Reaction rate equations Langmuir-Hinshelwood

Kinetic analysis based on the Langmuir-Hinshelwood model was performed on the assumption that ethylene and water vapor molecules were adsorbed on the same active site competitively [2]. We assumed then that overall photocatalytic decomposition rate was controlled by the surface reaction of adsorbed ethylene. Under the water vapor concentration from 10,200 to 28,300ppm, and the ethylene concentration from 30 to 100 ppm, the reaction rate equation can be represented by Eq.(l), based on the fitting procedure of 1/r vs. 1/ Ccm ... 

The redox reaction rate equation always implies a monotonic dependence of the rate of reaction upon the concentration of the reacting species. On the other hand kinetic expressions based upon the Langmuir-Hinshelwood kinetics when two of the reactants are competing for the same active sites may show non-monotonic kinetics in certain regions of the parameters. For the reaction between a hydrocarbon and oxygen, the rate equation can be written in the... 

For the above three reactions, the following Langmuir—Hinshelwood types of rate equations developed by Sheppard, Maier, and Caram (1986) are used ... 

The kinetics of H2 formation (and other surface reactions) via the Langmuir-Hinshelwood (diffusive) mechanism can be treated by rate equations, as in Eq. (1.52), or by stochastic methods.There are two main objections to the former approach it does not handle random-walk correctly and it fails in the limit of small numbers of reactive species. The latter objection is a far more serious one in the interstellar medium because dust particles are small, and the number of reactive atoms and radicals on their surfaces can be, on average, less than unity. Nevertheless, with rare exceptions, the few large models of interstellar chemistry that include surface processes as well as gas-phase chemistry do so via the rate equation approach, so we discuss it here. In the treatment below, we do not use the ordinary units of surface chemistry — areal concentrations or mono-layers — but instead refer to nmnbers of species on the mantle of an individual but average grain. Numbers can be converted to bulk concentrations, as used in Eq. (1.52), by multiplication by the grain number density n. ... 

If the rate of both single reactions is expressed separately, e.g. by means of the equations of Langmuir-Hinshelwood type (when written in a more general way and if the mechanism of both reactions with common reagent X will be the same), we obtain... 

The plots are practically linear and show that the rates are constant. Consequently the order of reaction is zero at both initial pressures. If a Langmuir-Hinshelwood rate equation,... 

Equation (2), usually referred as the Langmuir-Hinshelwood (LH) equation, interprets die rate as tlie product of a specific rate constant k for reaction of photogenerated surface species with the absorbed substrate r=A LH Redi, the extent of absorption being determined by K. The role of other species was coherently interpreted as a competition for absorption, adding to the denominator the proper terms for competing species i [17,21], The role of the electron... 

The kinetics of the ethylene oxidation are rather complicated as they depend not only on ethylene and oxygen pressure but also on the concentration of the reaction products. These influence the rate by adsorption competition with the reactants. Moreover, different forms of adsorbed oxygen may occur on the catalyst surface. Consequently, the rate equations proposed in the literature consist of either Langmuir—Hinshelwood and Eley—Rideal types or power rate models with non-integer coefficients. Power rate models are less appropriate as their coefficients inevitably depend on the reaction conditions. 

A silica-supported Sn—V—P—O catalyst (Sn/V/P = 1/9/3) was investigated by Onsan and Trimm [244]. Working with a flow reactor at about 520°C, a maximum selectivity of 75% to acrylonitrile was reached at a contact time of ca. 230 g sec l-1 and an oxygen/propene/ammonia ratio of 2/1/1.75. The authors assume that the six principal products (acrylonitrile, acetonitrile, HCN, CO, C02, N2) are formed by six parallel reactions and in the first instance apply power rate equations. A more detailed analysis reveals that a Langmuir—Hinshelwood type rate equation, surface reaction being rate-determining, properly describes the production of acrolein plus acrylonitrile from propene, viz. 

The ammoxidation of isobutene has not received much attention. The only contribution in this field is by Onsan and Trimm [2.44] for a rather unusual catalyst, a mixture of the oxides of Sn, V and P (ratio 1/9/3) supported on silica. At 520 C, a maximum selectivity to methacrylonitrile + methacrolein of 80% was reached with a Sn—V—P oxide catalyst (ratio 1/9/3), an isobutene/ammonia/oxygen ratio of 1/1.2/2.5 and a contact time of 120 g sec l ]. The kinetics are very similar to those for the pro-pene ammoxidation. Again, the data are initially analysed by means of (parallel) power rate equations, for which the parameters were calculated, while a more detailed analysis proves that a Langmuir—Hinshelwood model with surface reaction as the rate-controlling step provides the best fit with regard to the two main products. At 520° C, the equation which applies for the production of methacrolein plus methacrylonitrile is... 

Regarding the kinetics, the oxidation of o-xylene and o-tolualdehyde were compared for catalysts with different V/Ti ratios (Table 36). The ratio between partial and complete oxidation (X for o-xylene and Y for o-tolualdehyde) are influenced similarly, indicating that a change in the catalyst structure influences all the reaction steps. The oxidation of o-tolualdehyde in mixtures with o-xylene revealed that o-tolualdehyde reduces the o-xylene oxidation rate by a factor of about 2. The authors conclude that a redox model is inadequate and that hydrocarbon adsorption cannot be rate-determining. Adsorption of various products should be included, and equations of the Langmuir—Hinshelwood type are proposed. It should be noted that the observed inhibition is not necessarily caused by adsorption competition, but may also stem from different... 

For the reaction of diethylether giving either ethylene and ethanol or ethylene and water, the validity of the Langmuir—Hinshelwood type rate equations has again been confirmed [82],... 

The other approach is based on the Langmuir—Hinshelwood kinetics. In all the work using this approach, the surface reaction of adsorbed olefin and water was found, or postulated, to be the rate-determining step. The corresponding rate equation has the form... 

The Langmuir—Hinshelwood rate equation (16) used by several authors for other types of catalyst was interpreted by Tanabe and Nitta [290] on the basis of their results with NiS04. The authors assume that the surface reaction of adsorbed ethylene and water molecules, which was found to be the slowest process, may be written in greater detail as... 

Equation (24) is, in fact, a Langmuir—Hinshelwood-type equation. Similar models with a single site surface reaction as the rate-determining step were used for other liquid phase esterifications [448,451]. Experimental data for the l-butanol-x>leic acid system were best fitted by eqn. (24) [452] or eqn. (25) [451]... 

The kinetics of the ammoxidation of xylenes over a vanadium catalyst and mixed vanadium catalysts were studied. The reaction rate data obtained were correlated with the parallel consecutive reaction scheme by the rate equations based upon the Langmuir-Hinshelwood mechanism where the adsorption of xylenes was strong. The reaction rates of each path are remarkably affected by the kind of xylene and catalyst. The results of the physical measurement of catalysts indicated that the activity and the selectivity of reaction were affected by the nature and the distribution of metal ions and oxygen ion on catalyst surface. 

The Langmuir-Hinshelwood treatment of the kinetics of surface catalyzed reactions affords a useful representation of some of the characteristics of catalytic hydrogenation. It is a limiting form of more exact equations which recognize that, even though the elementary steps are reversible, few if any will be at equilibrium (ref. 15). Not surprisingly, alternative assumptions regarding the relative rates of the forward and reverse elementary reactions can lead to approximate equations of the same form. 

---