Bodensteins stationary state hypothesis

This hypothesis consists of supposing that after a period of time during which the reaction takes off, steady-state conditions will estabhsh themselves, characterized by constant intermediate compound concentrations. Such a hypothesis implies that the reaction time is long enongh for the steady-state conditions to be reached, and this is especially trae for systems that are open to inlet and outlet reactants. 

Just as for the pure kinetic cases, this relation naturally results in Vi = V2 =. .. Vn, but the processes are no longer necessarily at equilibrium We are then led to solve a system of algebraic equations with n-1 undetermined variables  

Solving this system makes it possible to express all the concentrations of intermediate species as functions of the physico-chemical system s parameters. 

The rates all being equal, the kinetic process can be described by either one of them by copying out, in the expression of its rate, the rates of the affected intermediate species Xj. 

The solutions are necessarily different from those we have obtained using the hypothesis of pure kinetic cases because they only involve kinetic constants ki, unlike the pure cases which bring into play the kinetic constants k, as well as the equilibrium constants Ki. 

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This procedure constitutes an application of the steady-state approximation [also called the quasi-steady-state approximation, the Bodenstein approximation, or the stationary-state hypothesis]. It is a powerful method for the simplification of complicated rate equations, but because it is an approximation, it is not always valid. Sometimes the inapplicability of the steady-state approximation is easily detected for example, Eq. (3-143) predicts simple first-order behavior, and significant deviation from this behavior is evidence that the approximation cannot be applied. In more complex systems the validity of the steady-state approximation may be difficult to assess. Because it is an approximation in wide use, much critical attention has been directed to the steady-state hypothesis. 

Reaction mechanisms may be developed to explain rate laws, but often they are developed in parallel, one helping the other. In translating a mechanism into a rate law a useful tool is Bodenstein s steady state approximation (SSA) or stationary state hypothesis. This approximation assumes that after a very short interval of time any reactive intermediate, which because of its reactivity will only be present in negligible proportions, will have its rate of decay equal to its rate of production, i.e., it will reach a steady concentration on a vanishingly small time scale. If this did not happen the amount of the intermediate would build up to measureable proportions and it would become an intermediate product. It is assumed at any instant that dcj /dt = 0, where R is the reactive intermediate. 

The Bodenstein hypothesis [13] can also be called a hypothesis of the stationary or quasi-stationary state. It makes the following assumptions ... 

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