# Single-Route Linear Catalytic Mechanism: A New, Kinetico-Thermodynamic Form of the Complex Reaction Rate

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results

#### 2.1. Formulation of the Problem

#### 2.2. Research Analysis

**Proof**

**of**

**Equation**

**(6).**

#### 2.3. Special Cases

#### 2.3.1. Single-Route Catalytic Reaction: All Reactions Are Irreversible

#### 2.3.2. Single-Route Catalytic Reaction: One Step Is Irreversible and Rate Limiting.

#### 2.4. Extension of the Single-Route Result: Application to Other Mechanisms

#### 2.4.1. Single-Route Catalytic Reaction with a Buffer Step

#### 2.4.2. Two Cycles that Have a Common Intermediate

#### 2.5. Examples

#### 2.5.1. Two Step Single Route Mechanism (Water-Gas Shift Mechanism)

- $\mathrm{Z}+{\mathrm{H}}_{2}\mathrm{O}\underset{{k}_{1}^{-}}{\overset{{k}_{1}^{+}}{\rightleftarrows}}\mathrm{Z}\mathrm{O}+{\mathrm{H}}_{2}$
- $\mathrm{Z}\mathrm{O}+\mathrm{C}\mathrm{O}\underset{{k}_{2}^{-}}{\overset{{k}_{2}^{+}}{\rightleftarrows}}\mathrm{Z}+\mathrm{C}{\mathrm{O}}_{2},\mathrm{t}$

#### 2.5.2. Three Step Mechanism of Sulfur Dioxide Oxidation

- $\mathrm{Z}\mathrm{O}+\mathrm{S}{\mathrm{O}}_{2}\underset{{k}_{1}^{-}}{\overset{{k}_{1}^{+}}{\rightleftarrows}}\mathrm{Z}+\mathrm{S}{\mathrm{O}}_{3}$
- $\mathrm{Z}+\mathrm{S}{\mathrm{O}}_{2}\underset{{k}_{2}^{-}}{\overset{{k}_{2}^{+}}{\rightleftarrows}}\mathrm{Z}\mathrm{S}{\mathrm{O}}_{2}$
- $\mathrm{Z}\mathrm{S}{\mathrm{O}}_{2}+{\mathrm{O}}_{2}\underset{{k}_{3}^{-}}{\overset{{k}_{3}^{+}}{\rightleftarrows}}\mathrm{Z}\mathrm{O}+\mathrm{S}{\mathrm{O}}_{3}$

## 3. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- King, E.; Altman, C. A schematic method of deriving the ratelaws for enzyme-catalyzed reactions. J. Phys. Chem.
**1956**, 60, 1375–1378. [Google Scholar] [CrossRef] [Green Version] - Volkenstein, M.V.; Goldstein, B.N. A new method for solving the problems of the stationary kinetics of enzymological reactions. Biochim. Biophys. Acta
**1966**, 115, 471–477. [Google Scholar] [CrossRef] - Volkenstein, M.V.; Goldstein, B.N. Method for derivation of enzyme kinetics equations. Biokhimiya
**1966**, 31, 541–547. (In Russian) [Google Scholar] - Yablonskii, G.S.; Bykov, V.I. Structured kinetic equations of complex catalytic reactions. Dokl. Akad. Nauk SSSR
**1977**, 238, 645–648. [Google Scholar] - Yevstignejev, V.A.; Yablonskii, G.S.; Bykov, V.I. A General steady-state kinetic equation (multi-route linear catalytic mechanism). Dokl. Akad. Nauk SSSR
**1979**, 245, 871–874. [Google Scholar] - Yablonskii, G.S.; Bykov, V.I.; Gorban, A.N. Kinetic Models of Catalytic Reactions; Nauka: Novossibirsk, Russia, 1983; 256p. (In Russian) [Google Scholar]
- Yablonskii, G.S.; Bykov, V.I.; Gorban, A.N.; Elokhin, V.I. Kinetic Models of Catalytic Reactions; Compton, R.G., Ed.; Elsevier: Amsterdam, The Netherlands, 1991; 396p. [Google Scholar]
- Marin, G.B.; Yablonsky, G.S.; Constales, D. Kinetics of Chemical Reactions: Decoding Complexity, 2nd ed.; Wiley-VCH: Weinheim, Germany, 2019; 442p. [Google Scholar]
- Lazman, M.Z.; Yablonsky, G.S. Overall reaction rate equation of single-route complex catalytic reactions in terms of hypergeometric series. In Advances in Chemical Engineering—Mathematics in Chemical Engineering and Kinetics; Marin, G.B., West, D.H., Yablonsky, G.S., Eds.; Elsevier: Amsterdam, The Netherlands, 2008; pp. 47–102. [Google Scholar]
- Bykov, V.I.; Kytmanov, A.M.; Lazman, M.Z. Elimination Methods in Polynomial Computer Algebra; Passare, M., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1998; 252p. [Google Scholar]
- Lazman, M.Z.; Yablonskii, G.S.; Bykov, V.I. Steady-state kinetic equation (adsorption mechanism of catalytic reaction). Chem. Fiz.
**1983**, 2, 413–423, (Translated in Sov. J. Chem. Phys.**1985**, 2, 693–703.). [Google Scholar] - Lazman, M.Z.; Yablonskii, G.S.; Bykov, V.I. Steady-state kinetic equation, Nonlinear single pathway mechanism. Sov. J. Chem. Phys.
**1985**, 2, 404–418. [Google Scholar] - Murzin, D. Requiem for the Rate-Determining Step in Complex Heterogeneous Catalytic Reactions? Reactions
**2020**, 1, 37–46. [Google Scholar] [CrossRef]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yablonsky, G.S.; Constales, D.; Marin, G.B.
Single-Route Linear Catalytic Mechanism: A New, Kinetico-Thermodynamic Form of the Complex Reaction Rate. *Symmetry* **2020**, *12*, 1748.
https://doi.org/10.3390/sym12101748

**AMA Style**

Yablonsky GS, Constales D, Marin GB.
Single-Route Linear Catalytic Mechanism: A New, Kinetico-Thermodynamic Form of the Complex Reaction Rate. *Symmetry*. 2020; 12(10):1748.
https://doi.org/10.3390/sym12101748

**Chicago/Turabian Style**

Yablonsky, Gregory S., Denis Constales, and Guy B. Marin.
2020. "Single-Route Linear Catalytic Mechanism: A New, Kinetico-Thermodynamic Form of the Complex Reaction Rate" *Symmetry* 12, no. 10: 1748.
https://doi.org/10.3390/sym12101748