First-order unimolecular surface reaction

A spherical non-porous particle of radius R is considered, on the external surface of which a unimolecular first order irreversible chemical reaction is taking place catalyzed by the surface of the pellet. The solid particle has a finite thermal conductivity and is immersed in an infinite medium. 

First-Order Unimolecular Surface Reaction For the reaction... 

We have thus far written unimolecular surface reaction rates as r" = kCAs assuming that rates are simply first order in the reactant concentration. This is the simplest form, and we used it to introduce the complexities of external mass transfer and pore diffusion on surface reactions. In fact there are many situations where surface reactions do not obey simple rate expressions, and they frequently give rate expressions that do not obey simple power-law dependences on concentrations or simple Arrhenius temperatures dependences. 

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. 

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. 

Products are olefins and the corresponding acids. These reactions are among the most widely studied and best understood of all gas phase unimolecular reactions. With few exceptions they are experimentally and kinetically well behaved cleanly first-order, no surface sensitivity, and no free radical chain complications. Reactions involve 1,5-hydrogen transfer from the f -carbon to the carbonyl oxygen, migration of the carbonyl Jt-bond, rupture of the ester (C-O) bond, and formation of a (Cg-Cf) 7t-bond. All present evidence favors a mechanism in which the above occur in a concerted manner. However, a two-step consecutive mechanism (see later) cannot be entirely ruled out at this time. 

The thermal cis-trans isomerization of crotonitrile has been studied in the gas phase at pressures from 0.2 to 20 torr and temperatures from 300° to 560° C . The isomerization is a homogeneous unimolecular reversible first order reaction, the rate coefficient for the direction cis trans being given by exp((-51.3 3.7)//i7 ) sec. Calculated thermodynamic parameters are = 0.17 + 0.12 kcal.mole and AS = —0.39+0.19 eu. The only side reaction with an appreciable rate was a surface polymerization. 

A different model [11] that can be used to obtain the kinetics equation for a pyrolytic reaction is adapted from the theory developed for the kinetics of heterogeneous catalytic reactions. This theory is described in literature for various cases regarding the determining step of the reaction rate. The case that can be adapted for a pyrolytic process in solid state is that of a heterogeneous catalytic reaction with the ratedetermining step consisting of a first-order unimolecular surface reaction. For the catalytic reaction of a gas, this case can be written as follows ... 

The closeness of fit may be gauged from the experimental and theoretical rate vs. concentration curves for hydrolysis of p-nitrophenyl carboxylates catalysed by quaternary ammonium surfactant micelles (Figure 3). The shape of the curve is satisfactorily explained for unimolecular, bimolecular, and termolecular reactions. An alternative speculative model is effectively superseded by this work. Romsted s approach has been extended in a set of model calculations relating to salt and buffer effects on ion-binding, acid-dissociation equilibria, reactions of weakly basic nucleophiles, first-order reactions of ionic substrates in micelles, and second-order reactions of ionic nucleophiles with neutral substrates. In like manner the reaction between hydroxide ion and p-nitrophenyl acetate has been quantitatively analysed for unbuffered cetyltrimethylammonium bromide solutions. This permits the derivation of a mieellar rate constant km = 6-5 m s compared to the bulk rate constant of kaq =10.9m s . The equilibrium constant for ion-exchange at the surface of the micelle Xm(Br was estimated as 40 10. The... 

It seems worthwhile to examine critically this transcription of the Slater method into the standard absolute reaction rate theory. In the simple unimolecular bond break, it does appear reasonable that the coordinate q between the tvfo atoms A and B must reach and go beyond a critical extension q0 in order that decomposition takes place. In Slater s calculations account is taken of the different energies involved in stretching q to q0. In regarding q as the mode of decomposition in the transition state method, one must, however, first look at the potential energy surface. The decomposition path involves passage over the lowest possible barrier between reactants and products. It does not seem reasonable to assume that this path necessarily only involves motion of the atoms A and B at the activated complex. Possibly, a more reasonable a priori formulation in a simple decomposition process would be to choose q as the coordinate which tears the two decomposition fragments apart. Such a coordinate would lead roughly to the relation... 

Unimolecular (desorption of intact molecules =MOH- OH2 =MOH -I- H2O) or associative (=M(OH)—0(H)— =M-0-M= + H2O or =M(OH)—O—(HO)M= -> =M(Oo)M= + H2O) desorption of water molecules can be described by the rate with Equation (37.12) of first or second order, respectively. The relationship between the ion current measured and the reaction rate constants was described elsewhere [29]. The fumed oxide surfaces are heterogeneous and every type of surface sites can influence the corresponding desorption peak and the corresponding center (E ) in a desorption energy distribution for this peak. If the TPD spectrum is convoluted into several peaks without any restriction that the activation energy calculated over the total temperature ranges for each of the peaks can be underestimated due to the overestimation of the peak width. Therefore, we used some modification of the calculations described in detail elsewhere [25,29]. 

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