Hydrogenation rate equations

Over the usual hmited range of conditions, a power law rate equation often appears to be as satisfactory a fit of the data as a more complex Langmuir-Hinshelwood equation. The example of the hydrogenation of oc tenes is shown in Fig. l-2d and l-2e, and another case follows. 

Data on Illinois No. 6 and Kentucky No. 9 coals were used by Wen and Han (Prepi Pap.—Am. Chem. Soc., Div. Fuel Chem. 20(1) 216-233, 1975) to obtain a rate equation for coal dissolution under hydrogen pressure. These data included a temperature range of 648 to 773 K (705 to 930°F) and pressures up to 13.8 MPa (2000 psia). An empirical rate expression was proposed as... 

First, the kinetics of the reactions of 0-, m-, and p-xylene as well as of toluene were studied separately (96) at various combinations of initial partial pressures of the hydrocarbon and hydrogen. From a broader set of 23 rate equations, using statistical methods, we selected the best equations for the initial rate and determined the values of their constants. With xylenes and toluenes, these were Eqs. (17a) and (17b). 

The kinetics of hydrogenation of phenol has already been studied in the liquid phase on Raney nickel (18). Cyclohexanone was proved to be the reaction intermediate, and the kinetics of single reactions were determined, however, by a somewhat simplified method. The description of the kinetics of the hydrogenation of phenol in gaseous phase on a supported palladium catalyst (62) was obtained by simultaneously solving a set of rate equations for the complicated reaction schemes containing six to seven constants. The same catalyst was used for a kinetic study also in the liquid phase (62a). 

Further interpretation of Bruner s results were that the loss of hydrogen bromide from the first formed ArHBr2 complex was proportional to [IBr]3 and the bromination of toluene in carbon tetrachloride at 25 °C was found to give a maximum rate at [I2][Br2] = 0.8, and said to follow the rate equation... 

At pH < 5.0, the reaction rate was dependent upon the first power of the hydrogen ion concentration and at pH > 5.0 upon the square of this concentration as indicated by the data in Table 257. It was pointed out that the rate equation (300) was equivalent to... 

This third-order rate equation is interpreted as meaning that the process is first-order in each reactant, viz. N-chloroacetanilide, chloride ion and hydrogen ion. This has been confirmed10 for the reaction of N-chloroacetanilide with hydrogen bromide in a variety of aqueous media, under conditions where the dechlorination is rate-determining. The rate equation is... 

Aromatic hydrogenation is accounted for using earlier developed rate equations [23]. The lower hydrogenation activity of NiMo compared to Pt is accounted for by increasing the activation energy by 23 kJ mol". The inhibition by hetero atom containing components on the... 

Along with Cu ", MnO and Ag" , the two oxidation states of mercury are reduced by molecular hydrogen -Halpern " considers that hydrogen is oxidised by two general mechanisms corresponding to rate equations of the type... 

To understand this induced reaction it is necessary to examine the reaction between hydrogen peroxide and peroxydisulphuric acid. The rate equation based on the careful experiments of Tsao and Wilmarth is... 

In principle there is a competition for the HO2 radical between peroxydisulphate and hydrogen peroxide [reactions (63) and (86)] however, when the stoichiometry is 1 1 reaction (86) can be neglected. Assuming that the chain length is large, with the usual steady-state approximation, we obtain the following rate equation ... 

So far, what has been examined is the effect of the concentrations of the reactants and the products on the reaction rate at a given temperature. That temperature also has a strong influence on reaction rates can be very effectively conveyed by considering the experimentally found data on the formation of water from a mixture of hydrogen and oxygen. At room temperature the reaction will not take place hence the reaction rate is zero. At 400 °C it is completed in 1920 h, at 500 °C in 2 h, and at 600 °C the reaction takes place with explosive rapidity. In order to obtain the complete rate equation, it is also necessary to know the role of temperature on the reaction rate. It will be recalled that a typical rate equation has the following form ... 

Gomez-Sainero et al. (11) reported X-ray photoelectron spectroscopy results on their Pd/C catalysts prepared by an incipient wetness method. XPS showed that Pd° (metallic) and Pdn+ (electron-deficient) species are present on the catalyst surface and the properties depend on the reduction temperature and nature of the palladium precursor. With this understanding of the dual sites nature of Pd, it is believed that organic species S and A are chemisorbed on to Pdn+ (SI) and H2 is chemisorbed dissociatively on to Pd°(S2) in a noncompetitive manner. In the catalytic cycle, quasi-equilibrium ( ) was assumed for adsorption of reactants, SM and hydrogen in liquid phase and the product A (12). Applying Horiuti s concept of rate determining step (13,14), the surface reaction between the adsorbed SM on site SI and adsorbed hydrogen on S2 is the key step in the rate equation. 

Based on the assumption that hydrogen atoms are adsorded in pairs, instead of the expression of dissociative hydrogen atom adsorption, it s adequate to use H2 adsorption as the fractional surface coverage for the rate equation. 

Reaction rate data were reported as a function of temperature and are shown in Figure 12P.4. Although the form of the intrinsic rate equation for ethylene hydrogenation for this specific catalyst is not known, one might anticipate an equation of the form... 

Thiophene is the typical model compound, which has been extensively studied for typifying gasoline HDS. Although, some results are not completely understood, a reaction network has been proposed by Van Parijs and Froment, to explain their own results, which were obtained in a comprehensive set of conditions. In this network, thiophene is hydrodesulfurized to give a mixture of -butenes, followed by further hydrogenation to butane. On the considered reaction conditions, tetrahydrothiophene and butadiene were not observed [43], The consistency between the functional forms of the rate equations for the HDS of benzothiophene and thiophene, based on the dissociative adsorption of hydrogen, were identical [43,44], suggesting equivalent mechanisms. 

NASA conducted studies on the development of the catalysts for methane decomposition process for space life-support systems [94], A special catalytic reactor with a rotating magnetic field to support Co catalyst at 850°C was designed. In the 1970s, a U.S. Army researcher M. Callahan [95] developed a fuel processor to catalytically convert different hydrocarbon fuels to hydrogen, which was used to feed a 1.5 kW FC. He screened a number of metals for the catalytic activity in the methane decomposition reaction including Ni, Co, Fe, Pt, and Cr. Alumina-supported Ni catalyst was selected as the most suitable for the process. The following rate equation for methane decomposition was reported ... 

Note that the pre-exponential factors indicate only small entropies of activation in the Eyring form of the rate equations. This is a significant observation which indicates that the decrease of entropy associated with the incorporation of a hydrogen molecule at or prior to the transition state must be compensated for by a dissociation or decrease of coordination number. 

Based on Scheme 19.4, the following mathematical equation can be derived for calculating the hydrogenation rate ... 

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