On the derivation of a general thermodynamic expression for the reaction rate constant for cosolvent reaction systems

Wiseman, Floyd L.; Scott, Dane W.; Tamine, J.; O'Connell, R.; Smarra, A.; Mitchell, N.

doi:10.1002/kin.21222

Cited by 2 publications

(12 citation statements)

References 31 publications

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“…In terms of the reactant and transition state activation free energies,

Δ G^{‡, {normals}^{*} s}

Δ G^{‡, {normals}^{*} s} = Δ G^{TS, {normals}^{*} s} - \sum Δ G^{R, {normals}^{*} s} = \sum Δ G^{i, {normals}^{*} s} .

…”

Section: Discussionmentioning

confidence: 99%

“…With this in mind, the relative permittivity has been identified as the measure of the electrostatic effect and the mole fraction as the measure of the effect of solvent-solute interactions. 5 Although Δ ‡,s * s * = 0, Δ ‡,s * s * , and Δ ‡,s * s * are not zero. Hence, for dilute solutions the expressions for ΔH ‡ and ΔS ‡ are, respectively: Δ ‡ = Δ ‡,vac + Δ ‡,el + Δ ‡,s * s + Δ ‡,s * s * ,…”

Section: The Fundamental Thermodynamic Expressionsmentioning

confidence: 95%

“…The protocol for evaluating these integrals is discussed in Ref. 5. The usual form of Equation (13) has been multiplied by T to make T conveniently part of the dependent variable.…”

Section: The Integrated Isobaric Eyring Expressionsmentioning

confidence: 99%

“…Analyzing any thermodynamic parameter requires correlating that parameter to some measurable bulk property of the system. With this in mind, the relative permittivity has been identified as the measure of the electrostatic effect and the mole fraction as the measure of the effect of solvent‐solute interactions …”

Section: Introductionmentioning

confidence: 99%

“…As will be shown in the Analysis section, the isomole fraction plots in this work are linear, and therefore

{false(\partial normalΔ G^{‡, el} / \partial ε false)}_{normalX, normalP, normalT}

is negligible. The integral forms of the Eyring expressions derived from Equations – with

{(\partial Δ G^{‡, el} / \partial ε)}_{X, P, T} = 0

are, respectively:

Y_{P, X} = - \frac{Δ G_{P, X}^{‡} (T_{0}, ε_{0})}{T} + \frac{1}{T} \int_{T_{0}}^{T} Δ S_{P, X, ε}^{‡} (ε_{0}) d T_{P, X},

\begin{matrix} true \\ right T Y_{normalT, normalP} = - normalΔ G_{normalT, normalP}^{‡} ((), X_{0}, ε_{0}) - \int_{X_{0}}^{X} {(\frac{\partial normalΔ G^{‡, s^{*} normals}}{\partial X})}_{normalT, normalP, ε} ((), ε_{0}) d X_{normalT, normalP}, \end{matrix}

…”

Section: Introductionmentioning

confidence: 99%

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Analyses of reaction rate data for the simple hydrolysis of acetic anhydride in the acetonitrile/water and acetone/water cosolvent systems using recently developed thermodynamic rate equations

Wiseman

Scott

Tamine

et al. 2019

Int J of Chemical Kinetics

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This article presents reaction rate data for the simple hydrolysis of acetic anhydride in the acetonitrile/water and acetone/water cosolvent systems and regression analyses using recently developed thermodynamic rate equations that contain electrostatic and solvent‐solute terms. The isomole fraction plots for these reaction systems are linear, and previous theoretical work has shown that the electrostatic term is negligible for such systems. On the other hand, the reaction rates are dependent upon the cosolvent mole fraction, indicating that the solvent‐solute term, which is modeled empirically, is significant. The results of the analyses provide the foundation for a paradigm shift away from the emphasis on electrostatic effects to more tenable explanations of kinetic behavior in solvent systems.

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“…In terms of the reactant and transition state activation free energies,

Δ G^{‡, {normals}^{*} s}

Δ G^{‡, {normals}^{*} s} = Δ G^{TS, {normals}^{*} s} - \sum Δ G^{R, {normals}^{*} s} = \sum Δ G^{i, {normals}^{*} s} .

…”

Section: Discussionmentioning

confidence: 99%

Section: The Fundamental Thermodynamic Expressionsmentioning

confidence: 95%

“…The protocol for evaluating these integrals is discussed in Ref. 5. The usual form of Equation (13) has been multiplied by T to make T conveniently part of the dependent variable.…”

Section: The Integrated Isobaric Eyring Expressionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…As will be shown in the Analysis section, the isomole fraction plots in this work are linear, and therefore

{false(\partial normalΔ G^{‡, el} / \partial ε false)}_{normalX, normalP, normalT}

is negligible. The integral forms of the Eyring expressions derived from Equations – with

{(\partial Δ G^{‡, el} / \partial ε)}_{X, P, T} = 0

are, respectively:

Y_{P, X} = - \frac{Δ G_{P, X}^{‡} (T_{0}, ε_{0})}{T} + \frac{1}{T} \int_{T_{0}}^{T} Δ S_{P, X, ε}^{‡} (ε_{0}) d T_{P, X},

\begin{matrix} true \\ right T Y_{normalT, normalP} = - normalΔ G_{normalT, normalP}^{‡} ((), X_{0}, ε_{0}) - \int_{X_{0}}^{X} {(\frac{\partial normalΔ G^{‡, s^{*} normals}}{\partial X})}_{normalT, normalP, ε} ((), ε_{0}) d X_{normalT, normalP}, \end{matrix}

…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analyses of reaction rate data for the simple hydrolysis of acetic anhydride in the acetonitrile/water and acetone/water cosolvent systems using recently developed thermodynamic rate equations

Wiseman

Scott

Tamine

et al. 2019

Int J of Chemical Kinetics

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A thermodynamic approach to analyzing relative permittivity and solvent mole fraction models, and application to S_N1 reactions

Wiseman,

Scott

2024

Phys. Chem. Chem. Phys.

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On the derivation of a general thermodynamic expression for the reaction rate constant for cosolvent reaction systems

Cited by 2 publications

References 31 publications

Analyses of reaction rate data for the simple hydrolysis of acetic anhydride in the acetonitrile/water and acetone/water cosolvent systems using recently developed thermodynamic rate equations

Analyses of reaction rate data for the simple hydrolysis of acetic anhydride in the acetonitrile/water and acetone/water cosolvent systems using recently developed thermodynamic rate equations

A thermodynamic approach to analyzing relative permittivity and solvent mole fraction models, and application to S_N1 reactions

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On the derivation of a general thermodynamic expression for the reaction rate constant for cosolvent reaction systems

Cited by 2 publications

References 31 publications

Analyses of reaction rate data for the simple hydrolysis of acetic anhydride in the acetonitrile/water and acetone/water cosolvent systems using recently developed thermodynamic rate equations

Analyses of reaction rate data for the simple hydrolysis of acetic anhydride in the acetonitrile/water and acetone/water cosolvent systems using recently developed thermodynamic rate equations

A thermodynamic approach to analyzing relative permittivity and solvent mole fraction models, and application to SN1 reactions

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A thermodynamic approach to analyzing relative permittivity and solvent mole fraction models, and application to S_N1 reactions