# Approach for the Description of Chemical Equilibrium Shifts in the Systems with Free and Connected Chemical Reactions

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## Abstract

**:**

## 1. Introduction

- temperature of the system, that is, when it is heated or cooled;
- pressure in the system, that is, when it is compressed or expanded;
- concentration of one of the participants in the reversible reaction.

- (A)
- Attempts to extend the well-known principle of shifting chemical equilibrium to systems, in the case of the initial substances or reaction products belonging to phases with large (sometimes extremely large) positive deviations from ideality. In these cases, the contribution of the excess partial thermodynamic functions of the components to the equilibrium shift may be comparable and even exceed the contribution of the standard thermodynamic functions of the reaction participants. This aspect, in the opinion of the authors, has not been considered before.
- (B)
- Attempts to extend the well-known principle of shifting chemical equilibrium to systems of several chemical reactions with common reagents, products, or intermediates. In these cases, there is competition between several chemical reactions for both participants in the reaction, and the displacement of the equilibrium in one reaction affects the displacement of the equilibrium in the other reaction. This aspect has not been considered before, as far as the authors know.

## 2. Isolated “Free” Reaction Systems

#### Comparison of Equations with the Classical Formulation of the Le Chatelier-Brown Principle for Chemical Equilibrium Shift

- (A)
- The extremely unlikely variant of random coincidences: $\Delta {H}^{(0)}\approx 0;\Delta {V}^{(0)}\approx 0$, when values of $\Delta {H}^{(mix)};\Delta {V}^{(mix)}$ can become decisive.
- (B)
- Very high and extreme values of positive deviations of excess partial molar functions (activity coefficients -${\gamma}_{i}$ from the ideality). These cases are realized, particularly in the systems with strong hierarchical association, when standard state of dissolved component (normalized on infinitely diluted solution) is far away from its state in real solutions with finite concentrations. Example of such systems are $U{O}_{2}C{l}_{2}-{H}_{2}O$ at 25 °C, where in the solutions close to saturation ${\gamma}_{U{O}_{2}C{l}_{2}}\approx $1500–1700 a.u. [11].Another examples are ${C}_{60}Su{b}_{n}-{H}_{2}O$ systems at 25 °C (${C}_{60}Su{b}_{n}$ is water soluble derivative of fullerene ${C}_{60},Sub$$\u2014$ is substituent—carboxy, hydroxy, amino-acid, protein etc. residues), where in the comparatively concentrated (but diffusionally stable) solutions: $\mathrm{ln}{\gamma}_{{C}_{60}Su{b}_{n}}\approx $10–100 a.u. [12].

## 3. Once Connected “Un-Free” Reaction Systems

## 4. Un-Free Connected Reactions

#### 4.1. Case of Common Reagents or Common Products

- With an increase in temperature for a pair of once-connected reactions, the equilibrium shifts towards products more (less) for the reaction, whose specific heat (normalized by 1 mole of the common component) is greater (lower) than the other reaction;
- With an increase in pressure for a pair of once-connected reactions, the equilibrium shifts towards products more (less) for the reaction, whose specific volume change (normalized by 1 mole of the common component) is lower (greater) than the other reaction;

#### 4.2. Case of Common Reagent of One Reaction and Product of Other Reaction

- With an increase in temperature for a pair of once-connected reactions, common component-intermediate was accumulated (consumed) in the reaction phase, if sum heat of the reactions (normalized by 1 mole of the common component) was positive (negative);
- With an increase in pressure for a pair of once-connected reactions, the common component-intermediate was accumulated (consumed) in the reaction phase, if sum volume change of the reactions (normalized by 1 mole of the common component) was negative (positive).

^{3}-B

^{5}systems), once-connected by:

Ga + As = GaAs (reaction-2);

In + GaAs = Ga + InAs (quasi-reaction-12)

Ga + As = GaAs (reaction-2);

InAs + GaSb = Ga + As + InSb (quasi-reaction-12)

InAs + AlP = InP + AlAs (reaction-2);

In + As + AlP = InP + AlAs(quasi-reaction-12)

## 5. Case of Several (More Than One) Common Reagents or Common Products with the Proportional (in Particular, Equal) Stoichiometric Coefficients of Common Participants

_{6}H

_{5}CH

_{3}+ Br

_{2}= 1,2-C

_{6}H

_{4}CH

_{3}Br + HBr (reaction-1);

C

_{6}H

_{5}CH

_{3}+ Br

_{2}= 1,4-C

_{6}H

_{4}CH

_{3}Br + HBr(reaction-2);

1,2-C

_{6}H

_{4}CH

_{3}Br = 1,4-C

_{6}H

_{4}CH

_{3}Br(quasi-reaction-12)

## 6. About the Possibility of Passing of Composition Variables, Temperature, and Pressure in the System of Components, Connected by Chemical Reaction, through the Extreme

**(n**passes through the extreme at P=const and T=const. Naturally in these cases:

_{2}^{(1)})_{x}Ga

_{1/2-x}As

_{y}Sb

_{1/2-y}composition.

#### 6.1. Polytherm Isobar Conditions $\left(dT\ne 0,dP=0\right)$

**Connected reaction systems**. Let us number common components in the 1-st. Imagine that molar number of some non-common 2-d participant of the 1-st from pair of (1 and 2) once-connected reactions passes through the extreme at P = const. Naturally, in these cases:

_{0.11}Ga

_{0.39}As

_{0.08}Sb

_{0.42}. This composition corresponds to the pass of the concentrations in solid solution through the extreme, and this applies both to the simple components A

^{3}(In, Ga) and B

^{5}(As, Sb), and “complex compounds” A

^{3}B

^{5}(InAs, InSb, GaAs, GaSb), as seen in Figure 1. These data also correspond to the value of the argument, ${X}_{As}^{(l)}+{X}_{Sb}^{(l)}\approx 0.5$. Temperature of phase equilibrium in Figure 1 (873 K) should correspond to the extreme of liquidus temperature at the same value ${X}_{As}^{(l)}+{X}_{Sb}^{(l)}\approx 0.5$. This is confirmed by Figure 2. Justice of Equation (88) was demonstrated.

#### 6.2. Isotherm Polybar Conditions $\left(dT=0ordP\ne 0\right)$

_{1}→5→6→7→8 shows the method of passing the composition of the solution through R

_{1}point as the result of H

_{2}O-add +$3NaCl\cdot 4CdC{l}_{2}\cdot 14{H}_{2}O$(1→2→3→4→R

_{1}) and H

_{2}O-evaporation + $3NaCl\cdot 4CdC{l}_{2}\cdot 14{H}_{2}O$-crystallization (R

_{1}→5→6→7→8).

_{2}-H

_{2}O system at 25 °C consists of four branches: NaCl; congruently soluble compounds, $3NaCl\cdot 4CdC{l}_{2}\cdot 14{H}_{2}O$, and $2NaCl\cdot CdC{l}_{2}\cdot 3{H}_{2}O$. Diagram contains three non-variant points E

_{i}, all eutonics [15]. In the diagram, there are two point types. Van Rijn points in fusibility diagrams, R

_{i}, are realized when all three equilibrium phase points, liquid (l) (R

_{i}), solid compound (s) ($3NaCl\cdot 4CdC{l}_{2}\cdot 14{H}_{2}O$ and $2NaCl\cdot CdC{l}_{2}\cdot 3{H}_{2}O$), and vapor (v) H

_{2}O, belong to the same straight lines [15,16,17]. In the points, R

_{i}isopotentials of H

_{2}O touch the curves of mono-variant equilibrium (E

_{i}→R

_{j}→E

_{i+1}) when moving along these curves, and chemical potential H

_{2}O in the points R

_{i}passes through the extremes (specifically the maximum) [17,18], as in Figure 3 and Figure 4.

**Figure 3.**Solubility diagrams in ternary NaCl–CdCl

_{2}–H

_{2}O system at 25 °C in rectangular Schreinemakers concentration triangle in the salt molalities: open black circles, calculated by Extended Pitzer’s Method [16]; red solid circles, non-variant experimental data [16,17]; blue solid points (R

_{i}), solubility diagram points type Van Rijn points in fusibility diagrams [17]; little open blue points, H

_{2}O isopotentials (${\mu}_{{H}_{2}O}=const$); gray points, figurative points of coexisting equilibrium vapor (H

_{2}O) and solid compounds phases

_{c}and $3NaCl\cdot 4CdC{l}_{2}\cdot 14{H}_{2}O$; E

_{i}, eutonics [17,18]; dots with two-directed arrows are nodes: vapor (v), saturated solutions (R

_{i}), and solid compounds (s).

**Figure 4.**Solubility diagrams in ternary NaCl–CdCl

_{2}–H

_{2}O system at 25 °C in the variables: salt Yeneske index H

_{2}O partial pressure: open black circles, calculation by Extended Pitzer’s Method [14]; red solid circles, non-variant calculated eutonics data (E

_{i}); blue solid points (R

_{i}), solubility diagram points type Van Rijn points in fusibility diagrams [17,18]; red arrows show the direction.

_{3}→R

_{1}→E

_{2}), imagine a thought experiment. It is possible to organize such process only with mass transfer. In a mass transfer in heterogeneous system or conduct such isotherm-isobar open phase process [19]:

- To the heterogeneous system (liquid is point 1 in Figure 4), add some liquid H
_{2}O (liquid pass to point 2); - Dissolve part of the equilibrium solid compound $3NaCl\cdot 4CdC{l}_{2}\cdot 14{H}_{2}O$ in solution until saturation (liquid pass to point 3);
- Repeat this two-stage process until liquid comes to the point R
_{1}(liquid pass to point 4, to point 5, … to point R_{1}(Figure 4); - Evaporate H
_{2}O from liquid R_{1}(liquid pass to point 5); - Crystallize from supersaturated liquid crystals $3NaCl\cdot 4CdC{l}_{2}\cdot 14{H}_{2}O$ until liquid become saturated (liquid pass to point 6);
- Repeat this two-stage process until liquid comes to the point E
_{2}(liquid pass to point 7, to point 8, … to point E_{2}), as in Figure 4.

_{1}, molar number dissolved in liquid $3NaCl\cdot 4CdC{l}_{2}\cdot 14{H}_{2}O$ increased, so simultaneously increased molar numbers of $NaCl;CdC{l}_{2}$ in liquid. In the second half of process, R

_{1}→5→6→7→8, molar number dissolved in liquid $3NaCl\cdot 4CdC{l}_{2}\cdot 14{H}_{2}O$ decreased, so simultaneously decreased molar numbers of $NaCl;CdC{l}_{2}$ in liquid. In R

_{1}, molar numbers of $NaCl;CdC{l}_{2}$ pass through the extreme. H

_{2}O molar numbers in R

_{1}also pass through the maximum, according to criterion of diffusional liquid stability (values of H

_{2}O chemical potential, activity, and partial pressure always (at P, T = const) change). It is clear that the compound $3NaCl\cdot 4CdC{l}_{2}\cdot 14{H}_{2}O$’s molar number in the solid phase in R

_{1}also passes through the extreme. Thus, we have confirmed that molar numbers of the substances were connected by a heterogeneous chemical reaction:

_{3}→R

_{1}→E

_{2}), we can use the well-known Gibbs rule [9,20]: Temperature (at P = const) or pressure (at T = const) passes through the extreme when the composition of equilibrium coexisting phases were linearly dependent. In our case, the three-phase equilibrium figurative points of (v)-(l)-(s) are in the points R

_{i}belonging to one curve, as seen in Figure 3 and Figure 4. From Figure 4, one can see that in R

_{i}, partial pressure (${P}_{{H}_{2}O}$), but not sum pressure (P = const = 1 atm), passes through the extreme. The contradiction here is apparent, because moderate pressure does not have an impact on the equilibrium between condensed phases. Thus, in experiment, we can remove the main components of the gas phase (air) from the system and leave only the water vapor equilibrium with the solution, and this fact should not affect the solubility diagram. In this case, ${P}_{{H}_{2}O}\approx P$ (at T = const) and pressure in points R

_{i}passes through the extreme.

## 7. About Chemical Equilibrium Shift in the Conditions of Continuous Isothermal-Isobar Input of Reagents or Output of the Products of the Reaction

- (A)
- Assuming that chemical reaction is in the state of chemical equilibrium, equilibrium constant (K
_{e}) as well as chemical variable ($\xi $), corresponds to equilibrium. - (B)
- Reagents are continuously introduced into reaction phase in stoichiometric ratios, or products are outputting from reaction phase also in stoichiometric ratios;
- (C)
- Reaction phase are artificially knocked out of equilibrium all and the system strives to return to it all the time.
- (D)
- Thus, one can write that if one artificially changes molar numbers of components (without system drive to equilibrium constant), then the following inequalities are valid:

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Ott, B.J.; Boerio-Goates, J. Chemical Thermodynamics—Principles and Applications; Academic Press: Cambridge, MA, USA, 2000. [Google Scholar]
- Servos, J.W. Physical Chemistry from Ostwald to Pauling; Princeton University Press: Princeton, NJ, USA, 1990. [Google Scholar]
- Bryson, B. A Short History of Nearly Everything; Broadway Books: New York, NY, USA, 2003; pp. 116–117. [Google Scholar]
- Gibbs, W.J. Transactions of the Connecticut Academy, III; Academy: New Haven, CT, USA, 1876; pp. 108–248. [Google Scholar]
- Prigogine, I.; Defay, R. Thermodynamique Chimique ConformЙnt aux Methods de Gibbs et De Donder; Dunod: Paris, France, 1944; Volume VI. [Google Scholar]
- Gibbs, J.W. A Commentary on the Scientific Writings VI and II; Donnan, F.G., Haas, A., Eds.; Yale University Press: New Haven, CT, USA, 1936. [Google Scholar]
- Guggenheim, E.A. Thermodynamics; North Holland: Amsterdam, The Netherlands, 1950; p. 25. [Google Scholar]
- Louis Le Châtelier, H. Recherches Expérimentales Et Théoriques Sur les Équilibres Chimiques, In Annales des Mines Et des Carburants, 8th series; Dunod: Paris, France, 1888; pp. 157–380. [Google Scholar]
- Storonkin, A.V. Thermodynamics of Heterogeneous Systems.; Book I. Part I, II.; LGU: Leningrad, Russia, 1967. [Google Scholar]
- “Le Chatelier’s Principle (Video)”. Khan Academy. Available online: https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:equilibrium/x2eef969c74e0d802:le-chatelier-s-principle/v/le-chateliers-principle-changing-concentration?v=4-fEvpVNTlE (accessed on 20 April 2021).
- Helmenstine, A.M. “Le Chatelier’s Principle Definition”. ThoughtCo. 2020. Available online: https://www.thoughtco.com/definition-of-le-chateliers-principle-605297 (accessed on 9 March 2022).
- Charykov, N.A.; Semenov, K.N.; Kurilenko, A.V.; Keskinov, V.A.; Letenko, D.G.; Kulenova, N.A.; Zolotarev, A.A.; Klepikov, V.V. Modeling of systems with aqueous solutions of UO
_{2}^{2+}salts.An asymmetric model of redundant thermodynamic functions based on the virial decomposition of the Gibbs free energy of the solution—VD-AS. Radiochemistry**2017**, 59, 119–126. [Google Scholar] [CrossRef] - Charykov, N.A.; Semenov, K.N.; López, E.R.; Fernández, J.; Serebryakov, E.B.; Keskinov, V.A.; Murin, I.V. Excess thermodynamic functions in aqueous systems containing soluble fullerene derivatives. J. Mol. Liq.
**2018**, 256, 305–311. [Google Scholar] [CrossRef] - Litvak, A.M.; Charykov, N.A. New Thermodynamic Method of Calculation of Melt-Solid Phase Equilibria (for the Example of A
^{3}B^{5}Systems). Russ. J. Phys. Chem. A**1990**, 64, 2331. [Google Scholar] - Charykov, N.A.; Litvak, A.M.; Mikhaǐlova, M.P.; Moiseev, K.D.; Yakovlev, Y.P. Solid Solution In
_{X}Ga_{1-X}As_{Y}Sb_{Z}P_{1-Y-Z}: A new Material for Ifrared Optoelectronics. I. Thermodynamic Analysis of the Conditions for Obtaining Solid Solutions, Isoperiodic to InAs and GaSb substrates, by Liquid-Phase Epitaxy. Semiconductors**1997**, 31, 344–349. [Google Scholar] [CrossRef] - Filippov, V.K.; Charykov, N.A.; Rumyantsev, A.V. Distribution of Pitzer’s equations on the systems with complex formation in the solutions. Reports Acad. Sci. USSR. Ser. Phys. Chem.
**1987**, 296, 665–668. [Google Scholar] - Charykova, M.V.; Charykov, N.A. Thermodynamic Modeling of the Processes of Evaporate Sedimentation; Nauka: Sain-Petersburg, Russia, 2003; p. 262. [Google Scholar]
- Charykov, N.A.; Rumyantsev, A.V.; Charykova, M.V. Topological isomorphism of solubility and fusibility phase diagrams. Non-variant points in multicomponent systems. Rus. J. Phys. Chem.
**1998**, 72, 1746–1750. [Google Scholar] - Charykov, N.A.; Rumyantsev, A.V.; Charykova, M.V. Extremes of solvent activity in multicomponent systems. Rus. J. Phys. Chem.
**1998**, 72, 39–44. [Google Scholar] - Charykov, N.A.; Charykova, M.V.; Semenov, K.N.; Keskinov, V.A.; Kurilenko, A.V.; Shaimardanov, Z.K.; Shaimardanova, B.K. Multiphase Open Phase Processes Differential Equations. Processes
**2019**, 7, 148. [Google Scholar] [CrossRef]

**Figure 1.**Molar fraction of components A

^{3}(In, Ga) and B

^{5}(As, Sb), top fragment, compounds A

^{3}B

^{5}(InAs, InSb, GaAs, GaSb), and bottom fragment in solid solution In

_{x}Ga

_{1/2-x}As

_{y}Sb

_{1/2-y}(isoperiodic to the substrate GaSb)—X

^{(s)}, depending on the sum molar fraction of B

^{5}components in the equilibrium to solid solution melt: ${X}_{As}^{(l)}+{X}_{Sb}^{(l)}$ at T = 873 K and P = 1 atm. (Points are experimental data, lines are calculated by EFLCP model for A

^{3}-B

^{5}semiconductor systems [13,14].

**Figure 2.**Equilibrium temperature T(K), depending on the sum molar fraction of B

^{5}components in the equilibrium to solid solution melt:${X}_{As}^{(l)}+{X}_{Sb}^{(l)}$ for solid solutions with constant composition In

_{0.11}Ga

_{0.39}As

_{0.08}Sb

_{0.42}. Points are experimental data, line is calculated by EFLCP model [13,14].

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**MDPI and ACS Style**

Shaymardanov, Z.; Shaymardanova, B.; Kulenova, N.A.; Sadenova, M.A.; Shushkevich, L.V.; Charykov, N.A.; Semenov, K.N.; Keskinov, V.A.; Blokhin, A.A.; Letenko, D.G.; Kuznetsov, V.V.; Sadowski, V. Approach for the Description of Chemical Equilibrium Shifts in the Systems with Free and Connected Chemical Reactions. *Processes* **2022**, *10*, 2493.
https://doi.org/10.3390/pr10122493

**AMA Style**

Shaymardanov Z, Shaymardanova B, Kulenova NA, Sadenova MA, Shushkevich LV, Charykov NA, Semenov KN, Keskinov VA, Blokhin AA, Letenko DG, Kuznetsov VV, Sadowski V. Approach for the Description of Chemical Equilibrium Shifts in the Systems with Free and Connected Chemical Reactions. *Processes*. 2022; 10(12):2493.
https://doi.org/10.3390/pr10122493

**Chicago/Turabian Style**

Shaymardanov, Zhasulan, Botogyz Shaymardanova, Natalia A. Kulenova, Marjan A. Sadenova, Ludmila V. Shushkevich, Nikolay A. Charykov, Konstantin N. Semenov, Victor A. Keskinov, Alexander A. Blokhin, Dmitriy G. Letenko, Vladimir V. Kuznetsov, and Voitech Sadowski. 2022. "Approach for the Description of Chemical Equilibrium Shifts in the Systems with Free and Connected Chemical Reactions" *Processes* 10, no. 12: 2493.
https://doi.org/10.3390/pr10122493