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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.
The steady-state solution is proportional to the driving force with an induced phase change : = (+), where = + is the absolute value of the impedance or linear response function, and = + is the phase of the oscillation relative to the driving force.
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.
Determining the parameters of the Michaelis–Menten equation typically involves running a series of enzyme assays at varying substrate concentrations , and measuring the initial reaction rates , i.e. the reaction rates are measured after a time period short enough for it to be assumed that the enzyme-substrate complex has formed, but that the ...
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 ...
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.
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.