# Acid Site Density as a Kinetic Descriptor of Catalytic Reactions over Zeolites

## Abstract

**:**

## 1. Introduction

## 2. Site Density Dependence for Adsorption

_{A}is Avogadro’s number, and $\phi $ is lumped constant $\phi ={N}_{A}{e}^{2}/4\pi {\epsilon}_{0}\epsilon $.

## 3. Two-Step Sequence

_{1}↔ *I + B

_{1}

2. *I + A

_{2}↔ * + B

_{2}

A

_{1}+ A

_{2}↔ B

_{1}+ B

_{2}

_{1}and A

_{2}are reactants, B

_{1}, and B

_{2}are products, * is the surface vacant site, and I is an adsorbed intermediate.

_{A1}, etc., are concentrations of reagents, and k

_{i}is the rate constants.

_{1}is the Polanyi parameter of the first step. Similarly, for the backward reaction of the second step, one obtains

## 4. Christiansen Sequence

_{1}↔ *I

_{1}+ B

_{1}

2.* I

_{1}↔ *I

_{2}

3. * I

_{2}+ A

_{2}↔ * + B

_{2}

A

_{1}+ A

_{2}↔ B

_{1}+ B

_{2}

_{1}and I

_{2}.

_{1}and I

_{2}.

_{1}and I

_{2}will be

## 5. Parallel Reactions: Coupling between Cycles

_{1}↔ * I

_{1}+ B

_{1}1 1

2. * I

_{1}+ A

_{2}↔ * + B

_{2}1 0

3. * I

_{1}+ A

_{3}↔ * + B

_{3}0 1

N

^{(1)}A

_{1}+ A

_{2}↔ B

_{1}+ B

_{2}; N

^{(2)}A

_{1}+ A

_{3}↔ B

_{1}+ B

_{3}

^{(1)}and N

^{(2)}, taking place simultaneously. On the right-hand side of the equations for the steps, the respective stoichiometric (Horiuti) numbers are given, which should be multiplied by the equations of steps to yield the chemical equations along the different routes. For example, after multiplying the equations of the first and the second steps in Equation (45) by unity and the third step by zero and summing up all concentrations on the left and right sides, concentrations of the surface species are cancelled, giving the equation for the first route, i.e., A

_{1}+ A

_{2}↔ B

_{1}+ B

_{2}.

_{2}can be easily obtained from Equations (48) and (49), giving

## 6. Parallel Reactions: Separate Cycles

_{1}↔ * I

_{1}+ B

_{1}1 0

2. *I

_{1}+ A

_{2}↔ * + B

_{2}1 0

3.* +A

_{1}↔ * I

_{2}+ B

_{3}0 1

4. *I

_{2}+ A

_{3}↔ * + B

_{4}0 1

N

^{(1)}: A

_{1}+ A

_{2}↔ B

_{1}+ B

_{2}; N

^{(2)}: A

_{1}+ A

_{3}↔ B

_{3}+ B

_{4}

_{2}is the same as A

_{3}reflecting for example different adsorption modes through different functional groups, or when B

_{1}is the same as B

_{3}. The corresponding equations can be easily derived from a more general consideration.

## 7. Consecutive Reactions

2. * A → * B 1 1 0

3. * B ≡ B + * 1 0 −1

4. * B → * C 0 1 1

5. * C ≡ *+ C 0 1 1

N

^{(1)}: A ↔ B; N

^{(2)}: A ↔ C; N

^{(3)}: B ↔ C

^{(1)}to N

^{(3)}are not independent ones, as route N

^{(3)}can be obtained by the subtraction of route N

^{(1)}from the route N

^{(2)}as discussed previously in the literature for similar reaction networks [28]. Subsequently, the reaction network can be described with just two routes having the reaction rates

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Dependence of ${({\rho}_{{H}^{+}})}_{\mathrm{max}}{(\phi {}^{\prime})}^{2}$ as a function of the ratio of the frequencies of the first and second steps in the forward direction according to Equation (26).

**Figure 2.**The ratio of reaction products in the Prins condensation of isopulegol with acetone as a function of the total concentration of acid sites. Points—experimental data from [19], calculations—Equation (55). The calculated values of $\mathrm{ln}({k}_{+3}{C}_{{A}_{3}}/{k}_{+2}{C}_{{A}_{2}})$ and $({\alpha}_{2}-{\alpha}_{3})\phi {}^{\prime}$ are respectively 0.50338 ± 0.46502 and 0.13566 ± 0.03495.

**Figure 3.**Mechanisms of parallel reactions: (

**a**) with kinetic coupling and a joint edge, (

**b**) with one joint node. A

_{1},A

_{2},A

_{3},A

_{4}—reactants, B

_{1},B

_{2},B

_{3},B

_{4}—products.

**Figure 4.**Dependence of selectivity vs. conversion according to Equation (73) for different values of M’.

**Figure 5.**Dependence of the ratio of iso to normal hydrocarbons vs. a degree of proton exchange in transformations of syngas over mesoporous H-ZSM-5 supported cobalt nanoparticles. The experimental data are digitalized from [30].

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**MDPI and ACS Style**

Murzin, D.Y.
Acid Site Density as a Kinetic Descriptor of Catalytic Reactions over Zeolites. *Chemistry* **2022**, *4*, 1609-1623.
https://doi.org/10.3390/chemistry4040105

**AMA Style**

Murzin DY.
Acid Site Density as a Kinetic Descriptor of Catalytic Reactions over Zeolites. *Chemistry*. 2022; 4(4):1609-1623.
https://doi.org/10.3390/chemistry4040105

**Chicago/Turabian Style**

Murzin, Dmitry Yu.
2022. "Acid Site Density as a Kinetic Descriptor of Catalytic Reactions over Zeolites" *Chemistry* 4, no. 4: 1609-1623.
https://doi.org/10.3390/chemistry4040105