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For zero-order reactions, the reaction rate is independent of the concentration of a reactant, so that changing its concentration has no effect on the rate of the reaction. Thus, the concentration changes linearly with time. The rate law for zero order reaction is [] = [] =,
b) The straight portion of the graph for substrate concentration over time is indicative of a zero-order dependence on substrate for most of the reaction, but the curve at low [A] is indicative of a change to (in this case) a first-order dependence on [A].
The reaction changes from approximately first-order in substrate concentration at low concentrations to approximately zeroth order at high concentrations. At small values of the substrate concentration this approximates to a first-order dependence of the rate on the substrate concentration:
Derivation of equations that describe the time course of change for a system with zero-order input and first-order elimination are presented in the articles Exponential decay and Biological half-life, and in scientific literature. [1] [7] = C t is concentration after time t
Therefore, it is valid to apply the steady state approximation only if the second reaction is much faster than the first (k 2 /k 1 > 10 is a common criterion), because that means that the intermediate forms slowly and reacts readily so its concentration stays low. The graphs show concentrations of A (red), B (green) and C (blue) in two cases ...
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.
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
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: