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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]
where A and B are reactants C is a product a, b, and c are stoichiometric coefficients,. the reaction rate is often found to have the form: = [] [] Here is the reaction rate constant that depends on temperature, and [A] and [B] are the molar concentrations of substances A and B in moles per unit volume of solution, assuming the reaction is taking place throughout the volume of the ...
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.
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.
Although the net formula for decomposition or isomerization appears to be unimolecular and suggests first-order kinetics in the reactant, the Lindemann mechanism shows that the unimolecular reaction step is preceded by a bimolecular activation step so that the kinetics may actually be second-order in certain cases. [7]
Here k is the first-order rate constant, having dimension 1/time, [A](t) is the concentration at a time t and [A] 0 is the initial concentration. The rate of a first-order reaction depends only on the concentration and the properties of the involved substance, and the reaction itself can be described with a characteristic half-life. More than ...
For a first-order reaction, it has units of s −1. For that reason, it is often called frequency factor . According to collision theory , the frequency factor, A, depends on how often molecules collide when all concentrations are 1 mol/L and on whether the molecules are properly oriented when they collide.
Since the reaction rate determines the reaction timescale, the exact formula for the Damköhler number varies according to the rate law equation. For a general chemical reaction A → B following the Power law kinetics of n-th order, the Damköhler number for a convective flow system is defined as: