# Determination of Thermodynamical Data of Calcium Hydroxichloride

K. M. Allal, J. C. Dolignier, G. Martin

► To cite this version:

K. M. Allal, J. C. Dolignier, G. Martin. Determination of Thermodynamical Data of Calcium Hydroxichloride. Revue de l'Institut Français du Pétrole, 1997, 52 (3), pp.361-368. 10.2516/ogst:1997046 hal-02079115

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Distributed under a Creative Commons Attribution 4.0 International License
DETERMINATION OF
THERMODYNAMICAL DATA OF
CALCIUM HYDROXICHLORIDE

K.M. ALLAL, J.C. DOLIGNIER and G. MARTIN

Institut français du pétrole¹

DÉTERMINATION DES DONNÉES
THERMODYNAMIQUES DE L'HYDROXYCHLORURE
DE CALCIUM

La réaction de l'acide chlorhydrique avec des adsorbants alcalins tels que la chaux au niveau de stations d'incinération entraîne la formation de chlorure ainsi que de l'hydroxychlorure de calcium. Une étude thermodynamique des différentes réactions mises en jeu dans le procédé de déchloruration serait nécessaire, afin de montrer qu'un tel produit serait théoriquement susceptible d'être formé. Cependant, les données thermodynamiques de CaClOH permettant de mener à bien une telle étude ne sont pas disponibles dans la littérature. Par conséquent, une méthode permettant de prédire ces données a été développée dans ce présent travail. Des valeurs d'énergie de Gibbs et d'entropie de formation de CaClOH prédites par cette méthode à différentes températures ont été comparées à celles déterminées à l'aide du modèle de Mostafa, et des résultats satisfaisants ont été obtenus.

DETERMINATION OF THERMODYNAMICAL DATA OF
CALCIUM HYDROXICHLORIDE

The reaction of hydrochloric acid with dry alkaline sorbents such as hydrated lime in the incineration units leads to the formation of not only calcium chloride but calcium hydroxichloride as well. A thermodynamic study of the chemical reactions involved in the dechlorination process is required in order to show if such a product is theoretically possible to be formed. However, the data of CaClOH necessary to carry out such a study are not available in the literature. Hence, a method of predicting these data is developed in the present work. Predicted values of Gibbs energy and entropy of formation of CaClOH at different temperatures are compared to values calculated by Mostafa's model and satisfactory results were obtained.

DETERMINACIÓN DE LOS DATOS TERMODINÁMICOS
DEL HIDROXICLORURO DE CALCIO

La reacción del ácido clorhídrico con adsorbentes alcalinos, como, por ejemplo, la cal, a nivel de las estaciones de incineración provoca la formación de cloruro, así como de hidroxicloruro de calcio. Un estudio termodinámico de las diversas reacciones que intervienen en el procedimiento de descloruración serían necesarias con objeto de demostrar que semejante producto sería susceptible de formación. No obstante, los datos termodinámicos de CaClOH que permitan llevar a buen término semejante estudio no se encuentran disponibles en la literatura. Por consiguiente, se ha desarrollado con motivo del presente trabajo, un método que permite predecir tales datos. Los valores se energía de Gibbs y de entropía de formación de CaClOH predecidos por este método con distintas temperaturas, se han comparado con aquellos determinados mediante el modelo de Mostafa, habiéndose obtenido así resultados satisfactorios.

<footnote>(1) 1 et 4, avenue de Bois-Préau
92852 Rueil-Malmaison Cedex - France</footnote>
INTRODUCTION

It is nowadays frequent to use incineration processes as an alternative to land filling of municipal solid waste. In spite of the obvious advantages such as a significant volume reduction and the energy recovery, such a technology involves aerial releases of acid gases which are very harmful for the environment. Among the most important ones is hydrochloric acid, formed during combustion of PVC. The need for a purification step is therefore compulsory.

A way to reduce the HCl contents in the flue gases is by reaction with dry, fine alkaline sorbents such as calcium hydroxide [1] and [2]. The reaction mechanism of the dechlorination process remains however not fairly well known. As a matter of fact, in some previous works [3, 4, 5], calcium chloride was identified as being the only reaction product formed as shown by reaction 1.

It seems that the reaction mechanism is more complex. Gullet *et al.* [6] were able to identify the presence of other solid phases in the reaction products, in particular calcium hydroxichloride. This compound was in fact detected as soon as 1990 by Kosnyrev [7] when mixing hydrated lime with hydrated calcium chloride. Jozewicz *et al.* [8] have shown afterwards that calcium hydroxide can react with calcium chloride, and have finally proposed the following reaction mechanism:

$$ \begin{array}{l} \mathrm{Ca(OH)_2} + 2 \mathrm{HCl} \rightarrow \mathrm{CaCl_2} + 2 \mathrm{H_2O} \\ \Delta H_f^{298} = -25.787 \mathrm{kcal/mol} \end{array} \qquad (1) $$

$$ \begin{array}{l} \mathrm{Ca(OH)_2} + \mathrm{HCl} \rightarrow \mathrm{CaClOH} + \mathrm{H_2O} \\ \Delta H_f^{298} = -17.754 \mathrm{kcal/mol} \end{array} \qquad (2) $$

$$ \begin{array}{l} \mathrm{Ca(OH)_2} + \mathrm{CaCl_2} \rightarrow 2 \mathrm{CaClOH} \\ \Delta H_f^{298} = -9.725 \mathrm{kcal/mol} \end{array} \qquad (3) $$

For a complete representation, the formation of calcium chloride from calcium hydroxichloride is added to the reaction mechanism:

$$ \begin{array}{l} \mathrm{CaClOH} + \mathrm{HCl} \rightarrow \mathrm{CaCl_2} + \mathrm{H_2O} \\ \Delta H_f^{298} = -8.029 \mathrm{kcal/mol} \end{array} \qquad (4) $$

It is therefore important to identify accurately the reaction product because it influences the ratio Ca/Cl, which determines the amount of Ca-based sorbents to be used in the dechlorination process. So a thermodynamic study of the above mentioned reactions

is required. The data necessary to carry out such a study are however not available in the literature. In the present work, a method to predict them is therefore proposed. It is important to mention also that all these reactions happen at atmospheric pressure and that all the calcium based substances, namelly, Ca(OH)₂, CaCl₂ and CaClOH are in a solid state whereas H₂O and HCl are in a gas state. Note that reactions 1 to 4 are not independent and that, for instance, reaction 1 is the sum of reactions 2 and 4.

1 DEVELOPMENT OF THE METHOD

The same approach as Kosnyrev [9], but taking into consideration in the present study the effects of the temperature, is proposed to evaluate the free enthalpy of formation of the earth alkali hydroxichloride compounds and particularly calcium hydroxichloride.

The aim hence is to relate the Gibbs energy of formation to the enthalpy of formation. Values of ΔGf versus ΔHf for MeCl₂ and Me(OH)₂, where Me stands for Be, Mg, Ca, Sr, and Ba, are plotted at different temperatures, and the results are shown in Figures 1 and 2 respectively. It can be seen that a linear relation is obtained in both cases.

$$ \Delta G_{f,MeCl_2}^T = a_1(T)\Delta H_{f,MeCl_2}^T + b_1(T) \qquad (5) $$

$$ \Delta G_{f,Me(OH)_2}^T = a_2(T) \cdot \Delta H_{f,Me(OH)_2}^T + b_2(T) \qquad (6) $$

<figure><img src="image_2.png" /><figcaption>Figure 1</figcaption></figure>

Gibbs energy of formation of MeCl₂ compounds as a function of the enthalpy of formation and the temperature.
<figure><img src="image_3.png" /><figcaption>Figure 2</figcaption></figure>

Gibbs energy of formation of Me(OH)₂ compounds as a function of the enthalpy of formation and the temperature.

Because the values of the ionic radius of OH-, 0.168 nm [10] and Cl-, 0.181 nm [11] are very close, one can expect a regular variation of the thermodynamic characteristics in the series hydroxide, hydroxichloride and chloride of earth alkali respectively. Since MeClOH is an intermediate compound between MeCl₂ and Me(OH)₂ (substitution of Cl- by OH-), one can as previously relate ΔG<sub>f</sub> to ΔH<sub>f</sub> linearly:

$$ \Delta G_{f,MeClOH}^{T} = a(T) \cdot \Delta H_{f,MeClOH}^{T} + b(T) \quad (7) $$

where

$$ a(T) = \frac{a_{1}(T) + a_{2}(T)}{2} \quad (8) $$

$$ b(T) = \frac{b_{1}(T) + b_{2}(T)}{2} \quad (9) $$

and ΔH<sub>f,MeClOH</sub><sup>T</sup>, the enthalpy of formation of the considered earth alkali hydroxichloride at a given temperature. The values of a and b of the earth alkali hydroxichloride reported in Table 1 have been calculated from equation (8) and (9) respectively.

<caption>TABLE 1</caption>

Temperature effect on the coefficient a and b

<table><thead><tr><th>T (K)</th><th>a</th><th>b (kcal/mol)</th></tr></thead><tbody><tr><td>298.15</td><td>1.010</td><td>18.429</td></tr><tr><td>400</td><td>1.016</td><td>25.423</td></tr><tr><td>500</td><td>1.023</td><td>32.323</td></tr><tr><td>600</td><td>1.036</td><td>40.525</td></tr><tr><td>700</td><td>1.019</td><td>42.036</td></tr><tr><td>800</td><td>0.993</td><td>41.932</td></tr><tr><td>900</td><td>0.975</td><td>43.3144</td></tr><tr><td>1000</td><td>0.935</td><td>39.081</td></tr></tbody></table>

## 2 DISCUSSION

To validate and strengthen this approach, the predicted values of the free enthalpy of formation of magnesium hydroxichloride have been compared to those mentioned in the literature. Table 2 shows that the calculated values are in good agreement with those reported in the Janaf's tables.

<caption>TABLE 2</caption>

Comparison between the predicted and the literature values of the Gibbs energy as a function of the temperature for MgOHCl

<table><thead><tr><th>T (K)</th><th>ΔH<sub>f,literature</sub><br>(kcal/mol)</th><th>ΔG<sub>f,literature</sub><br>(kcal/mol)</th><th>ΔG<sub>f,predicted</sub><br>(kcal/mol)</th></tr></thead><tbody><tr><td>298.15</td><td>-191.199</td><td>-174.773</td><td>-174.68</td></tr><tr><td>400</td><td>-191.080</td><td>-169.313</td><td>-168.840</td></tr><tr><td>500</td><td>-190.868</td><td>-163.893</td><td>-163.271</td></tr><tr><td>600</td><td>-190.555</td><td>-158.526</td><td>-157.563</td></tr><tr><td>700</td><td>-190.140</td><td>-153.219</td><td>-152.804</td></tr><tr><td>800</td><td>-189.623</td><td>-147.979</td><td>-147.933</td></tr><tr><td>900</td><td>-189.006</td><td>-142.809</td><td>-143.114</td></tr><tr><td>1000</td><td>-190.346</td><td>-137.544</td><td>-139.691</td></tr></tbody></table>

The determination of the Gibbs energy of formation of calcium hydroxichloride from equation (7) requires the knowledge of the enthalpy of formation. It has been thought that it would be interesting to evaluate it from our own measurements and compare it with the values reported in the literature. So it is necessary to prepare a given amount of this compound in order to carry out these measurements.

### 2.1 Preparation

A solid mixture containing 80% (mol) Ca(OH)₂ and 20% (mol) CaCl₂·2H₂O was first prepared and then analysed by X-ray diffraction. Figure 3 shows that the same phases as the ones mentioned in a previous work [8] were detected, namely, calcium hydroxide and calcium hydroxichloride. This result suggests that CaClOH is formed when Ca(OH)₂ and CaCl₂·2H₂O are contacted according to:

$$ \mathrm{Ca(OH)_2} + \mathrm{CaCl_2} \cdot 2\mathrm{H_2O} \rightarrow 2 \mathrm{CaClOH} \cdot 2\mathrm{H_2O} \quad (10) $$
<figure><img src="image_4.png" /><figcaption>Figure 3
X-ray diffraction spectrum of a 80% Ca(OH)₂-20% CaCl₂·2H₂O sample.</figcaption></figure>

## 2.2 Determination of ΔH<sub>f</sub>

A few mg of this physical mixture were analysed afterwards by thermogravimetry (TGA), and the thermogram obtained has shown a series of weight losses, as illustrated in Figure 4.

<figure><img src="image_5.png" /><figcaption>Figure 4
TGA scan thermogram of a sample containing 70% Ca(OH)₂ and 30% CaCl₂·2H₂O.</figcaption></figure>

The mass balance suggests that the first weight loss corresponds to the dehydration of the hydrated

calcium hydroxichloride according to:

$$2 \text{CaClOH} \cdot 2\text{H}_2\text{O} \rightarrow 2 \text{CaClOH} + 2 \text{H}_2 \quad (11)$$

the second loss, to the dehydration of the remaining Ca(OH)₂ according to:

$$\text{Ca(OH)}_2 \rightarrow \text{CaO} + \text{H}_2\text{O} \quad (12)$$

the third, to the dehydration of CaClOH as:

$$2 \text{CaClOH} \rightarrow \text{CaO} \cdot \text{CaCl}_2 + \text{H}_2\text{O} \quad (13)$$

and the fourth, to the decarbonation of CaCO₃ initially present in the mixture,

$$\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \quad (14)$$

A differential scan calorimetry (DSC) was performed simultaneously to the TGA, and the results are shown in Figure 5.

It can be seen that each of the above mentioned reactions, corresponds an endothermic peak, the area of which is related to the reaction enthalpy. So a graphical integration of the peak corresponding to reaction 13 between 479 and 564°C has given a value of ΔH<sub>R</sub> equal to 23.718 kcal/mol. One can therefore deduce the enthalpy of formation of calcium hydroxichloride from the following equation:
$$ \Delta H_{f,\text{CaClOH}}^{\text{T}} = \frac{(\Delta H_{f,\text{CaO-CaCl}_2}^{\text{T}} + \Delta H_{f,\text{H}_2\text{O}}^{\text{T}} - \Delta H_{R}^{\text{T}})}{2} \quad (15) $$

<figure><img src="image_6.png" /><figcaption>Figure 5</figcaption></figure>

Differential scan calorimetry of a sample containing 70% Ca(OH)2 and 30% CaCl2·2H2O.

A value of $\Delta H_{f,\text{CaClOH}}$ equal to – 218.409 kcal/mol has been found. This result agrees fairly well with the literature since a value of – 217.700 kcal/mol was given by Kosnyrev [9].

In addition to this, a sample of Ca(OH)₂ exposed to HCl stream in a drop tube furnace was prepared for X-ray diffraction (XRD) analysis. The operating conditions were 250°C reaction temperature and 1000 ppm HCl.

It appears from the XRD spectrum represented in Figure 6, that no calcium chloride is formed since the only phase containing chloride detected, is calcium hydroxichloride. Now that the enthalpy of formation has been evaluated, one can use the proposed method to determine the thermodynamic data of CaClOH.

Table 3 gives these data at different temperatures. It is important to note that the specific heat Cp is given as a function of the temperature by means of Mostafa's model [12], which uses a group contribution technique. It is expressed as:

$$ C_p = \sum_j n_j \Delta_{a,j} + \left( \sum_j n_j \Delta_{b,j} \cdot 10^{-3} \right) \cdot T + \left( \sum_j n_j \Delta_{c,j} \cdot 10^{-6} \right) \cdot T^{-2} + \left( \sum_j n_j \Delta_{d,j} \cdot 10^{-6} \right) \cdot T^2 \quad (16) $$

<figure><img src="image_7.png" /><figcaption>Figure 6</figcaption></figure>

X-ray diffraction spectrum a Ca(OH)₂ sample exposed to a HCl gas stream.
<table><caption>TABLE 3
Predicted thermodynamical data of calcium hydroxichloride</caption><thead><tr><th>T (K)</th><th>Cp<br>(cal/mol.K)</th><th>ΔH<sub>f</sub><br>(kcal/mol)</th><th>ΔG<sub>f</sub><br>(kcal/mol)</th><th>ΔS<sub>f</sub><br>(kcal/mol)</th></tr></thead><tbody><tr><td>298.15</td><td>18.240</td><td>-217.700</td><td>-201.448</td><td>-54.509</td></tr><tr><td>400</td><td>20.186</td><td>-214.761</td><td>-192.773</td><td>-54.967</td></tr><tr><td>500</td><td>21.523</td><td>-215.598</td><td>-188.234</td><td>-54.708</td></tr><tr><td>600</td><td>22.641</td><td>-215.587</td><td>-182.823</td><td>-54.606</td></tr><tr><td>700</td><td>23.656</td><td>-215.348</td><td>-177.404</td><td>-54.206</td></tr><tr><td>800</td><td>24.619</td><td>-215.003</td><td>-171.660</td><td>-54.180</td></tr><tr><td>900</td><td>25.552</td><td>-214.594</td><td>-165.916</td><td>-54.088</td></tr><tr><td>1000</td><td>26.468</td><td>-214.317</td><td>-161.137</td><td>-52.999</td></tr></tbody></table>

where nj is the number of groups of jth type in a single compound, and Δi,j the group contribution for i of the jth ionic, atomic or ligand molecule group. Substituting the values of Δi,j for CaClOH, given in Table 4, into equation (10) leads to:

$$C_{p,\text{CaClOH}} = 18.181 + 8.345 \cdot 10^{-3} T + 0.216 \cdot 10^{6} T^{-2} + 0.166 \cdot 10^{-6} T^{2} \quad (\text{cal/mol.K}) \quad (17)$$

<table><caption>TABLE 4
Group contribution involved in equation (17) for the prediction of the specific heat of calcium hydroxide</caption><thead><tr><th>Group</th><th>nj</th><th>Δa,j</th><th>Δb,j</th><th>Δc,j</th><th>Δd,j</th></tr></thead><tbody><tr><td>Ca++</td><td>1</td><td>4.897</td><td>-1.489</td><td>-0.006</td><td>-0.770</td></tr><tr><td>Cl-</td><td>1</td><td>6.366</td><td>2.482</td><td>-0.060</td><td>0.157</td></tr><tr><td>OH-</td><td>1</td><td>6.918</td><td>7.352</td><td>-0.150</td><td>0.779</td></tr></tbody></table>

The values of the enthalpy of formation reported in Table 2 are determined from the widely known relation given by (13), expressing the enthalpy as a function of the specific heats. In the case of CaClOH formation, the specific heat variation is expressed as:

$$\Delta C_p = C_{p,\text{CaClOH}} - C_{p,\text{Ca}} - 0.5(C_{p,\text{O}_2} + C_{p,\text{H}_2} + C_{p,\text{Cl}_2}) \quad (18)$$

The values of the entropy given in Table 2 were deduced when equalizing equation (7) with the following relation:

$$\Delta G_f^T = \Delta H_f^T - T \cdot \Delta S_f^T \quad (19)$$

hence,

$$\Delta S_f^T = \frac{\Delta H_f^T [1 - a(T)] - b(T)}{T} \quad (20)$$

Figure 7 shows a comparison between the values of ΔSf determined from the proposed model

represented by equation (20) and those predicted when substituting equation (18) into the following relation:

$$\Delta S_f^T = \Delta S_f^{298} + \int_{298}^{T} \frac{\Delta C_p}{T} \cdot dT \quad (21)$$

<figure><img src="image_8.png" /><figcaption>Figure 7
Comparison between predicted values of DSf versus the temperature.</figcaption></figure>

It can be seen that a fairly good agreement is obtained, particularly at low temperature. Similarly, a comparison between the values of the Gibbs energy estimated by the proposed method (equation (7)) and those determined by the known thermodynamic relation expressing the Gibbs energy as a function of the specific heats and the temperature, are presented in Figure 8. Here too, a good agreement is obtained. Note that the use of Mostafa's model is necessary to determine the value of ΔCp.

<figure><img src="image_9.png" /><figcaption>Figure 8
Comparison between predicted values of DGf versus the temperature.</figcaption></figure>
Now that the thermodynamic data of CaClOH have been evaluated and validated by the above mentioned comparisons, a thermodynamic study of the chemical reactions involved during the dechlorination process could be done.

The effect of temperature on the equilibrium constant K of reactions 1, 2, 3 and 4 is represented in Figure 9. It can be seen first, as far as equilibrium thermodynamics is concerned, that all the reactions involved in the mechanism are possible in the temperature range considered.

<figure><img src="image_10.png" /><figcaption>Figure 9
Influence of the temperature on the equilibrium constant.</figcaption></figure>

In addition, a temperature increase leads to a decrease of the equilibrium constant, agreeing therefore with thermodynamic laws since all the considered reactions are exothermic.

The results as presented here give the final equilibrium state of the considered system but no informations about the reaction mechanism. However, the analytical measurements conducted by X-ray diffraction and thermogravimetry seem to indicate that calcium hydroxichloride is actually formed during the dechlorination process according to reactions 2 and 3.

To broaden the range of validity of this proposed method, values of $\Delta G_f^{298}$ of other compounds from an other class of elements of the periodic table, for instance the aluminium class, have been calculated.

Table 5 shows, indeed, that the predicted values agree fairly well with the ones mentioned in the literature [14].

<caption>TABLE 5</caption>

Comparison between the predicted and the literature values of the Gibbs energy of formation of other compounds at 298 K

<table><thead><tr><th>Compounds</th><th>ΔG (literature)<br>(kcal/mol)</th><th>ΔG (predicted)<br>(kcal/mol)</th><th>% error</th></tr></thead><tbody><tr><td>AIOOH</td><td>-210.59</td><td>-214.39</td><td>1.80</td></tr><tr><td>AIOCI</td><td>-175.58</td><td>-168.65</td><td>3.94</td></tr><tr><td>BOOH</td><td>-176.37</td><td>-173.29</td><td>1.75</td></tr><tr><td>BOCI</td><td>-152.54</td><td>-149.75</td><td>1.83</td></tr></tbody></table>

## CONCLUSION

A method of evaluating the thermodynamical data of the earth alkali hydroxichlorides and in particular CaClOH has been developed in the present work. The predicted values of $\Delta G_f$ and $\Delta S_f$ have shown to be in good agreement with those either evaluated by other technics or mentioned in the literature. The thermodynamical study of the reactions involved as well as the experimental analysis indicate that, calcium hydroxichloride could be formed during the dechlorination process, and that the formation of calcium chloride seems to be subsequent to the total conversion of calcium hydroxide into calcium hydroxichloride.

## NOMENCLATURE

a coefficient in the linear relation for the prediction of $\Delta G_f$ of MeClOH

a₁ coefficient in the linear relation for the prediction of $\Delta G_f$ of MeCl₂

a₂ coefficient in the linear relation for the prediction of $\Delta G_f$ of Me(OH)₂

b coefficient in the linear relation for the prediction of $\Delta G_f$ of MeClOH in kcal/mol

b₁ coefficient in the linear relation for the prediction of $\Delta G_f$ of MeCl₂ in kcal/mol

b₂ coefficient in the linear relation for the prediction of $\Delta G_f$ of Me(OH) in kcal/mol

Cp specific heat in cal/(mol·K)

nj number of groups of the jth type in a single compound being predicted

T absolute temperature in K
Δa,j group contribution for a of the jth ionic, atomic,
or ligand molecule group in cal/(mol·K)

Δb,j group contribution for b of the jth ionic, atomic,
or ligand molecule group in cal/((mol·(K)₂)

Δc,j group contribution for c of the jth ionic, atomic,
or ligand molecule group in cal.K/mol

Δd,j group contribution for d of the jth ionic, atomic,
or ligand molecule group in cal/(mol·(K)₃)

ΔGf free enthalpy of formation in kcal/mol

ΔHf free enthalpy of formation in kcal/mol

ΔH<sub>R</sub> reaction enthalpy in kcal/mol

ΔS<sub>f</sub> entropy of formation in cal/(mol·K).

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*Final manuscript received in March 1997*