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Partitioning Entropy with Action Mechanics: Predicting Chemical Reaction Rates and Gaseous Equilibria of Reactions of Hydrogen from Molecular Properties.

ABSTRACT: Our intention is to provide easy methods for estimating entropy and chemical potentials for gas phase reactions. Clausius' virial theorem set a basis for relating kinetic energy in a body of independent material particles to its potential energy, pointing to their complementary role with respect to the second law of maximum entropy. Based on this partitioning of thermal energy as sensible heat and also as a latent heat or field potential energy, in action mechanics we express the entropy of ideal gases as a capacity factor for enthalpy plus the configurational work to sustain the relative translational, rotational, and vibrational action. This yields algorithms for estimating chemical reaction rates and positions of equilibrium. All properties of state including entropy, work potential as Helmholtz and Gibbs energies, and activated transition state reaction rates can be estimated, using easily accessible molecular properties, such as atomic weights, bond lengths, moments of inertia, and vibrational frequencies. We conclude that the large molecular size of many enzymes may catalyze reaction rates because of their large radial inertia as colloidal particles, maximising action states by impulsive collisions. Understanding how Clausius' virial theorem justifies partitioning between thermal and statistical properties of entropy, yielding a more complete view of the second law's evolutionary nature and the principle of maximum entropy. The ease of performing these operations is illustrated with three important chemical gas phase reactions: the reversible dissociation of hydrogen molecules, lysis of water to hydrogen and oxygen, and the reversible formation of ammonia from nitrogen and hydrogen. Employing the ergal also introduced by Clausius to define the reversible internal work overcoming molecular interactions plus the configurational work of change in Gibbs energy, often neglected; this may provide a practical guide for managing industrial processes and risk in climate change at the global scale. The concepts developed should also have value as novel methods for the instruction of senior students.

SUBMITTER: Kennedy IR

PROVIDER: S-EPMC8392617 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Reported herein are the hydrogen atom transfer (HAT) reactions of two closely related dicationic iron tris(alpha-diimine) complexes. FeII(H2bip) (iron(II) tris[2,2'-bi-1,4,5,6-tetrahydropyrimidine]diperchlorate) and FeII(H2bim) (iron(II) tris[2,2'-bi-2-imidazoline]diperchlorate) both transfer H* to TEMPO (2,2,6,6-tetramethyl-1-piperidinoxyl) to yield the hydroxylamine, TEMPO-H, and the respective deprotonated iron(III) species, FeIII(Hbip) or FeIII(Hbim). The ground-state thermodynamic parameters in MeCN were determined for both systems using both static and kinetic measurements. For FeII(H2bip) + TEMPO, DeltaG degrees = -0.3 +/- 0.2 kcal mol-1, DeltaH degrees = -9.4 +/- 0.6 kcal mol-1, and DeltaS degrees = -30 +/- 2 cal mol-1 K-1. For FeII(H2bim) + TEMPO, DeltaG degrees = 5.0 +/- 0.2 kcal mol-1, DeltaH degrees = -4.1 +/- 0.9 kcal mol-1, and DeltaS degrees = -30 +/- 3 cal mol-1 K-1. The large entropy changes for these reactions, |TDeltaS degrees | = 9 kcal mol-1 at 298 K, are exceptions to the traditional assumption that DeltaS degrees approximately 0 for simple HAT reactions. Various studies indicate that hydrogen bonding, solvent effects, ion pairing, and iron spin equilibria do not make major contributions to the observed DeltaS degrees HAT. Instead, this effect arises primarily from changes in vibrational entropy upon oxidation of the iron center. Measurement of the electron-transfer half-reaction entropy, |DeltaS degrees Fe(H2bim)/ET| = 29 +/- 3 cal mol-1 K-1, is consistent with a vibrational origin. This conclusion is supported by UHF/6-31G* calculations on the simplified reaction [FeII(H2N=CHCH=NH2)2(H2bim)]2+...ONH2 left arrow over right arrow [FeII(H2N=CHCH=NH2)2(Hbim)]2+...HONH2. The discovery that DeltaS degrees HAT can deviate significantly from zero has important implications on the study of HAT and proton-coupled electron-transfer (PCET) reactions. For instance, these results indicate that free energies, rather than enthalpies, should be used to estimate the driving force for HAT when transition-metal centers are involved.

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Partitioning Entropy with Action Mechanics: Predicting Chemical Reaction Rates and Gaseous Equilibria of Reactions of Hydrogen from Molecular Properties.

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