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Using the Eyring equation, there is a straightforward relationship between ΔG ‡, first-order rate constants, and reaction half-life at a given temperature. At 298 K, a reaction with ΔG ‡ = 23 kcal/mol has a rate constant of k ≈ 8.4 × 10 −5 s −1 and a half life of t 1/2 ≈ 2.3 hours, figures that are often rounded to k ~ 10 −4 s ...
The general form of the Eyring–Polanyi equation somewhat resembles the Arrhenius equation: = ‡ where is the rate constant, ‡ is the Gibbs energy of activation, is the transmission coefficient, is the Boltzmann constant, is the temperature, and is the Planck constant.
As an example, consider the gas-phase reaction NO 2 + CO → NO + CO 2.If this reaction occurred in a single step, its reaction rate (r) would be proportional to the rate of collisions between NO 2 and CO molecules: r = k[NO 2][CO], where k is the reaction rate constant, and square brackets indicate a molar concentration.
The relationship between Hammond's postulate and the BEP principle can be understood by considering a S N 1 reaction. Although two transition states occur during a S N 1 reaction (dissociation of the leaving group and then attack by the nucleophile), the dissociation of the leaving group is almost always the rate-determining step .
The free energy change, dG r, can be expressed as a weighted sum of change in amount times the chemical potential, the partial molar free energy of the species. The chemical potential, μ i , of the i th species in a chemical reaction is the partial derivative of the free energy with respect to the number of moles of that species, N i
Such linear relationships correspond to linear free energy relationships, which strongly imply that the effect of the substituents are exerted through changes of potential energy and that the steric and entropy terms remain almost constant through the series. The linear relationship fit well in the Hammett Equation.
The relationship between a species' concentration and the measured quantity is specific for the measurement technique, as indicated in each section above. Using this relationship, the set of parameters, the stability constant values and values of properties such as molar absorptivity or specified chemical shifts, may be refined by a non-linear ...
In thermodynamics, the thermodynamic free energy is one of the state functions of a thermodynamic system.The change in the free energy is the maximum amount of work that the system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden.