos. Res. Bull. 15 (2002) 119-124. [18] M. Jemal, A. Ben Chérifa, I. Khattech, I. Ntahomvukiye, Standard enthalpies of formation and mixing of hydroxy-and fluorapatites, Thermochim. Acta. 259 (1995) 13-21. [19] S. Lazić, S. Zec, N. Miljević, S. Milonjić, The effect of temperature on properties of hydroxyapatite precipitated from calcium hydroxide and phosphoric acid, Thermochim. Acta. 374 (2001) 13-22.
10
[20] C.J. Liao, F.H. Lin, K.S. Chen, J.S. Sun, Thermal decomposition and reconstitution of hydroxyapatite in air atmosphere, Biomaterials. 20 (1999) 1807-1813. [21] S. Jebri, H. Boughzala, A. Bechrifa, M. Jemal, Rietveld structural refinement of «A » type phosphostrontium carbonate hydroxyapatites, Powder Diffraction. 28 (2013) S409-S424. [22] H. Takahashi, M. Yashima, M. Kakihana, M. Yoshimura, A differential scanning calorimeter study of the monoclinic (P21/b) ↔ hexagonal (P63/m) reversible phase transition in hydroxyapatite, Thermochim. Acta. 371 (2001) 53-56. [23] M.E. Fleet, X. Liu, Local structure of channel ions in carbonate apatite, Biomaterials. 26 (2005) 7548-7554. [24] K.D Rogers, P. Daniels, An X-ray diffraction study of the effects of heat treatment on bone mineral microstructure, Biomaterials. 23 (2002) 2577-2585. [25] C. Drouet, A comprehensive guide to experimental and predicted thermodynamic properties of phosphate apatite minerals in view of applicative purposes, J. Chem. Thermodynamics. 81 (2015) 143-159. [26] A. Bechrifa, Synthèse, caractérisation et détermination de grandeurs thermochimiques de phosphates à base de calcium et/ou de cadmium, Thesis. Tunis El Manar University, 2002. [27] A. Ben Chérifa, M. Jemal, Sur la réaction de dissolution des phosphates dans les acides: Enthalpie de dissolution du phosphate tricacique β dans l’acide nitrique, Ann. Chim. Sci. Mat. Fr. 10 (1985) 543-548. [28] J.O. Hill, G. Öjelund, I. Wadsö, Thermochemical results for “tris” as a test substance in solution calorimetry, J. Chem. Thermodyn. 1 (1969) 111-116. [29] C. Camlong-Viot, G. Morgant, Évaluations comparatives: Presentation de deux outils statistiques. Two statistical methods of comparison, Immunoanal Biol Spéc. 20 (2005) 320-328. [30] I. Wadsö, R.N. Goldberg, Standards in isothermal microcalorimetry, Pure App. Chem. (2001) 1625-1639. [31] D.E. Sands, Weighting Factors in Least Squares, J. Chem. Educ. 51 (1974) 473-474. [32] M.D. Pattengill, D.E. Sands, Statistical Significance of Linear Last-Squares Parameters, J. Chem. Educ. 56 (1979) 244-247. [33] W.J. Guedens, J. Yperman, J. Mullens, L.C. Van Poucke, Statistical Analysis of Errors: A Practical Approach of an Undergraduate Chemistry Lab, J. Chem. Educ. 70 (1993) 776-779. [34] R. Lide David, Editor, Handbook of Chemistry and Physics, 87th ed. CRC Press, 2006/2007. [35] NBS, Tables of Chemical Thermodynamics Properties, Phys. Chems. Ref. Data, Suppl. 2 (1982) 11. [36] J.C. Elliott, G. Bonel, J.C. Trombe, Space group and lattice constants of Ca10(PO4)6CO3, J. Appl. Cryst. 13 (1980) 618-621. [37] M. Nadal, J.P. Legros, G. Bonel. Mise en évidence d’un phénomène d’ordre- désordre dans le réseau des carbonate-apatites strontiques. C. R. Acad. Sci (Paris) 272 (1971) 45-48.
11
Standard enthalpy, entropy and Gibbs free energy of formation of « A» type carbonate phosphocalcium hydroxyapatites
Sonia Jebri1
Ismail Khattech2*
Mohamed Jemal2
1
Research Centre and Water Technology, Natural Water Treatment Laboratory, Borj Cédria BP 273, 8020 Soliman, Tunisia; 2
Université de Tunis El Manar, Faculty of Science, Chemistry Department, Materials Cristal Chemistry and Applied Thermodynamics Laboratory LR15SE01, 2092 Tunis, Tunisia; *Corresponding author: Ismail Khattech. E-mail adresses: [email protected]. Tel.: +216 98 208 884. Journal of Chemical Thermodynamics
List of figures Fig. 1. Infrared spectra of A-CO3-Hap with x = 0.394, 0.578, 0.840 compared to that of pure hydroxyapatite (x = 0).
Fig. 2. X-ray diffraction patterns of A-CO3-Hap with x = 0.394, 0.578, 0.840 and 0 (hydroxyapatite).
Fig. 3. Variation of ‘a’ parameter and the lattice volume ‘V’ versus the carbonate content ‘x’.
Fig. 4. Standard enthalpy of solution at temperature T = 298.15 K and pressure p = 0.1 MPa measured for ACO3-Hap in 9 wt% HNO3 versus the rate of CO32- ions per unit cell.
12
Fig. 5. Comparative results of the standard formation enthalpy at temperature T = 298.15 K and pressure p = 0.1 MPa of carbonate hydroxyapatites M10(PO 4)6(OH)(2-2x)(CO3)x, where M = Ca, Sr and Ba: (♦) Calcium apatites; (■) Strontium apatites; (▲) Barium apatites.
Fig. 6. Enthalpy of formation of A-CO3-Hap at temperature T = 298.15 K and pressure p = 0.1 MPa: (♦) Experimental data; (■) Determined based on the calculated enthalpy of dissolution of Ca(OH)2.
Fig. 7. Variation of the mixing enthalpy of the solid solution versus ‘x’, determined from the solution enthalpies at temperature T = 298.15 K and pressure p = 0.1 MPa : (♦) Calcium apatites; (▲) Barium apatites.
Fig. 8. Variation of standard entropy of formation at temperature T = 298.15 K and pressure p = 0.1 MPa of ACO3-Hap versus the CO32- content.
Fig. 9. Variation of standard Gibbs free energy of formation at temperature T = 298.15 K and pressure p = 0.1 MPa of A-CO3-Hap versus the CO32- content.
13
Fig. 1. Infrared spectra of A-CO3-Hap with x = 0.394, 0.578, 0.840 compared to that of pure hydroxyapatite (x = 0).
7000
7000
1 1 2
6000 5000 yt is 4000 n te3000 n I 2000
x=0
0 0 1
1000
2 0 2
0 1 22 0 1
0 11 0 1 2
20
30
2 2 2
0 1 3 1 33 1 10 3 12
0 10
5000 y its 4000 n et 3000 n I 2000
2 1 10 0 3
2 0 0
2?
40
7000
50
5000
3 1 2
0 2 14 2 4 0 2 1 30 0 1 3 4
1000
0 11 02 1
0 5
15
25
20 1
01 2
2?
35
20 2
01 20 2 1
1 002 11
15
25
0 1 3
3 2 2 1 2 2 1 2 2 4 1 1 00 3 3 3 30 1 1 10 42 3 1 40 2
45
3 2 1 2 2 2 0 2 44 10 0 2 1 2 1 0 11 3 3 3 3 4 3 11 02
103
35
2?
55
45
7000
55
x=0.840
1 1 2
6000 5000
020 001
00 1
5
x=0.578
2 0 2
20 0
0
2 1 10 0 3
tyi 4000 s n et 3000 In 2000
x=0.394 121 003
1000
60
112
6000
11 2
6000
2 1 1 0 0 3
4000 ty si n et3000 n I2000
2 0 0 0 0 1
1000
01 0 21 1
0 5
15
25
2 0 1
0 1 2
2?
2 0 2
0 1 3
35
3 2 21 22 1 21 23 00 4 0 1 3 30 3 1424 0 1 1 3 1 2
45
Fig. 2. X-ray diffraction patterns of A-CO3-Hap with x = 0.394, 0.578, 0.840 and 0 (hydroxyapatite).
15
55
9,54 9,52 9,5
a/Å
9,48 9,46 9,44 9,42 9,4 0
0,1
0,2
0,3
0,4
0,5 x
0,6
0,7
0,8
0,9
1
0,6
0,7
0,8
0,9
1
540 the carbonate content ‘x’.
538
V /Å3
536 534 532 530 528 0
0,1
0,2
0,3
0,4
0,5
x
Fig. 3. Variation of ‘a’ parameter and the lattice volume ‘V’ versus the carbonate content ‘x’.
Fig. 4. Standard enthalpy of solution at temperature T = 298.15 K and pressure p = 0.1 MPa measured for A-CO3-Hap in 9 wt% HNO3 versus the rate of CO32- ions per unit cell.
Fig. 5. Comparative results of the standard formation enthalpy at temperature T = 298.15 K and pressure p = 0.1 MPa of carbonate hydroxyapatites M10(PO4)6(OH)(2-2x)(CO3)x, where M = Ca, Sr and Ba: (♦) Calcium apatites; (■) Strontium apatites; (▲) Barium apatites.
Fig. 6. Enthalpy of formation of A-CO3-Hap at temperature T = 298.15 K and pressure p = 0.1 MPa: (♦) Experimental data; (■) Determined based on the calculated enthalpy of dissolution of Ca(OH)2.
Fig. 7. Variation of the mixing enthalpy of the solid solution versus ‘x’, determined from the solution enthalpies at temperature T = 298.15 K and pressure p = 0.1 MPa : (♦) Calcium apatites; (▲) Barium apatites.
Fig. 8. Variation of standard entropy of formation at temperature T = 298.15 K and pressure p = 0.1 MPa of A-CO3-Hap versus the CO32- content.
Fig. 9. Variation of standard Gibbs free energy of formation at temperature T = 298.15 K and pressure p = 0.1 MPa of A-CO3 -Hap versus the CO32- content.
Standard enthalpy, entropy and Gibbs free energy of formation of «A» type carbonate phosphocalcium hydroxyapatites
Sonia Jebri1
Ismail Khattech2*
Mohamed Jemal2
1
Research Centre and Water Technology, Natural Water Treatment Laboratory, Borj Cédria BP 273, 8020 Soliman, Tunisia; 2
Université de Tunis El Manar, Faculty of Science, Chemistry Department, Materials Cristal Chemistry and Applied Thermodynamics Laboratory LR15SE01, 2092 Tunis, Tunisia; *Corresponding author: Ismail Khattech. E-mail adresses: [email protected]. Tel.: +216 98 208 884. Journal of Chemical Thermodynamics
List of Tables Table 1 Provenance and mass fraction purity of the compounds used in synthesis and calorimetric study a.
Table 2 Percentages of carbon weight, carbonate composition per unit cell ‘x’, lattice parameters, molar weight Mw and density ρ of A-CO3-Hap at temperature T = 298.15 K and pressure p = 0.1 MPa a.
Table 3 Mass m, “d” shift recorded between the baselines, measured enthalpy ∆Hi and standard molar enthalpies of solution ∆solH° measured for A-CO3-Hap in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa a.
Table 4 Mass m, “d” shift recorded between the baselines and enthalpy of dissolution ∆Hi with expanded uncertainty measured for CaCO 3 in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa (level of confidence = 0.95) a.
23
Table 5 Mass m, “d” shift recorded between the baselines and enthalpy of dissolution ∆Hi with expanded uncertainty measured for Ca(OH)2 in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa (level of confidence = 0.95) a.
Table 6 Mass m, “d” shift recorded between the baselines and enthalpy of dissolution ∆Hi with expanded uncertainty measured for Ca3(PO4)2 in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa (level of confidence = 0.95) a.
Table 7 Standard molar enthalpies of solution ∆solH°, formation enthalpy ∆fH° and entropies S° of entities involved in complementary reactions at temperature T = 298.15 K and pressure p = 0.1 MPa a.
Table 8 Standard enthalpies of formation ∆fH°, entropies S°, standard entropies and Gibbs free energies of formation ∆fS° and ∆fG° of A-CO3-Hap at temperature T = 298.15 K and pressure p = 0.1 MPa a. Table 9 Standard enthalpies of solution ∆solH° and formation ∆fH°, of the chemical products and entities at temperature T = 298.15 K and pressure p = 0.1 MPa.
24
Table 1 Provenance and mass fraction purity of the compounds used in synthesis and calorimetric study a . Compound
Source
Mass fraction purity
Ca(NO3)2.4H2O
Merck
0.990
(NH4)2HPO4
Fluka
0.999
(NH3; 2.43 H2O)
Fluka
0.999
Ar
Air Liquide
0.999
CO2
Air Liquide
0.999
(HOCH2)3CNH2
Acros
0.990
KCl
Merck
0.995
(HNO3; 1.88 H2O)
Fluka
0.999
CaCO3
Fluka
0.990
Ca(OH)2
Aldrich
0.990
Ca3(PO4)2 b
Synthesis
0.990
a
No further purification was made.
b
Control of purity of tricalcium phosphate was achieved by IR spectroscopy and X-ray diffraction.
25
Table 2 Percentages of carbon weight, carbonate composition per unit cell ‘x’, lattice parameters, molar weight Mw and density ρ of A-CO3-Hap at temperature T = 298.15 K and pressure p = 0.1 MPa a.
Mw /g mol-1
ρ /g cm-3
528.8 ± 0.2
1004.8
3.155
6.880 ± 0.002
529.0± 0.3
1010.3
3.171
9.439 ± 0.003
6.888 ± 0.005
531.6± 0.5
1015.1
3.174
0.474
9.464 ± 0.002
6.888 ± 0.001
534.3 ± 0.2
1018.1
3.164
0.681
0.578
9.468 ± 0.002
6.885 ± 0.001
534.5 ± 0.2
1019.9
3.168
0.823
0.701
9.470 ± 0.001
6.889 ± 0.001
535.0 ± 0.1
1023.0
3.175
0.982
0.840
9.481 ± 0.002
6.887 ± 0.001
536.1 ± 0.2
1026.7
3.180
1.066
0.913
9.511 ± 0.002
6.875 ± 0.001
538.5 ± 0.2
1028.6
3.173
1.173
1
9.527 ± 0.002
6.868 ± 0.002
539.8 ± 0.3
1030.8
3.172
wt% C
x
b
0
0
9.414 ± 0.002
6.890 ± 0.001
0.252
0.212
9.423 ± 0.003
0.466
0.394
0.559
a
a /Å
b
c /Å
b
V /Å3
Standard uncertainties u are u(wt% C)=0.050 u(x) = 0.050, u(T) = 0.01 K, u(p) = 10 kPa, u(MW) = 1.3 g mol-1
and u(ρ) = 0.004 g cm-3. b
Lattice parameters with standard uncertainties.
26
Table 3 Mass m, “d” shift recorded between the baselines, measured enthalpy ∆Hi and standard molar enthalpies of solution ∆solH° measured for A-CO3-Hap in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa a. Chemical formula
Ca10(PO4)6(OH)2
Ca10(PO4)6(OH)1.576(CO3)0.212
Ca10(PO4)6(OH)1.212(CO3)0.394
m/
d/
-∆Hi /
b
-∆solH°/
b
mg
mm
J
J
kJ mol-1
kJ mol-1
128.3
132.0
42.26
0.45
336.2
5.2
142.7
147.5
47.23
0.48
101.8
103.5
33.14
0.41
70.1
74.0
23.69
0.37
93.3
99.5
31.86
0.40
82.6
86.0
27.54
0.38
134.4
145.0
46.43
0.48
83.4
68.5
21.93
0.36
267.5
4.3
120.3
100.0
32.02
0.40
100.9
83.0
26.57
0.38
93.8
76.5
24.49
0.37
132.5
110.0
35.22
0.42
125.6
104.0
33.30
0.41
138.2
114.5
36.66
0.42
77.9
65.0
20.81
0.36
79.0
58.0
18.57
0.35
233.7
5.0
66.9
48.0
15.37
0.34
46.2
32.5
10.41
0.33
88.0
64.0
20.49
0.35
85.2
60.0
19.21
0.35
112.3
84.0
26.89
0.38
U(∆Hi) /
U(∆solH°) /
27
Ca10(PO4)6(OH)1.052(CO3)0.474
Ca10(PO4)6(OH)0.844(CO3)0.578
Ca10(PO4)6(OH)0.598(CO3)0.701
53.7
39.0
12.49
0.33
142.2
99.2
31.76
0.40
141.3
99.0
31.70
0.40
80.7
60.0
19.21
0.35
70.2
50.0
16.01
0.34
102.3
72.0
23.05
0.36
92.1
65.0
20.81
0.36
121.4
85.5
27.38
0.38
154.0
111.5
35.70
0.42
95.4
67.0
21.45
0.36
68.3
48.0
15.37
0.34
78.4
57.0
18.25
0.35
74.5
54.0
17.29
0.35
90.4
67.5
21.61
0.36
155.6
115.5
36.98
0.43
96.6
70.0
22.41
0.36
101.2
76.0
24.33
0.37
122.1
90.5
28.98
0.39
52.6
38.0
12.17
0.33
129.9
92.0
29.46
0.39
88.3
64.5
20.65
0.36
100.9
72.0
23.05
0.37
81.5
61.0
19.53
0.35
96.5
75.5
24.17
0.37
71.7
55.0
17.61
0.35
64.1
50.0
16.01
0.34
31.0
23.5
07.52
0.32
231.8
3.7
238.8
3.7
252.8
5.2
28
Ca10(PO4)6(OH)0.320(CO3)0.840
Ca10(PO4)6(OH)0.174(CO3)0.913
Ca10(PO4)6(CO3)1
51.8
41.5
13.29
0.33
147.3
113.0
36.18
0.42
99.1
77.0
24.65
0.37
85.2
83.5
26.73
0.38
96.1
96.5
30.90
0.40
107.9
106.5
34.10
0.41
121.1
117.5
37.62
0.43
126.5
126.0
40.34
0.44
69.0
67.5
21.61
0.36
78.1
76.0
24.33
0.37
135.2
130.0
41.62
0.45
78.1
77.5
24.81
0.37
57.9
58.0
18.57
0.35
86.3
88.0
28.18
0.38
100.9
101.5
32.50
0.40
67.9
66.5
21.29
0.36
109.9
109.0
34.90
0.42
124.1
121.5
38.90
0.44
136.2
136.0
43.55
0.46
121.0
133.5
42.74
0.46
63.0
69.0
22.09
0.36
72.5
80.0
25.61
0.37
111.4
122.5
39.22
0.44
105.4
117.0
37.46
0.43
77.9
85.5
27.38
0.38
82.4
92.5
29.62
0.39
100.4
109.5
35.06
0.42
322.4
4.8
327.9
5.1
364.0
5.4
29
a
Standard uncertainties u are u(T) = 0.01 K, u(p) = 10 kPa, u(m) = 0.1 mg and u(d) = 1 mm, u(wt% HNO3) =
0.1%. b
U(∆Hi ) and U(∆solH°) are expanded uncertainty with 0.95 level of confidence.
30
Table 4 Mass m, “d” shift recorded between the baselines and enthalpy of dissolution ∆Hi with expanded uncertainty measured for CaCO3 in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa (level of confidence = 0.95) a .
m /mg
d /mm
-∆Hi /J
U(∆Hi) /J
82.3
50.0
16.01
0.34
157.1
99.5
31.86
0.40
105.6
65.0
20.81
0.36
122.9
79.5
25.45
0.37
200.9
129.0
41.30
0.45
144.4
95.0
30.42
0.39
96.4
64.5
20.65
0.36
166.8
105.5
33.78
0.41
101.5
63.0
20.17
0.35
158.2
102.5
32.82
0.40
75.4
49.0
15.69
0.34
209.4
136.0
43.55
0.46
135.8
87.0
27.86
0.38
a
Standard uncertainties u are u(T) = 0.01 K, u(p) = 10 kPa, u(m) = 0.1 mg and u(d) = 1 mm, u(wt% HNO3) =
0.1%.
31
Table 5 Mass m, “d” shift recorded between the baselines and enthalpy of dissolution ∆Hi with expanded uncertainty measured for Ca(OH)2 in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa (level of confidence = 0.95) a .
m /mg
d /mm
-∆Hi /J
U(∆Hi) /J
19.0
66.5
22.09
0.36
26.1
90.0
28.82
0.39
33.9
117.5
37.62
0.43
45.2
159.5
51.07
0.50
40.3
143.0
45.79
0.47
16.2
56.5
18.73
0.35
49.1
170.5
54.59
0.52
a
Standard uncertainties u are u(T) = 0.01 K, u(p) = 10 kPa, u(m) = 0.1 mg and u(d) = 1 mm, u(wt% HNO3) =
0.1%.
32
Table 6 Mass m, “d” shift recorded between the baselines and enthalpy of dissolution ∆Hi with expanded uncertainty measured for Ca3(PO4)2 in 350 ml of 9.0 wt% HNO3 at temperature T = 298.15 K and pressure p = 0.1 MPa (level of confidence = 0.95) a.
m /mg
d /mm
-∆Hi /J
U(∆Hi) /J
93.0
85.0
27.21
0.38
106.6
97.5
31.22
0.40
68.4
60.0
19.21
0.35
125.3
111.5
35.70
0.42
141.9
126.5
40.50
0.44
157.3
140.5
44.99
0.47
a
Standard uncertainties u are u(T) = 0.01 K, u(p) = 10 kPa, u(m) = 0.1 mg and u(d) = 1 mm, u(wt% HNO3) =
0.1%.
33
Table 7 Standard molar enthalpies of solution ∆solH°, formation enthalpy ∆fH° and entropies S° of entities involved in complementary reactions at temperature T = 298.15 K and pressure p = 0.1 MPa a. Compound
U(∆solH) /
∆fH° /
S° /
kJ mol-1
kJ mol-1
kJ mol-1
J K-1 mol-1
CaCO3
-20.54
0.24
-1207.6
91.62
[34]
Ca(OH)2
-82.92
1.29
-985.2
83.30
[34]
Ca3(PO4)2
-89.07
1.64
-4120.8
235.75
[34]
Ca(crystal)
41.55
[34]
P(white, crystal)
41.05
[34]
C(graphite)
5.73
[34]
H2(gaz)
130.39
[34]
O2(gaz)
204.84
[34]
b
∆solH° /
Reference
Element
a
Standard uncertainties u are u(T) = 0.01 K and u(p) = 10 kPa.
b
Present work with expanded uncertainty U(∆solH) (level of confidence = 0.95).
34
Table 8 Standard enthalpies of formation ∆fH°, entropies S°, standard entropies and Gibbs free energies of formation ∆fS° and ∆fG° of A-CO3-Hap at temperature T = 298.15 K and pressure p = 0.1 MPa a. Chemical Formula
-∆fH° /
S° /
-∆fS° /
-∆fG° /
kJ mol-1
J K-1 mol-1
J K-1 mol-1
kJ mol-1
Ca10(PO4)6(OH)2
13361
790.5
2664.5
12567
Ca10(PO4)6(OH)1.576(CO3)0.212
13464
792.3
2658.1
12672
Ca10(PO4)6(OH)1.212(CO3)0.394
13527
793.8
2652.5
12736
Ca10(PO4)6(OH)1.052(CO3)0.474
13542
794.5
2650.0
12752
Ca10(PO4)6(OH)0.844(CO3)0.578
13551
795.3
2646.9
12762
Ca10(PO4)6(OH)0.598(CO3)0.701
13557
796.4
2643.1
12769
Ca10(PO4)6(OH)0.320(CO3)0.840
13510
797.5
2638.9
12723
Ca10(PO4)6(OH)0.174(CO3)0.913
13516
798.1
2636.7
12730
Ca10(PO4)6(CO3)1
13494
798.9
2634.0
12709
a
Standard uncertainties u are u(T) = 0.01 K and u(p) = 10 kPa, the combined expanded uncertainties Uc are
Uc(∆fH°) = 78 kJ mol-1, Uc(S°) = 0.8 J K-1 mol-1, Uc(∆fS°) = 3.0 J K-1 mol-1, Uc(∆fG°) = 78 kJ mol-1 with 0.95 level of confidence.
35
Highlights
•
A-type carbonate hydroxyapatites with 0≤x≤1 were prepared and characterized by DRX, IR spectroscopy and CHN analysis.
•
The heat of solution was measured in 9 wt% HNO3 using an isoperibol calorimeter.
•
The standard enthalpy of formation was determined by thermochemical cycle.
•
Gibbs free energy has been deduced by estimating standard entropy of formation.
•
Carbonatation increases the stability till x = 0.6 mole.
Table 9 Standard enthalpies of solution ∆solH° and formation ∆fH°, of the chemical products and entities at temperature T = 298.15 K and pressure p = 0.1 MPa. Compound
∆solH° /kJ mol-1
Reference
∆fH° /kJ mol-1
Reference
36
Ca(NO3)2. 4H2O
33.3
[35]
-2132.3
[35]
CO2 (g)
-
-
-393.51
[34]
H2Oliq
0
[35]
-285.83
[34]
{HNO3; 35.35H2O}
-
-
-206.8
[35]
{H3PO4;0.756H2O}
-7.87
[35]
-1271.8
[35]
37