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As useful rules of thumb, a first-order reaction with a rate constant of 10 −4 s −1 will have a half-life (t 1/2) of approximately 2 hours. For a one-step process taking place at room temperature, the corresponding Gibbs free energy of activation (Δ G ‡ ) is approximately 23 kcal/mol.
For a typical second-order reaction with rate equation = [] [], if the concentration of reactant B is constant then = [] [] = ′ [], where the pseudo–first-order rate constant ′ = []. The second-order rate equation has been reduced to a pseudo–first-order rate equation, which makes the treatment to obtain an integrated rate equation much ...
In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates.The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that the van 't Hoff equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and ...
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 ...
This is a bimolecular elementary reaction whose rate is given by the second-order equation = [] [], where k 2 is the rate constant for the second step. However N 2 O 2 is an unstable intermediate whose concentration is determined by the fact that the first step is in equilibrium , so that [ N 2 O 2 ] = K 1 [ NO ] 2 , {\displaystyle {\ce {[N2O2 ...
The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this rate is evaluated as xy, where x is the number of prey, y is the number of predator. This is a typical example of the law of mass action.
is the rate constant for surface adsorption, m 3 ·mol −1 ·s −1 k − 1 {\displaystyle k_{-1}} is the rate constant for surface desorption, s −1 C S {\displaystyle C_{\mathrm {S} }} is highly related to the total surface area of the adsorbent: the greater the surface area, the more sites and the faster the reaction.
is the relative diffusion constant between A and B, unit m 2 /s, and = +. [] and [] are the molar concentrations of A and B respectively, unit mol/L. is the diffusive collision rate constant, unit L 4/3 mol-4/3 s −1.