**3.1.1 The V – O2 – Cl2 stability diagram**

The relative stability of the possible chlorinated compounds of vanadium can be assessed through construction of predominance diagrams by fixing the temperature and systematic varying the values of *P*(Cl2) and *P*(O2).

For the temperature range usually found in chlorination praxis, three temperatures were considered, 1073 K, 1273 K and 1573 K. The partial pressure of Cl2 and O2 were varied in the range between 3.98.10-31atm and 1atm. All chlorinated species are considered to be formed at the standard state (pure at 1atm). The predominance diagrams can be observed on Figures (14), (15) and (16).

The stability field of VCl2(l) grows in relation to those associated to VCl4 and VOCl3. At 1573 K the VCl2(l) area is the greatest among the chlorides and the VCl3(g) field appears. So, as temperature achieves higher values the concentration of VCl3 in the gas phase should increase in comparison with the other chlorinated species, including VCl2. This behavior agrees with the one observed during the computation of the gas phase speciation and will be better discussed on topic (3.1.3.2).

investigations associated with measurements of the vapor pressure for the sublimation of VCl2 and VCl3, and the boiling of VOCl3 and VCl4. There are also evidences for the occurrence of specific thermal decomposition reactions (Eq. 34), such as those of VCl3,

VCl2 Solid Sublimation( McCarley Roddy (1964)

VCl4 Liquid Ebulition Oppermann (1962a)

VO2Cl Solid Thermal decomposition( Oppermann (1967) VOCl2 Solid Thermal decomposition( Oppermann (1967)

Table 1. Physical nature and phase equilibrium data for vanadium chlorinated compounds

3 24 2 3 25

 

2VCl s VCl s VCl g 3VO Cl s VOCl g VO s 2VOCl (s) VOCl g VOCl s

2 3

gaseous VOCl, VOCl3, and VOCl2 have already been published (Hackert et al., 1996).

tendency of this oxychloride to be stabilized in the gaseous state.

**3.1.1 The V – O2 – Cl2 stability diagram** 

varying the values of *P*(Cl2) and *P*(O2).

be better discussed on topic (3.1.3.2).

Figures (14), (15) and (16).

 

Chromatographic measurements conducted recently confirmed the possible formation of VCl, VCl2, VCl3, and VCl4 in the gas phase (Hildenbrand et al., 1988). In this study the molar Gibbs energy models for the mentioned chlorides were revised, and new functions proposed. In the case vanadium oxychlorides, models for the molar Gibbs energies of

For gaseous VO2Cl, on the other hand, no thermodynamic model exists, indicating the low

The relative stability of the possible chlorinated compounds of vanadium can be assessed through construction of predominance diagrams by fixing the temperature and systematic

For the temperature range usually found in chlorination praxis, three temperatures were considered, 1073 K, 1273 K and 1573 K. The partial pressure of Cl2 and O2 were varied in the range between 3.98.10-31atm and 1atm. All chlorinated species are considered to be formed at the standard state (pure at 1atm). The predominance diagrams can be observed on

The stability field of VCl2(l) grows in relation to those associated to VCl4 and VOCl3. At 1573 K the VCl2(l) area is the greatest among the chlorides and the VCl3(g) field appears. So, as temperature achieves higher values the concentration of VCl3 in the gas phase should increase in comparison with the other chlorinated species, including VCl2. This behavior agrees with the one observed during the computation of the gas phase speciation and will

Thermal decomposition McCarley Roddy (1964)

characterization( Schäffer at al. (1961)

Oppermann (1967)

(34)

Chloride Physical state Equilibrium data Reference VCl - - -

VOCl2 and VO2Cl (Oppermann, 1967).

VCl3 Solid Sublimation/

VOCl3 Liquid Ebulition(

VOCl Solid Synthesis and

Fig. 14. Predominance diagram for the system V – O – Cl at 1073 K

Finally, by starting in a state inside a field representing the formation of VCl4 or VCl3 and by making *P*(O2) progressively higher, a value is reached, after which VOCl3(g) appears. So, the mol fraction of VCl4 and VCl3 in gas should reduce when *P*(O2) achieves higher values. This is again consistent with the speciation computations developed on topic (3.1.3.2).

Fig. 15. Predominance diagram for the system V – O – Cl at 1273 K

On the Chlorination Thermodynamics 807

al., 2005). The compound decomposes producing graphite, which reacts with oxygen dislocating the chlorination equilibrium in the desired direction. A simpler route, however, would be to admit carbon as graphite together with the oxide sample into the reactor. If graphite is present in excess, the O2 concentration in the reactor's atmosphere is maintained at very low values, which are achievable through the formation of carbon oxides (Eq. 37)

2 2

(37)

(38)

2 COOC CO2O2C 

So, for the production of VCl4 in the presence of graphite, the reaction of C with O2 can lead

 gCO5g l,2VClsC5g4Clls,OV gCO5.2g l,2VClsC5.2g4Clls,OV

reactions associated with the formation of CO and CO2 for one mole of O2 (Eq. 37).

52 2 4 2 

The effect of the presence of graphite over the <sup>o</sup> *G*r x *T* curves for the formation of VCl4 can be seen in the diagram of Figure (17). As a matter of comparison, the plot for the formation of the same species in the absence of graphite is also shown, together with the curves for the

It can be readily seen that graphite strongly reduces the standard molar Gibbs energy of reaction, promoting in this way considerably the thermodynamic driving force associated with the chlorination process. The presence of graphite has also an impact over the standard molar reaction enthalpy. The direct action of Cl2 is associated with an endothermic reaction (positive linear coefficient), but by adding graphite the processes become considerably

52 2 4

to the evolution of gaseous CO or CO2 (Eq. 38).

Fig. 17. <sup>o</sup> *G*<sup>r</sup> vs. T for for the formation of VCl4

exothermic (negative linear coefficient).

Fig. 16. Predominance diagram for the system V – O – Cl at at 1573 K

### **3.1.2 V2O5 direct chlorination and the effect of the reducing agent**

The direct chlorination of V2O5 is a process, which consists in the reaction of a V2O5 sample with gaseous Cl2.

$$\text{V}\_2\text{O}\_5 + \text{Cl}\_2 = \text{Chloride} / \text{Oxychride} + \text{O}\_2 \tag{35}$$

In praxis, temperature lies usually between 1173 K and 1473 K. The chlorination equilibrium could then be dislocated in the direction of the formation of chlorides and oxychlorides if one removes O2 and or adds Cl2 to the reactors atmosphere. So, for low *P*(O2) (< 10-20 atm) and high *P*(Cl2) (between 0.1 and 1 atm) values, according to the predominance diagrams of Figures (14) and (15), VCl4 should be the most stable vanadium chloride, which is produced according to Eq. (36).

$$\text{V}\_2\text{O}\_5 + 2\text{Cl}\_2 = 2\text{V}\text{Cl}\_4 + 2.5\text{O}\_2\tag{36}$$


Table 2. Equilibrium constant for the reaction represented by Eq. (37)

The equilibrium constant for reaction represented by Eq. (36) is associated with very low values between 1173 K and 1473 K (see Table 2). So, it can be concluded that the formation of VCl4 has a very low thermodynamic driving force in the temperature range considered. One possibility to overcome this problem is to add to the reaction system some carbon bearing compound (Allain et al., 1997, Gonzallez et al., 2002a; González et al., 2002b; Jena et

Fig. 16. Predominance diagram for the system V – O – Cl at at 1573 K

**3.1.2 V2O5 direct chlorination and the effect of the reducing agent** 

K T (K) 1.76257.10-13 1173 5.82991.10-11 1273 1.0397.10-08 1473 Table 2. Equilibrium constant for the reaction represented by Eq. (37)

with gaseous Cl2.

according to Eq. (36).

The direct chlorination of V2O5 is a process, which consists in the reaction of a V2O5 sample

 V2O5 + Cl2 = Chloride/Oxychloride + O2 (35) In praxis, temperature lies usually between 1173 K and 1473 K. The chlorination equilibrium could then be dislocated in the direction of the formation of chlorides and oxychlorides if one removes O2 and or adds Cl2 to the reactors atmosphere. So, for low *P*(O2) (< 10-20 atm) and high *P*(Cl2) (between 0.1 and 1 atm) values, according to the predominance diagrams of Figures (14) and (15), VCl4 should be the most stable vanadium chloride, which is produced

V2O5 + 2Cl2 = 2VCl4 + 2.5O2 (36)

The equilibrium constant for reaction represented by Eq. (36) is associated with very low values between 1173 K and 1473 K (see Table 2). So, it can be concluded that the formation of VCl4 has a very low thermodynamic driving force in the temperature range considered. One possibility to overcome this problem is to add to the reaction system some carbon bearing compound (Allain et al., 1997, Gonzallez et al., 2002a; González et al., 2002b; Jena et al., 2005). The compound decomposes producing graphite, which reacts with oxygen dislocating the chlorination equilibrium in the desired direction. A simpler route, however, would be to admit carbon as graphite together with the oxide sample into the reactor. If graphite is present in excess, the O2 concentration in the reactor's atmosphere is maintained at very low values, which are achievable through the formation of carbon oxides (Eq. 37)

$$\begin{aligned} \text{2C} + \text{O}\_2 &= \text{2CO} \\ \text{C} + \text{O}\_2 &= \text{CO}\_2 \end{aligned} \tag{37}$$

So, for the production of VCl4 in the presence of graphite, the reaction of C with O2 can lead to the evolution of gaseous CO or CO2 (Eq. 38).

$$\begin{aligned} \text{V}\_2\text{O}\_3(\text{s}, \text{l}) + 4\text{Cl}\_2(\text{g}) + 2.5\text{C}(\text{s}) &\rightarrow 2\text{VCl}\_4(\text{l}, \text{g}) + 2.5\text{CO}\_2(\text{g})\\ \text{V}\_2\text{O}\_3(\text{s}, \text{l}) + 4\text{Cl}\_2(\text{g}) + 5\text{C}(\text{s}) &\rightarrow 2\text{VCl}\_4(\text{l}, \text{g}) + 5\text{CO}(\text{g}) \end{aligned} \tag{38}$$

The effect of the presence of graphite over the <sup>o</sup> *G*r x *T* curves for the formation of VCl4 can be seen in the diagram of Figure (17). As a matter of comparison, the plot for the formation of the same species in the absence of graphite is also shown, together with the curves for the reactions associated with the formation of CO and CO2 for one mole of O2 (Eq. 37).

Fig. 17. <sup>o</sup> *G*<sup>r</sup> vs. T for for the formation of VCl4

It can be readily seen that graphite strongly reduces the standard molar Gibbs energy of reaction, promoting in this way considerably the thermodynamic driving force associated with the chlorination process. The presence of graphite has also an impact over the standard molar reaction enthalpy. The direct action of Cl2 is associated with an endothermic reaction (positive linear coefficient), but by adding graphite the processes become considerably exothermic (negative linear coefficient).

On the Chlorination Thermodynamics 809

reduction of its inclination at the melting temperature of the oxide. However, the presence of the inflexion point is much more evident for the reactions with the lowest variation of number of moles of gaseous reactants, as is the case for the direct action of Cl2, which leads

The quantity *n*g controls the molar entropy of the reaction. By lowering the magnitude *n*<sup>g</sup> the value of the reaction entropy reduces, and the effect of melting of V2O5 over the

Based on the predominance diagrams of topic (3.1.1), VOCl3 should be formed for *P*(Cl2) close to 1atm as *P*(O2) gets higher. The presence of graphite has the same effect over the molar Gibbs energy of formation of VOCl3, promoting in this way the thermodynamic driving force for the reaction. Its curve is compared with the one for the formation of VCl4 on Figure (19). The inflexion around 954 K is again associated with the melting of V2O5. As the reaction associated with the formation of VCl4, the formation of VOCl3 has a negative molar reaction enthalpy. So, if the gas phase is considered ideal, for the production of both chlorinated compounds the system should transfer heat to its neighborhood (exothermic

On what touches the molar reaction entropy, the graphic of Figure (19) indicates, that the reaction associated with the formation of VCl4 should generate more entropy (more negative angular coefficient for the entire temperature range). This can be explained by the fact, that in the case of VCl4 the variation of the number of mole of gaseous reactants and products (*n*g = 3) is higher than the value for the formation of VOCl3 (*n*g = 2). This illustrates how

Finally, it should be pointed out that the standard molar Gibbs energy has the same order of magnitude for both chlorinated species considered. So, only by appreciating the <sup>o</sup> *G*<sup>r</sup> <sup>x</sup>*<sup>T</sup>* curves of these chlorides it is impossible to tell case which species should be found in the

important the magnitude of *n*g is for the molar entropy of a gas – solid reaction.

gas with the highest concentration. This problem will be covered on topic (3.2).

to the evolution of CO2 (*n*g = 0.5).

reaction).

standard molar reaction Gibbs energy becomes more evident.

Fig. 19. <sup>o</sup> *G*<sup>r</sup> vs. T for the formation of VOCl3 and VCl4

The curves associated with the VCl4 formation in the presence of the reducing agent cross each other at 973 K, the same temperature where the curves corresponding to the formation of CO and CO2 have the same Gibbs energy value. This point is defined by the temperature, where the Gibbs energy of the Boudouard reaction (C + CO2 = 2CO) is equal to zero.

The equivalence of this point and the intersection associated with the curves for the formation of VCl4 can be perfectly understood, as the Boudouard reaction can be obtained through a simple linear combination, according to Eq. (39). So, the molar Gibbs energy associated with the Boudouard reaction is equal to the difference between the molar Gibbs energy of the VCl4 formation with the evolution of CO and the same quantity for the reaction associated with the CO2 production. When the curves for the formation of VCl4 crosses each other, the difference between their molar Gibbs energies is zero, and according to Eq. (39) the same must happen with the molar Gibbs energy of the Boudouard reaction.

$$\begin{aligned} \text{1) V}\_{2}\text{O}\_{s}\text{(s},\text{l}) + 4\text{Cl}\_{2}\text{(g)} + 5\text{C(s)} &\xrightarrow{\text{AG}\_{2}} 2\text{VCl}\_{4}\text{(l,g)} + 5\text{CO(g)}\\ \text{2) V}\_{2}\text{O}\_{s}\text{(s,l)} + 4\text{Cl}\_{2}\text{(g)} + 2.5\text{C(s)} &\xrightarrow{\text{AG}\_{2}} 2\text{VCl}\_{4}\text{(l,g)} + 2.5\text{CO}\_{2}\text{(g)}\\ \text{3) C(s)}\text{(s)} + \text{CO}\_{2}\text{(g)} &\xrightarrow{\text{AG}\_{2}} 2\text{CO(g)} \end{aligned} \tag{39}$$

$$\begin{aligned} \Delta G\_{\mathfrak{z}} &= \Delta G\_{\mathfrak{z}} - \Delta G\_{\mathfrak{z}} \\ \lim\_{T \to 973 \,\mathrm{K}} \Big( \Delta G\_{\mathfrak{z}} \Big) &= \lim\_{T \to 973 \,\mathrm{K}} \Big( \Delta G\_{\mathfrak{z}} - \Delta G\_{\mathfrak{z}} \Big) = \Delta G - \Delta G = 0 \end{aligned}$$

2

Fig. 18. <sup>o</sup> *G*<sup>r</sup> vs. T the formation of VCl4 – melting of V2O5

The inflexion point present on the curves of Figure (17) is associated with the melting of V2O5. This inflexion is better evidenced on the graphic of Figure (18). As V2O5 is a reactant, according to the concepts developed on topic (2.2.1), the curve should experience a

The curves associated with the VCl4 formation in the presence of the reducing agent cross each other at 973 K, the same temperature where the curves corresponding to the formation of CO and CO2 have the same Gibbs energy value. This point is defined by the temperature,

The equivalence of this point and the intersection associated with the curves for the formation of VCl4 can be perfectly understood, as the Boudouard reaction can be obtained through a simple linear combination, according to Eq. (39). So, the molar Gibbs energy associated with the Boudouard reaction is equal to the difference between the molar Gibbs energy of the VCl4 formation with the evolution of CO and the same quantity for the reaction associated with the CO2 production. When the curves for the formation of VCl4 crosses each other, the difference between their molar Gibbs energies is zero, and according to Eq. (39) the same must happen with the molar Gibbs energy of the Boudouard reaction.

*G*

1

sC5g4Clls,OV 1) gCO5g l,2VCl

52 2 4

sC5.2g4Clls,OV 2) gCO5.2g l,2VCl

52 2 4 2

The inflexion point present on the curves of Figure (17) is associated with the melting of V2O5. This inflexion is better evidenced on the graphic of Figure (18). As V2O5 is a reactant, according to the concepts developed on topic (2.2.1), the curve should experience a

3

*G*

*g g*

*GGGGLimGLim*

<sup>1</sup> <sup>2</sup> <sup>973</sup> <sup>3</sup> <sup>973</sup>

COsC 3) CO2

2

Fig. 18. <sup>o</sup> *G*<sup>r</sup> vs. T the formation of VCl4 – melting of V2O5

3 1 2

*KT KT*

*GGG*

0

*G*

2

(39)

where the Gibbs energy of the Boudouard reaction (C + CO2 = 2CO) is equal to zero.

reduction of its inclination at the melting temperature of the oxide. However, the presence of the inflexion point is much more evident for the reactions with the lowest variation of number of moles of gaseous reactants, as is the case for the direct action of Cl2, which leads to the evolution of CO2 (*n*g = 0.5).

The quantity *n*g controls the molar entropy of the reaction. By lowering the magnitude *n*<sup>g</sup> the value of the reaction entropy reduces, and the effect of melting of V2O5 over the standard molar reaction Gibbs energy becomes more evident.

Based on the predominance diagrams of topic (3.1.1), VOCl3 should be formed for *P*(Cl2) close to 1atm as *P*(O2) gets higher. The presence of graphite has the same effect over the molar Gibbs energy of formation of VOCl3, promoting in this way the thermodynamic driving force for the reaction. Its curve is compared with the one for the formation of VCl4 on Figure (19). The inflexion around 954 K is again associated with the melting of V2O5. As the reaction associated with the formation of VCl4, the formation of VOCl3 has a negative molar reaction enthalpy. So, if the gas phase is considered ideal, for the production of both chlorinated compounds the system should transfer heat to its neighborhood (exothermic reaction).

Fig. 19. <sup>o</sup> *G*<sup>r</sup> vs. T for the formation of VOCl3 and VCl4

On what touches the molar reaction entropy, the graphic of Figure (19) indicates, that the reaction associated with the formation of VCl4 should generate more entropy (more negative angular coefficient for the entire temperature range). This can be explained by the fact, that in the case of VCl4 the variation of the number of mole of gaseous reactants and products (*n*g = 3) is higher than the value for the formation of VOCl3 (*n*g = 2). This illustrates how important the magnitude of *n*g is for the molar entropy of a gas – solid reaction.

Finally, it should be pointed out that the standard molar Gibbs energy has the same order of magnitude for both chlorinated species considered. So, only by appreciating the <sup>o</sup> *G*<sup>r</sup> <sup>x</sup>*<sup>T</sup>* curves of these chlorides it is impossible to tell case which species should be found in the gas with the highest concentration. This problem will be covered on topic (3.2).

On the Chlorination Thermodynamics 811

V O Cl C VCl CO /CO VCl 0.5Cl VCl VCl 0.5Cl VCl

(41)

25 2 2 2 223 324

 

Fig. 21. <sup>o</sup> *G*<sup>r</sup> x T for reaction paths of Eq. (41)

Fig. 22. <sup>o</sup> *G*<sup>r</sup> x T for reaction paths of Eq. (41)

### **3.1.2.1 Successive chlorination steps**

As discussed on topic (2.2.1), the standard free energy vs. temperature diagram is a valuable tool for suggesting possible reactions paths. Let's consider first the formation of VCl4. Such a process could be thought as the result of three stages. In the first one, a lower chlorinated compound (VCl) is formed. The precursor then reacts with Cl2 resulting in higher chlorinated species (Eq. 40).

$$\begin{aligned} \text{V}\_{2}\text{O}\_{3} + \text{Cl}\_{2} + \text{C} &\rightarrow \text{VCl} + \text{CO}\_{2} / \text{CO} \\ \text{VCl} + 0.5\text{Cl}\_{2} &\rightarrow \text{VCl}\_{2} \\ \text{VCl}\_{2} + 0.5\text{Cl}\_{2} &\rightarrow \text{VCl}\_{3} \\ \text{VCl}\_{3} + 0.5\text{Cl}\_{2} &\rightarrow \text{VCl}\_{4} \end{aligned} \tag{40}$$

Fig. 20. <sup>o</sup> *G*<sup>r</sup> x T for reaction paths of Eq. (38)

The <sup>o</sup> *G*<sup>r</sup> <sup>x</sup>*T* plots associated with reactions paths represented by mechanisms of Eq. (40) were included on Figure (20). Two inflexion points are evidenced in the diagram of Figure (20). The first one around 1000 K is associated with VCl2 melting. The second one, around 1100 K, is associated with the sublimation of VCl3. It can be deduced that only for temperatures greater than 1600 K the path described by Eq. (40) would be possible. For lower temperatures, the molar Gibbs energy of the first step is higher than the one associated with the second.

Another mechanism can be thought for the production of VCl4. This time, VCl2 is formed first, which then reacts to give VCl3 and finally VCl4 (Eq. 41). The characteristic <sup>o</sup> *G*<sup>r</sup> <sup>x</sup>*<sup>T</sup>* curves for the reactions defined in Eq. (41) are presented on Figures (21) and (22).

As discussed on topic (2.2.1), the standard free energy vs. temperature diagram is a valuable tool for suggesting possible reactions paths. Let's consider first the formation of VCl4. Such a process could be thought as the result of three stages. In the first one, a lower chlorinated compound (VCl) is formed. The precursor then reacts with Cl2 resulting in higher

> 3 2 4 2 2 3

VClCl5.0VCl VClCl5.0VCl VClCl5.0VCl

 

2 2 252 2

The <sup>o</sup> *G*<sup>r</sup> <sup>x</sup>*T* plots associated with reactions paths represented by mechanisms of Eq. (40) were included on Figure (20). Two inflexion points are evidenced in the diagram of Figure (20). The first one around 1000 K is associated with VCl2 melting. The second one, around 1100 K, is associated with the sublimation of VCl3. It can be deduced that only for temperatures greater than 1600 K the path described by Eq. (40) would be possible. For lower temperatures, the molar Gibbs energy of the first step is higher than the one

Another mechanism can be thought for the production of VCl4. This time, VCl2 is formed first, which then reacts to give VCl3 and finally VCl4 (Eq. 41). The characteristic <sup>o</sup> *G*<sup>r</sup> <sup>x</sup>*<sup>T</sup>*

curves for the reactions defined in Eq. (41) are presented on Figures (21) and (22).

(40)

CO/COVClCClOV

**3.1.2.1 Successive chlorination steps** 

Fig. 20. <sup>o</sup> *G*<sup>r</sup> x T for reaction paths of Eq. (38)

associated with the second.

chlorinated species (Eq. 40).

$$\begin{aligned} \text{V}\_2\text{O}\_5 + \text{Cl}\_2 + \text{C} &\rightarrow \text{VCl}\_2 + \text{CO}\_2 \text{ / CO} \\ \text{VCl}\_2 + 0.5\text{Cl}\_2 &\rightarrow \text{VCl}\_3 \\ \text{VCl}\_3 + 0.5\text{Cl}\_2 &\rightarrow \text{VCl}\_4 \end{aligned} \tag{41}$$

Fig. 21. <sup>o</sup> *G*<sup>r</sup> x T for reaction paths of Eq. (41)

Fig. 22. <sup>o</sup> *G*<sup>r</sup> x T for reaction paths of Eq. (41)

On the Chlorination Thermodynamics 813

The inflexion point around 800 K is associated with the sublimation of VOCl2, and around 1400 K with the sublimation of VOCl. According to the <sup>o</sup> *G*<sup>r</sup> <sup>x</sup>*T* curves presented on Figure (23), it can be deduced that the reaction steps will follow the proposed order only for temperatures higher than 1053 K. At lower temperatures VOCl2 should be formed directly from VOCl (Eq. 44). It is interesting to note that the sublimation of VOCl2 is the phenomenon responsible for the described inversion of behavior. Again, to attain thermodynamic consistency for temperatures higher than 1053 K, the curves associated with the formation of VOCl2 and VOCl3 according to Eq. (43) must be substituted for the curve associated with reaction represented by Eq. (44), which was drawn with red color in the diagram plotted on Figure (23). It should be mentioned indeed, that the reaction equations compared must be written with the same stoichiometric coefficient for Cl2, or equivalently,

Finally, some remarks may be constructed about the possible reaction order values in relation to Cl2. According to the discussion developed so far, for the temperature range between 1100 K and 1400 K, Eq. (45) describes the most probable reactions paths for the formation of VCl4 and VOCl3. As a result, depending on the nature of the slowest step, the

> 25 2 2 22 4

V O 2Cl 5C 2VCl 5CO

V O Cl 5C 2VOCl 5CO

As is evident from the discussion developed on topic (3.1.2), the chlorinated compounds VCl4 and VOCl3 are the most stable species in the gas phase as the atmosphere becomes concentrated in Cl2. The relative stability of these two chlorinated compounds will be first accessed on topic (3.1.3.1) by applying the method introduced by Kang Zuo (1989) and secondly on topic (3.1.3.2) through computing some speciation diagrams for the gas phase.

As shown in thon topic (2.2.2) the concentrations of VCl4 and VOCl3 can be directly computed by considering that each chlorinated compound is generated independently. It will be assumed that the inlet gas is composed of pure Cl2 (*P*(Cl2) = 1 atm). Further, two temperature values were investigated, 1073 K and 1373 K. At these temperatures, the presence of graphite makes the atmosphere richer in CO, so that for the computations the

> 25 2 4 25 2 3 V O 4Cl 5C 2VCl 5CO V O 3Cl 5C 2VOCl 3CO

The concentrations of VOCl3 and VCl4 can then be expressed as a function of *P*(CO) and

2 2 22 3

<sup>2</sup> VOClClVOCl <sup>3</sup> (44)

(46)

(45)

the Gibbs energy of reaction (44) must be multiplied by 1/2.

reaction order in respect with Cl2 can be equal to one, two or ½.

**3.1.3 Relative stability of VCl4 and VOCl3**

**3.1.3.1 Method of Kang and Zuo** 

following reactions will be considered:

temperature according to Eq. (47).

25 2

VCl Cl VCl

VOCl 0.5Cl VOCl VOCl 0.5Cl VOCl

 

The inflexion points have the same meaning as described for diagram of Figure (20). It can be seen that the first step has a much higher thermodynamic tendency as the other. Also, for temperatures lower than 953 K the second step leads to the formation of VCl3, which then reacts to give VCl4. However, for temperatures higher than 953 K and lower than 1539 K, the step associated with the formation of VCl4 is the one with the lowest standard Gibbs energy. So, in this temperature range, VCl4 should be formed directly from VCl2, as suggested by Eq. (42). In order to achieve thermodynamic consistency in the mentioned temperature interval, the curves associated with the formation of VCl3 and VCl4 according to Eq. (41) should be substituted for the curve associated with reaction defined by Eq. (42), which was represented with red color in the plots presented on Figures (21) and (22).

$$\text{VCl}\_2 + \text{Cl}\_2 = \text{VCl}\_4 \tag{42}$$

Fig. 23. <sup>o</sup> *G*<sup>r</sup> x T for reaction paths of Eq. (43)

For temperatures higher than 1539 K, however, the mechanism is again described by Eq. (41), VCl3 being formed first, which then reacts leading to VCl4. It is also interesting to recognize that the sublimation of VCl3 is responsible for the inversion of the behavior for temperatures higher than approximately 1400 K, where the second reaction step is again the one with the second lowest Gibbs energy of reaction.

On what touches the synthesis of VOCl3, a reaction path can be proposed (Eq. 43), in that VOCl is formed first, which then reacts to give VOCl2, which by itself then reacts to form VOCl3. The <sup>o</sup> *G*r x *T* diagrams associated with these reactions are presented on Figure (23).

$$\begin{aligned} \text{V}\_2\text{O}\_5 + \text{Cl}\_2 + \text{C} &\rightarrow \text{VOCl} + \text{CO/CO}\_2\\ \text{VOCl} + 0.\text{SCl}\_2 &\rightarrow \text{VOCl}\_2\\ \text{VOCl}\_2 + 0.\text{SCl}\_2 &\rightarrow \text{VOCl}\_3 \end{aligned} \tag{43}$$

The inflexion points have the same meaning as described for diagram of Figure (20). It can be seen that the first step has a much higher thermodynamic tendency as the other. Also, for temperatures lower than 953 K the second step leads to the formation of VCl3, which then reacts to give VCl4. However, for temperatures higher than 953 K and lower than 1539 K, the step associated with the formation of VCl4 is the one with the lowest standard Gibbs energy. So, in this temperature range, VCl4 should be formed directly from VCl2, as suggested by Eq. (42). In order to achieve thermodynamic consistency in the mentioned temperature interval, the curves associated with the formation of VCl3 and VCl4 according to Eq. (41) should be substituted for the curve associated with reaction defined by Eq. (42), which was

For temperatures higher than 1539 K, however, the mechanism is again described by Eq. (41), VCl3 being formed first, which then reacts leading to VCl4. It is also interesting to recognize that the sublimation of VCl3 is responsible for the inversion of the behavior for temperatures higher than approximately 1400 K, where the second reaction step is again the

On what touches the synthesis of VOCl3, a reaction path can be proposed (Eq. 43), in that VOCl is formed first, which then reacts to give VOCl2, which by itself then reacts to form VOCl3. The <sup>o</sup> *G*r x *T* diagrams associated with these reactions are presented on Figure (23).

252 2

Cl5.0VOCl VOCl Cl5.0VOCl VOCl VOClCClOV CO/CO

 

2 2 3

2 2

(43)

<sup>22</sup> VClClVCl <sup>4</sup> (42)

represented with red color in the plots presented on Figures (21) and (22).

Fig. 23. <sup>o</sup> *G*<sup>r</sup> x T for reaction paths of Eq. (43)

one with the second lowest Gibbs energy of reaction.

The inflexion point around 800 K is associated with the sublimation of VOCl2, and around 1400 K with the sublimation of VOCl. According to the <sup>o</sup> *G*<sup>r</sup> <sup>x</sup>*T* curves presented on Figure (23), it can be deduced that the reaction steps will follow the proposed order only for temperatures higher than 1053 K. At lower temperatures VOCl2 should be formed directly from VOCl (Eq. 44). It is interesting to note that the sublimation of VOCl2 is the phenomenon responsible for the described inversion of behavior. Again, to attain thermodynamic consistency for temperatures higher than 1053 K, the curves associated with the formation of VOCl2 and VOCl3 according to Eq. (43) must be substituted for the curve associated with reaction represented by Eq. (44), which was drawn with red color in the diagram plotted on Figure (23). It should be mentioned indeed, that the reaction equations compared must be written with the same stoichiometric coefficient for Cl2, or equivalently, the Gibbs energy of reaction (44) must be multiplied by 1/2.

$$\text{VOCl} + \text{Cl}\_2 = \text{VOCl}\_3 \tag{44}$$

Finally, some remarks may be constructed about the possible reaction order values in relation to Cl2. According to the discussion developed so far, for the temperature range between 1100 K and 1400 K, Eq. (45) describes the most probable reactions paths for the formation of VCl4 and VOCl3. As a result, depending on the nature of the slowest step, the reaction order in respect with Cl2 can be equal to one, two or ½.

$$\begin{aligned} \text{V}\_2\text{O}\_5 + 2\text{Cl}\_2 + 5\text{C} &\to 2\text{VCl}\_2 + 5\text{CO} \\ \text{VCl}\_2 + \text{Cl}\_2 &\to \text{VCl}\_4 \\ \text{V}\_2\text{O}\_5 + \text{Cl}\_2 + 5\text{C} &\to 2\text{VOCI} + 5\text{CO} \\ \text{VOCl} + 0.5\text{Cl}\_2 &\to \text{VOCl}\_2 \\ \text{VOCl}\_2 + 0.5\text{Cl}\_2 &\to \text{VOCl}\_3 \end{aligned} \tag{45}$$

### **3.1.3 Relative stability of VCl4 and VOCl3**

As is evident from the discussion developed on topic (3.1.2), the chlorinated compounds VCl4 and VOCl3 are the most stable species in the gas phase as the atmosphere becomes concentrated in Cl2. The relative stability of these two chlorinated compounds will be first accessed on topic (3.1.3.1) by applying the method introduced by Kang Zuo (1989) and secondly on topic (3.1.3.2) through computing some speciation diagrams for the gas phase.

#### **3.1.3.1 Method of Kang and Zuo**

As shown in thon topic (2.2.2) the concentrations of VCl4 and VOCl3 can be directly computed by considering that each chlorinated compound is generated independently. It will be assumed that the inlet gas is composed of pure Cl2 (*P*(Cl2) = 1 atm). Further, two temperature values were investigated, 1073 K and 1373 K. At these temperatures, the presence of graphite makes the atmosphere richer in CO, so that for the computations the following reactions will be considered:

$$\begin{aligned} \text{V}\_2\text{O}\_5 + 4\text{Cl}\_2 + 5\text{C} &\to 2\text{VCl}\_4 + 5\text{CO} \\ \text{V}\_2\text{O}\_5 + 3\text{Cl}\_2 + 5\text{C} &\to 2\text{VOC}l\_3 + 3\text{CO} \end{aligned} \tag{46}$$

The concentrations of VOCl3 and VCl4 can then be expressed as a function of *P*(CO) and temperature according to Eq. (47).

On the Chlorination Thermodynamics 815

quantitative description of equilibrium, as the species build a solution, and as so, their concentrations must be determined at the same time. This sort of information can only arises if one solves the system o equilibrium equations associated to all possible chemical reactions involving the species that form the gas. For the present system (V – O – Cl – C) this task becomes very tricky, as the number of possible species present is pretty significant (ex. CO, CO2, O2, VCl2, VCl3, VCl, VCl4, VOCl3, VOCl), and so the number of possible chemical reactions connecting them. So, we must think in another route for simultaneously computing the concentration of the gaseous species produced by our chlorination process. The only possible way consists in minimizing the total Gibbs energy of the system (see topic

The equilibrium state is defined by fixing *T*, *P*, *n*(V2O5), *P*(O2) and *P*(Cl2). The number of moles of V2O5 is fixed at one. If graphite is present in excess, the partial pressure of O2 is controlled by according to the Boudouard equilibrium (Eq. 39), so that, its presence forces *P*(O2) to attain very low values (typically lower than 10-20atm). The total pressure is fixed at

An excess of graphite is desirable, so that the chlorination reactions can achieve a considerable driving force at the desired conditions. Computationally speaking, this can be done in two ways. One possibility is to define an amount of carbon much greater than the number of moles of V2O5. Other possibility, which has been made accessible through modern computational thermodynamic software, consists in defining the phase "solid graphite" as fixed with a definite amount. The equilibrium compositions (intensive variables) are not a function of the amount of phases present (size of the system), depending only of temperature and total pressure. So we are free to choose any suitable value we desire, such for example zero (ngraphite = 0). This last alternative was implemented in the

1atm and *T* varies in the range between 1073 K and 1473 K.

computations conducted in the present topic.

Fig. 25. Number of moles of gas as a function of *P*(Cl2)

2.2.3).

$$\begin{aligned} P\_{\text{VCl}\_4} &= \sqrt{P\_{\text{CO}}^5 K\_1} \to \ln P\_{\text{VCl}\_4} = \frac{\ln K\_1}{2} + \frac{5}{2} \ln P\_{\text{CO}}\\ P\_{\text{VOC1}\_3} &= \sqrt{P\_{\text{CO}}^3 K\_2} \to \ln P\_{\text{VOC1}\_3} = \frac{\ln K\_2}{2} + \frac{3}{2} \ln P\_{\text{CO}} \end{aligned} \tag{47}$$

Where *K*1 and *K*2 represent, respectively, the equilibrium constants for the reactions associated with the formation of VCl4 and VOCl3 (Eq. 46). By applying Eq. (47) the partial pressure of VCl4 and VOCl3 were computed as a function of *P*(CO). The results were plotted on graphic contained in Figure (24). The significant magnitude of the partial pressure values computed for VOCl3 and VCl4 is a consequence of the huge negative standard Gibbs energy of reaction associated with the formation of these species in the temperature range considered (see Figure 19).

According to Figure (24), VCl4 is the chloride with the highest partial pressure for both specified temperatures. Also, for both temperatures, *P*(VOCl3) becomes higher than *P*(VCl4) only for significant values of *P*(CO). At 1073 K, for example, the partial pressures of the species have equal values only for *P*(CO) equal to 2.98.103atm, and at 1373 K the same happens for *P*(CO) equal to 8.91.103atm.

Fig. 24. Ln(P(VCl4)) and Ln(P(VOCl3)) as a function of Ln(P(CO))

As a result, it is expected that the formation of gaseous VCl4 should have a much greater tendency of occurrence in the temperature range studied. These results will be confirmed through construction of speciation diagrams for the gas phase, a task that will be accomplished on topic (3.1.3.2).

#### **3.1.3.2 Gas phase speciation**

The construction of speciation diagrams for the gas phase enables the elaboration of a complementary picture of the chlorination process in question. The word "speciation" means the concentration of all species in gas. This brings another level of complexity to the

3 2 VOCl CO 2 VOCl CO

Where *K*1 and *K*2 represent, respectively, the equilibrium constants for the reactions associated with the formation of VCl4 and VOCl3 (Eq. 46). By applying Eq. (47) the partial pressure of VCl4 and VOCl3 were computed as a function of *P*(CO). The results were plotted on graphic contained in Figure (24). The significant magnitude of the partial pressure values computed for VOCl3 and VCl4 is a consequence of the huge negative standard Gibbs energy of reaction associated with the formation of these species in the temperature range

According to Figure (24), VCl4 is the chloride with the highest partial pressure for both specified temperatures. Also, for both temperatures, *P*(VOCl3) becomes higher than *P*(VCl4) only for significant values of *P*(CO). At 1073 K, for example, the partial pressures of the species have equal values only for *P*(CO) equal to 2.98.103atm, and at 1373 K the same

ln 5 ln ln

2 2 ln 3 ln ln

2 2

(47)

5 1 VCl CO 1 VCl CO

*<sup>K</sup> P PK P <sup>P</sup>*

*<sup>K</sup> P PK P <sup>P</sup>*

4 4

considered (see Figure 19).

happens for *P*(CO) equal to 8.91.103atm.

accomplished on topic (3.1.3.2). **3.1.3.2 Gas phase speciation** 

Fig. 24. Ln(P(VCl4)) and Ln(P(VOCl3)) as a function of Ln(P(CO))

As a result, it is expected that the formation of gaseous VCl4 should have a much greater tendency of occurrence in the temperature range studied. These results will be confirmed through construction of speciation diagrams for the gas phase, a task that will be

The construction of speciation diagrams for the gas phase enables the elaboration of a complementary picture of the chlorination process in question. The word "speciation" means the concentration of all species in gas. This brings another level of complexity to the

3 3

quantitative description of equilibrium, as the species build a solution, and as so, their concentrations must be determined at the same time. This sort of information can only arises if one solves the system o equilibrium equations associated to all possible chemical reactions involving the species that form the gas. For the present system (V – O – Cl – C) this task becomes very tricky, as the number of possible species present is pretty significant (ex. CO, CO2, O2, VCl2, VCl3, VCl, VCl4, VOCl3, VOCl), and so the number of possible chemical reactions connecting them. So, we must think in another route for simultaneously computing the concentration of the gaseous species produced by our chlorination process. The only possible way consists in minimizing the total Gibbs energy of the system (see topic 2.2.3).

The equilibrium state is defined by fixing *T*, *P*, *n*(V2O5), *P*(O2) and *P*(Cl2). The number of moles of V2O5 is fixed at one. If graphite is present in excess, the partial pressure of O2 is controlled by according to the Boudouard equilibrium (Eq. 39), so that, its presence forces *P*(O2) to attain very low values (typically lower than 10-20atm). The total pressure is fixed at 1atm and *T* varies in the range between 1073 K and 1473 K.

An excess of graphite is desirable, so that the chlorination reactions can achieve a considerable driving force at the desired conditions. Computationally speaking, this can be done in two ways. One possibility is to define an amount of carbon much greater than the number of moles of V2O5. Other possibility, which has been made accessible through modern computational thermodynamic software, consists in defining the phase "solid graphite" as fixed with a definite amount. The equilibrium compositions (intensive variables) are not a function of the amount of phases present (size of the system), depending only of temperature and total pressure. So we are free to choose any suitable value we desire, such for example zero (ngraphite = 0). This last alternative was implemented in the computations conducted in the present topic.

Fig. 25. Number of moles of gas as a function of *P*(Cl2)

On the Chlorination Thermodynamics 817

Besides *P*(Cl2), temperature should also have an effect over the composition of the gas phase. This was studied as follows. Six temperature values were chosen in the range between 1073 K and 1473 K. Next, for each temperature the critical *P*(Cl2) value (the one associated with the formation of the first gas molecules) is identified. The composition of the most stable gaseous species is then computed and is presented in Table (4). During the

*T*(K) X(CO) X(CO2) X(VOCl3) X(VCl2) X(VCl3) X(VCl4) 1073 0.16 3.64.10-3 1.95.10-2 1.74.10-3 9.27.10-2 0.72 1100 0.12 1.23.10-3 1.02.10-2 2.61.10-3 0.12 0.75 1200 4.21.10-2 3.36.10-5 1.08.10-3 9.87.10-3 0.26 0.69 1300 1.76.10-2 1.60.10-6 1.45.10-4 2.98.10-2 0.43 0.52 1373 1.00.10-2 2.29.10-7 3.69.10-5 5.97.10-2 0.56 0.37 1400 8.26.10-3 1.17.10-7 2.27.10-5 7.6.10-2 0.59 0.32 1473 5.07.10-3 2.18.10-8 6.22.10-6 0.14 0.66 0.19

As expected, the mol fraction of CO is greater than the mol fraction of CO2 for the entire temperature range studied. Also, the chloride VCl4 has the highest concentration at 1073 K, a phase which occupies a large area of the predominance diagram at this temperature (Figure 14). As temperature attains higher values, the mol fraction of VCl4 and VOCl3 become progressive lower and the atmosphere more concentrated in VCl2 and VCl3. So, at 1473 K the situation is significant different from the equilibrium state observed at 1073 K. Such behavior is again consistent with the information contained on the predominance diagrams (Figures 14, 15 and 16) where can be seen that the stability fields of VCl4(g) and VOCl3(g) shrink while the area representing the phase VCl3(g) grows. At 1573 K it occupies a visible

It is worthwhile to mention that a more detailed look on the results seems to incorporate apparent inconsistencies. i) The minimum partial pressure of Cl2 for the formation of pure VCl4(g) at 1073 K (Figure 14) is higher than the critical pressure for the formation of the first gaseous species at this temperature (Figure 25). ii) Measurable amounts of VCl3 (greater or equal to 0.1) were detected for temperatures higher than 1100 K (Table 3) but no VCl3(g) field was observed in the predominance diagram computed at 1273 K (Figure 15). iii) Also, no field associated with the formation of VCl2(g) could be detected even at 1573 K (Figure 16) but the speciation computation predicts its presence in measurable amounts at the last temperature (x(VCl2) = 0.14) (Table 3). All these thermodynamic values differences are a consequence of the fact that the pure molar Gibbs energy of each component is higher than its chemical potential in the ideal gas solution, the former model being used for the predominance diagrams construction while the later is applied to the speciation calculations. Therefore, the driving force for the formation of the gaseous compounds is

> 3 3 2 gg g VCl VCl VCl

Another possible type of computation is to study the effect of *P*(O2) over the composition of the gas phase. This variable is restricted by the fact that the amount of graphite phase is fixed. So there is a maximum value of *P*(O2) at each temperature for which the

*g RT x* ln 0 (49)

calculations the partial pressure of O2 was fixed at 1.93.10-22atm.

Table 4. Composition of the "first" gas formed as a function of temperature

amount of the diagrams space (Figure 16).

reduced accordingly to Eq. (49).

On Figure (25), the number of moles of gas produced was plotted as a function of *P*(Cl2) for *T* equal to 1073 K, 1273 K, and 1473 K. The partial pressure of O2 was fixed at 1.93.10-22 atm, and the partial pressure of Cl2 is varied between 3.6.10-7atm and 0.61 atm.

Each curve is defined by three stages. First, for very low values of *P*(Cl2), no gas is formed. At this conditions VCl2(l) is present in equilibrium with graphite. The equilibrium ensemble does not experience any modification until a critical *P(*Cl2) value is reached, at which a discontinuity can be evidenced. The gas phase appears in equilibrium and for any *P*(Cl2) higher than the critical one, the number of moles VCl2(l) becomes equal to zero. This condition defines the second stage, where for higher *P*(Cl2) values the gas composition changes accordingly, through forming of chlorides and oxychlorides. Finally, a *P*(Cl2) value is reached, where all capacity of the system for forming chlorinated compounds is exhausted, and the effect of adding more Cl2 is only the dilution of the chlorinated species formed. As a consequence, the number of mole of gas phase experiences a significant elevation. At 1073 K, for example, Figure (26) describes the effect of *P*(Cl2) over the gas phase composition during the second and third stages. We see that the mol fraction of VCl4 raises (second stage) and after achieving a maximum value starts to decrease (third stage). The concentration variations during the second sage can be ascribed to the occurrence of reactions represented by Eq. (48), which have at 1073 K equilibrium constants much higher than unity (Table 3). The reduction of the mol fraction of VOCl3 can be understood as a dilution effect, which is motivated by the elevation of the mol fractions of VCl4 and Cl2.

$$\begin{aligned} \text{VCl}\_2 + \text{Cl}\_2 &\rightarrow \text{VCl}\_4\\ \text{VCl}\_3 + 0.5\text{Cl}\_2 &\rightarrow \text{VCl}\_4 \end{aligned} \tag{48}$$


Table 3. Equilibrium constants at 1073 K for the reactions represented by Eq. (48)

Fig. 26. Concentration of vanadium chlorides and oxychlorides as a function of *P*(Cl2) at 1073 K

On Figure (25), the number of moles of gas produced was plotted as a function of *P*(Cl2) for *T* equal to 1073 K, 1273 K, and 1473 K. The partial pressure of O2 was fixed at 1.93.10-22 atm,

Each curve is defined by three stages. First, for very low values of *P*(Cl2), no gas is formed. At this conditions VCl2(l) is present in equilibrium with graphite. The equilibrium ensemble does not experience any modification until a critical *P(*Cl2) value is reached, at which a discontinuity can be evidenced. The gas phase appears in equilibrium and for any *P*(Cl2) higher than the critical one, the number of moles VCl2(l) becomes equal to zero. This condition defines the second stage, where for higher *P*(Cl2) values the gas composition changes accordingly, through forming of chlorides and oxychlorides. Finally, a *P*(Cl2) value is reached, where all capacity of the system for forming chlorinated compounds is exhausted, and the effect of adding more Cl2 is only the dilution of the chlorinated species formed. As a consequence, the number of mole of gas phase experiences a significant elevation. At 1073 K, for example, Figure (26) describes the effect of *P*(Cl2) over the gas phase composition during the second and third stages. We see that the mol fraction of VCl4 raises (second stage) and after achieving a maximum value starts to decrease (third stage). The concentration variations during the second sage can be ascribed to the occurrence of reactions represented by Eq. (48), which have at 1073 K equilibrium constants much higher than unity (Table 3). The reduction of the mol fraction of VOCl3 can be understood as a dilution effect, which is motivated by the elevation of the mol fractions of VCl4 and Cl2.

> 22 4 324

(48)

VCl Cl VCl VCl 0.5Cl VCl 

Table 3. Equilibrium constants at 1073 K for the reactions represented by Eq. (48)

Fig. 26. Concentration of vanadium chlorides and oxychlorides as a function of *P*(Cl2) at

K Chemical reaction 1.95.105 <sup>22</sup> VClClVCl <sup>4</sup> 2.12.103 <sup>3</sup> <sup>2</sup> VCl4 VCl 0.5Cl

1073 K

and the partial pressure of Cl2 is varied between 3.6.10-7atm and 0.61 atm.

Besides *P*(Cl2), temperature should also have an effect over the composition of the gas phase. This was studied as follows. Six temperature values were chosen in the range between 1073 K and 1473 K. Next, for each temperature the critical *P*(Cl2) value (the one associated with the formation of the first gas molecules) is identified. The composition of the most stable gaseous species is then computed and is presented in Table (4). During the calculations the partial pressure of O2 was fixed at 1.93.10-22atm.


Table 4. Composition of the "first" gas formed as a function of temperature

As expected, the mol fraction of CO is greater than the mol fraction of CO2 for the entire temperature range studied. Also, the chloride VCl4 has the highest concentration at 1073 K, a phase which occupies a large area of the predominance diagram at this temperature (Figure 14). As temperature attains higher values, the mol fraction of VCl4 and VOCl3 become progressive lower and the atmosphere more concentrated in VCl2 and VCl3. So, at 1473 K the situation is significant different from the equilibrium state observed at 1073 K. Such behavior is again consistent with the information contained on the predominance diagrams (Figures 14, 15 and 16) where can be seen that the stability fields of VCl4(g) and VOCl3(g) shrink while the area representing the phase VCl3(g) grows. At 1573 K it occupies a visible amount of the diagrams space (Figure 16).

It is worthwhile to mention that a more detailed look on the results seems to incorporate apparent inconsistencies. i) The minimum partial pressure of Cl2 for the formation of pure VCl4(g) at 1073 K (Figure 14) is higher than the critical pressure for the formation of the first gaseous species at this temperature (Figure 25). ii) Measurable amounts of VCl3 (greater or equal to 0.1) were detected for temperatures higher than 1100 K (Table 3) but no VCl3(g) field was observed in the predominance diagram computed at 1273 K (Figure 15). iii) Also, no field associated with the formation of VCl2(g) could be detected even at 1573 K (Figure 16) but the speciation computation predicts its presence in measurable amounts at the last temperature (x(VCl2) = 0.14) (Table 3). All these thermodynamic values differences are a consequence of the fact that the pure molar Gibbs energy of each component is higher than its chemical potential in the ideal gas solution, the former model being used for the predominance diagrams construction while the later is applied to the speciation calculations. Therefore, the driving force for the formation of the gaseous compounds is reduced accordingly to Eq. (49).

$$\mathbf{x}\_{\rm VCl\_3}^{\rm g} - \mathbf{g}\_{\rm VCl\_3}^{\rm g} = RT \ln \mathbf{x}\_{\rm VCl\_2}^{\rm g} < 0 \tag{49}$$

Another possible type of computation is to study the effect of *P*(O2) over the composition of the gas phase. This variable is restricted by the fact that the amount of graphite phase is fixed. So there is a maximum value of *P*(O2) at each temperature for which the

On the Chlorination Thermodynamics 819

partial pressure range. The concentration variations associated with the vanadium chlorinated compounds is analogous to the variations observed in the concentrations of CO and CO2.

For *P*(O2) lower than 5.24.10-22atm the variations are much less significant. To get a better picture of the trend observed for the chlorides and oxychlorides, their concentrations were plotted as a function of *P*(O2), which was varied in the range spanned by the data of Table

Fig. 28. Mol fractions of VOCl3 and VCl2 as a function *P*(O2)

Fig. 29. Mol fraction of VOCl3 as a function of *P*(O2)

(5) (Figures 27, 28 and 29)

thermodynamic modeling remains consistent and the computation can be performed. By fixing the temperature at 1373K, the upper limit for *P*(O2) was equal to to 1.56.10-18atm and the value of *P*(Cl2) associated with the appearance of the first gaseous molecules is identified as 2.05.10-4atm. The composition of the gas is then computed by fixing *P*(Cl2) at 2.05.10-4atm. Three different *P*(O2) levels were studied, 1.3.10-24, 5.4.10-22 and 1.56.10-18atm. The results are presented on Table (5).


Table 5. Gas phase speciation as function of *P*(O2)

The mol fractions of CO and CO2 gets higher for higher values of *P*(O2). This is consistent with the dislocation of the equilibrium represented by Eq. (50) in the direction of the formation of the two carbon oxides.

$$\begin{aligned} \text{C} + \text{O}\_2 &\rightarrow \text{CO}\_2\\ 2\text{C} + \text{O}\_2 &\rightarrow 2\text{CO} \end{aligned} \tag{50}$$

Also, the Boudouard equilibrium demands that at the chosen temperature (1373 K) the atmosphere is more concentrated in CO. This was indeed observed for each equilibrium state investigated. It is interesting to observe that for *P*(O2) varying between 5.24.10-22atm and 1.56.10-18atm the mol fraction of CO and CO2 experience a much higher variation in comparison with the one observed for lower *P*(O2) values.

Fig. 27. Mol fractions of VCl3 and VCl4 as a function of *P*(O2)

In the case of the vanadium chlorides and oxychlorides an interesting trend is evidenced. The concentration of VOCl3 grows and of VCl2, VCl3 and VCl4 reduce appreciably for the same O2

thermodynamic modeling remains consistent and the computation can be performed. By fixing the temperature at 1373K, the upper limit for *P*(O2) was equal to to 1.56.10-18atm and the value of *P*(Cl2) associated with the appearance of the first gaseous molecules is identified as 2.05.10-4atm. The composition of the gas is then computed by fixing *P*(Cl2) at 2.05.10-4atm. Three different *P*(O2) levels were studied, 1.3.10-24, 5.4.10-22 and 1.56.10-18atm. The results are

P(O2)(atm) X(CO) X(CO2) X(VOCl3) X(VCl2) X(VCl3) X(VCl4) 1.30.10-24 8.22.10-4 1.54.10-9 3.05.10-6 0.0597 0.56 0.38 5.24.10-22 1.65.10-2 6.22.10-7 6.03.10-5 0.0588 0.55 0.37 1.56.10-18 0.902 1.85.10-3 3.21.10-4 5.72.10-3 0.054 0.036

The mol fractions of CO and CO2 gets higher for higher values of *P*(O2). This is consistent with the dislocation of the equilibrium represented by Eq. (50) in the direction of the

> 2 2 2 C O CO 2C O 2CO

Also, the Boudouard equilibrium demands that at the chosen temperature (1373 K) the atmosphere is more concentrated in CO. This was indeed observed for each equilibrium state investigated. It is interesting to observe that for *P*(O2) varying between 5.24.10-22atm and 1.56.10-18atm the mol fraction of CO and CO2 experience a much higher variation in

In the case of the vanadium chlorides and oxychlorides an interesting trend is evidenced. The concentration of VOCl3 grows and of VCl2, VCl3 and VCl4 reduce appreciably for the same O2

(50)

presented on Table (5).

Table 5. Gas phase speciation as function of *P*(O2)

comparison with the one observed for lower *P*(O2) values.

Fig. 27. Mol fractions of VCl3 and VCl4 as a function of *P*(O2)

formation of the two carbon oxides.

partial pressure range. The concentration variations associated with the vanadium chlorinated compounds is analogous to the variations observed in the concentrations of CO and CO2.

Fig. 28. Mol fractions of VOCl3 and VCl2 as a function *P*(O2)

For *P*(O2) lower than 5.24.10-22atm the variations are much less significant. To get a better picture of the trend observed for the chlorides and oxychlorides, their concentrations were plotted as a function of *P*(O2), which was varied in the range spanned by the data of Table (5) (Figures 27, 28 and 29)

Fig. 29. Mol fraction of VOCl3 as a function of *P*(O2)

On the Chlorination Thermodynamics 821

becomes progressively more endothermic. It is interesting to see that he explained behavior is consistent with the fact that the global formation reactions of VCl3 and VCl2 are associated with positive molar reaction enthalpies and that of VOCl3 and VCl4 with negative molar

Fig. 31. Molar reaction enthalpy for the formation of gaseous VCl3, VCl2, VCl4 and VOCl3 as

In this chapter three different approaches to the chlorination equilibrium study of an oxide were presented. The first two are based on the construction of <sup>o</sup> *G*<sup>r</sup> <sup>x</sup>*T* diagrams (topic 2.2.1) and on the calculations, first introduced by Kang Zuo (1989) (topic 2.2.2), respectively. Both of them take into consideration that each chlorinated compound is produced independently. The third one has its fundamental based on the total Gibbs energy

reactions enthalpies (Figure 31).

Fig. 30. Total as a function of *P*(Cl2)

a function of temperature

**4. Final remarks** 

The variations depicted on Figures (27), (28) and (29) are consistent with the occurrence of reactions represented by Eq. (51). As *P*(O2) achieves higher values, it reacts with VCl3, VCl2 and or VCl4 resulting in VOCl3. Such phenomena could explain the significant reduction of VCl3, VCl4 and VCl2 concentrations, and the concomitant elevation of the VOCl3 mol fraction.

$$\begin{aligned} \text{VCl}\_3 + 0.5 \text{O}\_2 &= \text{VOCl}\_3\\ \text{VCl}\_2 + \text{O}\_2 + \text{VCl}\_4 &= 2 \text{VOCl}\_3\\ \text{VCl}\_4 + 0.5 \text{O}\_2 &= \text{VOCl}\_3 + 0.5 \text{Cl}\_2 \end{aligned} \tag{51}$$

The participation of VCl4 in the second reaction is supported by the fact that its equilibrium concentration lowering is more sensible to LnP(O2) than observed for VCl3 (Figure 27). The consumption of VCl4 by the second reaction is also consistent with the maximum observed in the curve obtained for VOCl3 concentration (Figure 29). As less VCl4 is available, less VOCl3 can be produced.


Table 6. Equilibrium constants at 1373 K for reactions represented by Eq. (51)

The occurrence of reactions represented by Eq. (51) is supported by classical thermodynamics, as the equilibrium constant (*K*) computed at 1373 K for all chemical reactions above assume values appreciably greater than unity (see Table 6).
