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The steady state approximation, [1] occasionally called the stationary-state approximation or Bodenstein's quasi-steady state approximation, involves setting the rate of change of a reaction intermediate in a reaction mechanism equal to zero so that the kinetic equations can be simplified by setting the rate of formation of the intermediate equal to the rate of its destruction.
The rate equation for the rate of formation of product P may be obtained by using the steady-state approximation, in which the concentration of intermediate A* is assumed constant because its rates of production and consumption are (almost) equal. [8] This assumption simplifies the calculation of the rate equation.
Steady state is also used as an approximation in systems with on-going transient signals, such as audio systems, to allow simplified analysis of first order performance. Sinusoidal Steady State Analysis is a method for analyzing alternating current circuits using the same techniques as for solving DC circuits.
Consider the simple example where the catalyst associates with substrate A, followed by reaction with B to form product, P and free catalyst. Regardless of the approximation applied, multiple independent parameters (k 1, k −1, and k 2 in the case of steady-state; k 2 and K 1 in the case of pre-equilibrium) are required to define the system ...
In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form / =, where r is the perturbation to the steady state, A is a linear operator whose spectrum contains eigenvalues with positive real part.
The steady-state heat equation for a volume that contains a heat source (the inhomogeneous case), is the Poisson's equation: − k ∇ 2 u = q {\displaystyle -k\nabla ^{2}u=q} where u is the temperature , k is the thermal conductivity and q is the rate of heat generation per unit volume.
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.
An example of a reaction taking place with an S N 1 reaction mechanism is the ... is an approximation, the rate law derived from the steady state approximation ...