The MARI Approximation

The Most Abundant Reaction Intermediate (MARI) approximation is a further development of the quasi-equilibrium approximation. Often one of the intermediates adsorbs so strongly in comparison to the other participants that it completely dominates the surface. This intermediate is called the MARI. In this case Eq. (156) reduces to 

If molecule A in our reaction scheme (132-135) binds more strongly to the surface than either B or AB, and the pressures of B and AB are comparable with or lower than that of A, then A will be the MARI and the expressions for the coverages reduce to  

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In the MARI approximation, we have made one of the intermediates MARI at all reaction conditions. This has two consequences... 

In particular the latter consequence is troublesome as an estimate of the validity of this aspect of the MARI approximation amounts to solving the problem without using the MARI approximation. In other words, if the validity of the MARI approximation can be verified, only if it is superflous. 

The MARI approximation can be used for quantitative modeling, if we have verified that it is valid at the reaction conditions we are considering. 

The MARI approximation is very much used for the analysis of reaction mechanisms, both when we have difficulties in formulating a kinetic model for a complicated reaction mechanism and when we want to derive a limiting form of a kinetic model. 

In solving the kinetics of a catalytic reaction, what is the difference between the complete solution, the steady-state approximation, and the quasi-equilibrium approximation What is the MARI (most abundant reaction intermediate species) approximation ... 

It should be noted that two of these three XSs have very few data points and we cannot expect a good accuracy for the r parameter describing the asymmetry, even if the numerical uncertainty (Chi /DoF) of the fit is small. Note that the JPL data points are not the raw data but are determined from a fit of experimental data with a different analytic formula [23]. Below, the experimental XS of Marie [22] is used to test and compare the various approximations introduced in Sections 2 and 3 of this paper. 

The derivation of a rate equation from two-step sequences can also be generalized. First, if the rate-determining step consumes the mari, the concentration of the latter is obtained from the equilibrium relationship that is available. Second, if the steps of the two-step sequence are practically irreversible, the steady-state approximation leads to the solution. 

These simplifying assumptions must be adapted to some extent to explain the nature of some reactions on catalyst surfaces. The case of ammonia synthesis on supported ruthenium described in Example 5.3.1 presents a situation that is similar to rule 1, except the rate-determining step does not involve the mari. Nevertheless, the solution of the problem was possible. Example 5.3.2 involves a similar scenario. If a mari cannot be assumed, then a rate expression can be derived through repeated use of the steady-state approximation to eliminate the concentrations of reactive intermediates. 

Another indication of the low reactivity of the CH band is the strong competition between hydrocarbon adsorption and hydrogen adsorption. The rate of the ethylene hydrogenation shows a maximum at approximately ISO C Below this temper ature the rate of hydrogen dissociation is limiting, above it the surface coverage of ethylene becomes equilibrium limited and the rate of ethylene adsorption becomes the rate limiting step of the reaction. At that temperature adsorbed ethylene is the MARI (chapter 1) of the adsorbed phase. 

The organization employs the equivalent of approximately ten full-time staff members, including the Chief Executive Officer, Mrs. Mary Hemming, B Pharm., Grad Dip Epi Biostat. 

Figure 3 compares the molecular (left) and acetone (right) TPD data for the reaction of 3.0 L of oxygen (approximately 0.30 ML of O atoms, or 60% of monolayer saturation) with varying amounts of 2-propyl iodide on Ni( 100). A 0.5 L exposure of 2-propyl iodide leads to the desorption of hydrogen, propene and propane, but not acetone, and results in TPD traces quite similar to those obtained from the same 2-C3H7I dose on the clean surface. The onset of acetone formation is seen as a small peak around 350 K only after a 2.0 L alkyl halide dose, and the molecular desorption data shows that monolayer saturation of 2-propyl iodide on this surface occurs between 2.0 and 4.0 L. Notice in particular that the 2.0 L marie corresponds to the point at which all the nickel sites become occupied (see Figure 1). This suggests that, in order for acetone to be produced, a particular surface ensemble is required with the 2-propyl groups adsorbed next to oxygen atoms [19-21].

The heaviest member of the alkaline earth metals is radium (Ra), a naturally radioactive element discovered by Pierre and Marie Curie in 1898. Radium was initially isolated from the uranium ore pitchblende, in which it is present as approximately 1.0 g per 7.0 metric tons of pitchblende. How many atoms of radium can be isolated from 1.75 X 10 g pitchblende (1 metric ton =... 

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