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A first order reaction depends on the concentration of only one reactant (a unimolecular reaction). Other reactants can be present, but their concentration has no effect on the rate. The rate law for a first order reaction is [] = [], The unit of k is s-1. [18]
The units of the pre-exponential factor A are identical to those of the rate constant and will vary depending on the order of the reaction. For a first-order reaction, it has units of s −1. For that reason, it is often called frequency factor.
When like terms are cancelled and the limit dx → 0 is applied to Equation 2 the mass balance on species i becomes 3. =, [1] The temperature dependence of the reaction rate, r, can be estimated using the Arrhenius equation. Generally, as the temperature increases so does the rate at which the reaction occurs.
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 ...
[A] can provide intuitive insight about the order of each of the reagents. If plots of v / [A] vs. [B] overlay for multiple experiments with different-excess, the data are consistent with a first-order dependence on [A]. The same could be said for a plot of v / [B] vs. [A]; overlay is consistent with a first-order dependence on [B].
n th-order reaction (r = kC A n), where k is the reaction rate constant, C A is the concentration of species A, and n is the order of the reaction; isothermal conditions, or constant temperature (k is constant) single, irreversible reaction (ν A = −1) All reactant A is converted to products via chemical reaction; N A = C A V
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Then the Thiele modulus for a first order reaction is: = From this relation it is evident that with large values of , the rate term dominates and the reaction is fast, while slow diffusion limits the overall rate. Smaller values of the Thiele modulus represent slow reactions with fast diffusion.