Adsorption unimolecular

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

Irreversible Unimolecular Reactions. Consider the irreversible catalytic reaction A P of Example 10.1. There are three kinetic steps adsorption of A, the surface reaction, and desorption of P. All three of these steps must occur at exactly the same rate, but the relative magnitudes of the three rate constants, ka, and kd, determine the concentration of surface species. Suppose that ka is much smaller than the other two rate constants. Then the surface sites will be mostly unoccupied so that [S] Sq. Adsorption is the rate-controlling step. As soon as a molecule of A is absorbed it reacts to P, which is then quickly desorbed. If, on the other hand, the reaction step is slow, the entire surface wiU be saturated with A waiting to react, [ASJ Sq, and the surface reaction is rate-controlling. Finally, it may be that k is small. Then the surface will be saturated with P waiting to desorb, [PS] Sq, and desorption is rate-controlling. The corresponding forms for the overall rate are ... 

While all rates of these unimolecular reactions can be fit quantitatively by LH expressions. Equation 11, the heats of adsorption determined from the temperature dependence of the adsorption equillb-rium constant. Equation 14, do not agree with the measured reaction activation energy except for NH3 where = 16 2 kcal/mole. NO... 

Formation of products in paraffin cracking reactions over acidic zeolites can proceed via both unimolecular and bimolecular pathways [4], Based on the analysis of the kinetic rate equations it was suggested that the intrinsic acidity shows better correlation with the intrinsic rate constant (kinl) of the unimolecular hexane cracking than with the apparent rate constant (kapp= k K, where K is the constant of adsorption equilibrium). In... 

For the reaction, A B, there are two simultaneously controlling mechanisms, namely (1) adsorption of A and (2) unimolecular decomposition of adsorbed A. Given the tabulated data, find the rate equation. 

Prove that for a unimolecular surface reaction, the order of reaction with respect to reactant decreases from unity to zero as adsorption of the reactant increases from slight adsorption to strong adsorption. 

Hence, in both, in bimolecular and in unimolecular heterogeneous photoredox reactions the rate of photoproduct formation depends on the surface concentration of an electron donor or acceptor and on the adsorption properties of the adsorbing species. 

To calculate the site density, L, for a given reaction step we use Eq. (6). [Equation (6) is for a unimolecular reaction the appropriate change is made when the reaction is not unimolecular.] Suppose that the reaction step is the adsorption of a gas (B) on a catalytically active site (D) ... 

Instead we assume adsorption-desorption equilibrium (r, = ra Vr), and write Langmuir isotherms. These are exactly as for equilibrium among three adsorbed species in the unimolecular reaction... 

In the previous sections we have noted that the hypothesis of a unimolecular Gibbs layer for solutions of liquids of markedly different internal pressures together with the equation of Gibbs leads to values for molecular areas and thicknesses which are not at all unreasonably different from those determined by means of X-ray measurements, or from a study of insoluble substances on the surface of water, but cannot be said to be identical within the limits of experiment. In one respect, however, such soluble films differ from the insoluble films which we shall have occasion to examine in the next chapter the surface tension of solutions which according to the Gibbs adsorption equation... 

Spreading may occur by a process of surface solution or by vaporisation from the lens and condensation on the water surface. This latter, indeed, is the only method of spreading on a solid. The adsorption of vapours from a liquid onto a second liquid surface to the point of equilibrium results in the formation of a primary (unimolecular) film and this is doubtless followed in many cases by secondary film formation or a banking up of the layers on the primary film to a thickness which may be several hundred molecules thick. The conditions which have to be fulfilled are two (1) the surface tension of the film whether primary or secondary o- must attain the value... 

It will be noted that on Langmuir s hypothesis the surface becomes saturated when it is covered with a unimolecular thickness of adsorbed gas. By measuring the adsorption of gases on the surface of mica and of platinum Langmuir showed that with the exception of carbon monoxide, gases such as oxygen, nitrogen and methane apparently when adsorbed to a saturation value covered the surface with a unimolecular thickness of gas. 

We have so far discussed two possibilities alternative to the assumption of the existence of multimolecular films and enquiry is necessary to examine how far all existing data can be reconciled to the assumptions either of a capillary surface or a surface variable in accessibility. It must be admitted that these views do not seem adequate to explain all cases of adsorption. Thus in the data presented by Evans and George it is rather singular that the amount of nitrogen adsorbed on glass should be equal to the computed unimolecular film whilst the other easily liquefiable gases exceed this thickness. Langmuir s data on the adsorption of carbon... 

It must be concluded that although the first layer of adsorbed molecules is held extremely tenaciously and that a large decrease in free energy occurs on the adsorption of a unimolecular layer of gas, a further but smaller decrease in free energy may take place on the further adsorption of gas in the secondary films. We would anticipate that a surface of feeble adsorptive power such as diamond would be almost completely saturated with a unimolecular layer, but active surfaces such as of metals are not completely saturated. 

The characteristics of metals in exerting a specific action in adsorption of gases which for the more perfect gases results in the formation of a unimolecular layer and for vapours multimolecular... 

In some cases it has been found that the maximum on saturation adsorption of a solute from a solution corresponds to the formation of an adsorption layer one molecule thick. Thus Euler Zeit. Elehtrochem. xxviii. 446,1922) found that a maximum adsorption of silver ions by silver and gold leaf was attained in a 0 03 A solution. It was found that 5 5 and 8 5 to 9 mgm. of silver ions were adsorbed by a square metre of metallic silver and gold respectively, such a surface concentration is practically unimolecular. The adsorption of silver ions by silver bromide (K. Fajans, Zeit Phys. Ohem. cv. 256, 1928) was found on the other hand to be not complete, for only every fourth bromide ion in a silver bromide surface was found to adsorb a silver ion. Similar conclusions as to the unimolecular character of the adsorbed film in the case of chemical charcoal as an adsorbing agent for fatty and amino acids may be drawn from the data of Foder and Schonfeld Koll. Zeit xxxi. 76, 1922). 

Od6n Nova Acta Reg, Soc. Upsala, m. 4,1913) showed that the maximum adsorption of sodium chloride by sulphur particles 1000 A. in diameter yielded a value of 2 79 gms. NaCl for 100 gms. of the sulphur. If the density of colloidal sulphur be taken as A = 2 we find that one sulphur particle of area 8 x 10 sq. cm. adsorbs 3x10 molecules giving on the assumption of an unimolecular layer a mean area for the sulphur molecule of 10 sq. cm. or 10 A. which is a close approximation to the. value calculated in other ways. 

Based on the Langmuir-Hinshelwood expression derived for a unimolecular reaction system (6) Rate =k Ks (substrate) /[I + Ks (substrate)], Table 3 shows boththe apparent kinetic rate and the substrate concentration were used to fit against the model. Results show that the initial rate is zero-order in substrate and first order in hydrogen concentration. In the case of the Schiff s base hydrogenation, limited aldehyde adsorption on the surface was assumed in this analysis. Table 3 shows a comparison of the adsorption equilibrium and the rate constant used for evaluating the catalytic surface. 

The unimolecular nature of the adsorbed layer was emphasized by Langmuir, and has been regarded as an essential part of the theory. The alternative view is that the adsorption film is atmospheric in character with a high density of gas in immediate contact with the surface, thinning continuously with increasing distance until the normal density of the gas phase is reached. ... 

It is, on the other hand, necessary to adopt one or other of the really fundamental alternatives, namely, whether there is a definite saturation limit to adsorption, or whether the adsorption goes on increasing indefinitely with increasing concentration in the gaseous phase. The simplest form of the first alternative is the unimolecular layer theory, the simplest form of the second the atmospheric theory. It might be thought that an experimental decision between these two possibilities could be made quite easily. The matter is, however, not quite simple, since slow solution effects and other complications are often superposed on... 

The hydrides of phosphorus, arsenic, and antimony thus form an interesting transition series. On similar sorts of surface antimony hydride is the least stable, decomposing with measurable speed at ordinary temperatures, and phosphine is the most stable, not decomposing at an appreciable rate below a red heat. Arsine occupies an intermediate position. At low temperatures the adsorption is considerable, and, as a result, the stibine decomposition requires the pn equation, while the more stable hydrides, which only decompose rapidly at higher temperatures where the adsorption is smaller, obey the unimolecular law. It is interesting, moreover, that with stibine itself the exponent n increases towards unity as the temperature at which the reaction takes place is raised. 

GAS ADSORPTION. The unimolecular layer of a gas adsorbed on each particle at low temperature may be used for surface area measurements (J+T). 

To derive the corresponding kinetic expressions for a bimolecular-unimolecular reversible reaction proceeding via an Eley-Rideal mechanism (adsorbed A reacts with gaseous or physically adsorbed B), the term K Pt should be omitted from the adsorption term. When the surface reaction controls the rate the adsorption term is not squared and the term KgKg is omitted. 

Standard mechanisms for chain reactions generally miss out the surface termination steps, but these should be included. Such terminations are written as first order in radical since diffusion to the surface or adsorption on the surface are rate determining, rather than the second order bimolecular step of recombination of the two radicals adsorbed on the surface. A complete mechanism will also include the need for a third body in any unimolecular initiation or propagation steps, and in any gas phase termination steps. 

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