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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]
In mathematics and other formal sciences, first-order or first order most often means either: " linear " (a polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contrasted with "polynomials of higher degree", or
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.
Van 't Hoff plot for an endothermic reaction. For an endothermic reaction, heat is absorbed, making the net enthalpy change positive. Thus, according to the definition of the slope: =, When the reaction is endothermic, Δ r H > 0 (and the gas constant R > 0), so
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.
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 ...
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[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].