Bodenstein pseudo steady state

Applying the Bodenstein pseudo-steady-state approximation, where it is assumed that the excited molecule M is formed as quickly as it disappears, yields... 

Later, it became clear that the concentrations of surface substances must be treated not as an equilibrium but as a pseudo-steady state with respect to the substance concentrations in the gas phase. According to Bodenstein, the pseudo-steady state of intermediates is the equality of their formation and consumption rates (a strict analysis of the conception of "pseudo-steady states , in particular for catalytic reactions, will be given later). The assumption of the pseudo-steady state which serves as a basis for the derivation of kinetic equations for most commercial catalysts led to kinetic equations that are practically identical to eqn. (4). The difference is that the denominator is no longer an equilibrium constant for adsorption-desorption steps but, in general, they are the sums of the products of rate constants for elementary reactions in the detailed mechanism. The parameters of these equations for some typical mechanisms will be analysed below. 

Fri>ni time to time a paper emerges in the literature aimed at emphasising the net essity of the foundation of the principle of quasistationarity, pseudo-steady state hypothesis, or Bodenstein(-Semenov) method. The essence of the method seems to be an absolutely crazy idea — from the mathematical point ofview. In a system of differential equations let us consider the variables that late on small values to be constant. So if a function is small, so is its derivative It turns out that among the conditions that occur in chemical reaction kinetics it does work well. 

There may be situations where the rates of the individual steps are all of the same order of magnitude and we could not invoke the pseudoequilibrium hypothesis. In such a case, we can use the pseudo-steady-state hypothesis, or Bodenstein (1927) approximation At some point during the reaction, the rate of formation and the rate of disappearance of an intermediate are identical causing a steady-state concentration, or surface coverage, of the reactive intermediate. 

In these conditions, all the other steps will be regarded as constantly in equilibrium and the pseudo-steady state will have the meaning of the Bodenstein s quasi-steady state. 

Thus for a homogeneous system operating at constant volume, the pseudo-steady mode gives the same result as the Bodenstein quasi-steady state approximation. We can say that we have a quasi-steady state mode. 

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