Phase reactions, gas

For the ideal-gas (a good approximation for real gas mixtures at relatively low pressures) reaction A(g) -I- B(g) AB(g), the standard pressure equilibrium constant K° is 

From the stoichiometry of the reaction, Pa and Pb can be related to the initial pressures Pq,a and Pq,b. In the manometric method, the pressures Po,a, Po,b and P are successively measured in a vacuum line kept at a fixed temperature using a precision manometer. Thus, the equilibrium constant can be calculated using the equation 

Examples of determinations of pressure equilibrium constants by the manometric method can be found in the literature [52, 72] for the complexes of B(CH3)3 and CH3OH with amines. 

The equilibrium constant can also be expressed in terms of concentration C by using the ideal-gas relation  

Since the standard state of an ideal gas is defined as having 1 bar pressure, the standard complexation Gibbs energy AG° is directly related to K°  

For gas-phase reactions, the molar density is more useful than the mass density. Determining the equation of state for a nonideal gas mixture can be a difficult problem in thermodynamics. For illustrative purposes and for a great many industrial problems, the ideal gas law is sufficient. Here it is given in a form suitable for flow reactors  

If the reactor operates isothermally and if the pressure drop is sufficiently low, we have achieved closure. Equations (3.11) and (3.13) together allow a marching-ahead solution. The more common case requires additional equations to calculate pressure and temperature. An ODE is added to calculate pressure P(z), and Chapter 5 adds an ODE to calculate temperature T(z). 

For laminar flow in a circular tube of radius R, the pressure gradient is given by a differential form of the Poiseuille equation  

For turbulent flow, the pressure drop is calculated from 

More accurate correlations, which take factors like wall roughness into account, are readily available, but the form used here is adequate for most purposes. It has a simple, analytical form that lends itself to conceptual thinking and scaleup calculations, but see Problem 3.14 for an alternative. 

If the reactor operates isothermally and if the pressure drop is sufficiently low, we have achieved closure where Equations 3.11 and 3.13 together allow a marching-ahead 

Consider the reaction 2A — B. Derive an analytical expression for the fraction unreacted in a gas phase, isothermal PFR of length L. The pressure drop in the reactor is negligible. The reactor cross section is constant. There are no inerts. The feed is pure A and the gases are ideal. Test your mathematics with a numerical solution. 

These equations are the starting point for both the analytical and the numerical solutions. 

ANALYTICAL S0Lf/770iV A stoichiometric relationship can be used to eliminate 4 b. Combine Equations 3.15 and 3.16 to obtain 

Now we discuss how to calculate the equilibrium composition of a reacting non-ideal gas mixture. In order to use Eq. (12.7), we need an expression for the dependence of the chemical potential of each species in the system with its composition. In general, this can be expressed as (see Sec. 11)  

The equilibrium constant and the Gibbs free energy of reaction are independent of the composition and pressure of the system but are dependent on the temperature of the system and the choice of the reference pressure. The greater the value of the equilibrium constant (which corresponds to more negative values of the Gibbs free energy of reaction), the further the reaction proceeds to completion. Given a value for the equilibrium constant and the pressure of the system, Eq. (12.10) can be solved to determine the equilibrium composition of the system. In the next section, we discuss how to determine the value of the equilibrimn constant. 

Of the hundreds of reactions which have been observed to proceed in the gas phase relatively few, if any, can be described in terms of a single chemical transformation. The largo majority proceed through a more or less complex chemical mechanism that involves the formation and destruction of highly reactive free radicals and atoms. Because of the reactivity of these intermediates, they are usually present in extremely low concentrations, and their existence is generally inferred from indirect evidence rather than from direct observation.  

This leads, as we shall see, to a situation in which simple measurements of the rate constant, order, and activation energy of a chemical reaction do not provide sufficient data to establish uniquely the detailed mechanism of a chemical reaction. Instead, the task of determining an unambiguous mechanism confronts the experimenter with a problem which requires the application of the utmost ingenuity in devising criteria for testing the validity of the steps in any proposed mechanism. 

In the following sections we shall consider in detail some of the better-studied complex reaction systems and some of the methods which have been employed for studying their mechanisms. 

Gas-phase reactions will bo given an emphasis beyond the other areas of kinetics, precisely because the extensive development of quantitative thermodynamic data and semiquantitative theories makes it possible to interpret the details of these complex reactions of gases to a degree far beyond anything now available for reactions in condensed phases. 

In 1906, Bodenstein and Lind showed that the kinetics of the reaction of H2 and Br2 (which proceeds at a conveniently measurable rate between 230 and 300 C) could be presented empirically by the equation 

There is an additional point to be made about this type of processing. Many gas-phase processes are carried out in a continuous-flow manner on the macro scale, as industrial or laboratory-scale processes. Hence already the conventional processes resemble the flow sheets of micro-reactor processing, i.e. there is similarity between macro and micro processing. This is a fimdamental difference from most liquid-phase reactions that are performed typically batch-wise, e.g. using stirred glass vessels in the laboratory or stirred steel tanks in industrial pilot or production plants. 

Chemical Micro Process En neering Fundamentals, Modelling and Reactions Volker Hessel, Steffen Hardt, Holger Lowe 

Copyright 2004 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 3-527-30741-9 

Considering the major importance of catalysts, especially for gas-phase reactions, a separate section was allocated to the description of techniques for catalyst layer formation in micro channels and the respective analytical characterization (see Section 3.1). 

In reactor calculations, the important quantities in reaction kinetics, or concentrations of the components, are related to the stoichiometric quantities such as the extent of reaction and conversion. For practical reasons, gas- and liquid-phase reactions are discussed separately. For gas-phase reactions, the ideal gas law is assumed to be valid. 

Relationships 3.44 and 3.45 can be utilized to calculate the concentrations in a mixture constituting an ideal gas. The total concentration in the mixture is given according to the ideal gas law  

For a system with a single chemical reaction. Equations 3.61 and 3.67 are inserted into the expression of c, if the relation (Equation 3.87) is taken into account simrdtaneously, the result becomes 

For a system with multiple chemical reactions, the expression for the total concentration (Equation 3.87) is naturally still valid. By inserting expressions of the molar fractions. Equations 3.76 and 3.85, into the definition of the concentration. Equations 3.44 and 3.45, the following expressions are obtained for the concentrations  

The change in the volumetric flow rate is obtained by applying the ideal gas law to the entire reaction mixture, at the reactor inlet and in an arbitrary reactor coordinate (location)  

The thermodynamic analogy is not to be used as a method for establishing absolute values for the various activation parameters these are of limited significance since they derive from an equilibrium thermodynamic interpretation of intrinsically nonequilibrium properties. Furthermore, to accept such numbers uncritically ascribes a measure of definiteness to the activated complex which is unwarranted. On the other hand, trends and similarities may be useful in helping to characterize reaction mechanism. In Table 9.4 the values of and AHq calculated from (9.43) and (9.44) are given for a number of gas-phase reactions. For the bimolecular reactions the value of ASq depends upon the choice of standard state for rate constants in units of cm mol sec the natural standard state is a concentration of 1 mol cm.  

The activation entropies for the four unimolecular reactions are positive and can be interpreted if we assume that the molecule, in its activated state, is less ordered than in the ground state. Disordering occurs because a bond must be weakened or broken for reaction to be possible. The cyclopropane isomerization is a particularly good example. As a C-C bond breaks the molecule passes through an intermediate, possibly a diradical. 

The intermediate has greater rotational and vibrational freedom than either reactant or product. Thus it is not surprising that ASq ASJ. y the values are 50 and 28 J K, respectively. 

The trends in the other bimolecular examples are reasonably understandable. There are fewer orientational constraints in H-atom addition to ethylene than in methyl radical addition the values of ASq are in accord with this interpretation. The hydrogen-transfer reactions of methyl with ethane and ethylene have the same entropy of activation, indicative of similar orientational requirements. The addition of CH3 to CO has a large negative ASq, reflecting the severe geometric constraints necessary for this reaction to be possible. 

It is the Arrhenius -factor which is related to Zl5 o and thus to mechanistic models for the structure of the activated complex. The value of AHq is determined by the barrier to reaction and it cannot be simply related to a model for the reaction intermediate. 

1 Hurd, Pyrolysis of Organic Compounds. Chemical Catalog Co, New York (1929). 

The Fries rearrangement of phenyl acetate (PA) over solid-acid catalysts was first studied in a fixed bed reactor at 400 °C by Pouilloux et al. [9,10]. o- and p-Hydro-xyacetophenone (o- and p-HAP), p-acetoxyacetophenone (p-AXAP), and phenol (P) were the main reaction products. Fluorinated alumina and H-FAU zeolites afforded approximately the same product distribution, o-HAP being highly favored over the para isomer. The reaction scheme proposed was that PA dissociates into phenol (P) and ketene and that o-HAP results partly from an intramolecular rearrangement of PA and partly from transacylation (Eq. 2) whereas p-HAP results from the latter reaction only [10]. 

With H-MFI, the p-/o-HAP ratio was much higher this is indicative of shape-selectivity effects. With all the catalysts, HAP selectivity was poor, phenol being the main product because of the rapid dissociation of PA [9,10]. Very fast deactivation as a result of coke deposition and zeolite dehydroxylation was also observed. Catalyst stability can, however, be considerably improved by use of equimolar mixtures of PA and water or of phenol and acetic acid (AA) instead of PA [11]. 

Phenol acylation with acetic anhydride over MFI catalysts is also very o-HAP selective, although with this acylating agent o-HAP would result from direct C-acylation of phenol rather than secondary transformation of phenyl acetate [21]. 

The peak pressure generated by a detonation wave is twice as  

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The equilibrium conversion can be increased by employing one reactant in excess (or removing the water formed, or both). b. Inerts concentration. Sometimes, an inert material is present in the reactor. This might be a solvent in a liquid-phase reaction or an inert gas in a gas-phase reaction. Consider the reaction system... 

Catalytic gas-phase reactions play an important role in many bulk chemical processes, such as in the production of methanol, ammonia, sulfuric acid, and nitric acid. In most processes, the effective area of the catalyst is critically important. Since these reactions take place at surfaces through processes of adsorption and desorption, any alteration of surface area naturally causes a change in the rate of reaction. Industrial catalysts are usually supported on porous materials, since this results in a much larger active area per unit of reactor volume. 

Inlet pressure and pressure drop (gas-phase reactions)... 

By contrast, if the reactor is continuous well-mixed, then the reactor is isothermal. This behavior is typical of stirred tanks used for liquid-phase reactions or fluidized-bed reactors used for gas-phase reactions. The mixing causes the temperature in the reactor to be effectively uniform. 

It was pointed out that a bimolecular reaction can be accelerated by a catalyst just from a concentration effect. As an illustrative calculation, assume that A and B react in the gas phase with 1 1 stoichiometry and according to a bimolecular rate law, with the second-order rate constant k equal to 10 1 mol" see" at 0°C. Now, assuming that an equimolar mixture of the gases is condensed to a liquid film on a catalyst surface and the rate constant in the condensed liquid solution is taken to be the same as for the gas phase reaction, calculate the ratio of half times for reaction in the gas phase and on the catalyst surface at 0°C. Assume further that the density of the liquid phase is 1000 times that of the gas phase. 

The gas phase reaction shows a double minimum and a small barrier along the reaction coordinate which is the difference between the two C-CL distances. The minima disappear in aqueous solution and this is accompanied by an increase in the height of the barrier. The behaviour in dimethyl fonnamide is intennediate between these two. 

Gas-phase reactions play a fundamental role in nature, for example atmospheric chemistry [1, 2, 3, 4 and 5] and interstellar chemistry [6], as well as in many teclmical processes, for example combustion and exliaust fiime cleansing [7, 8 and 9], Apart from such practical aspects the study of gas-phase reactions has provided the basis for our understanding of chemical reaction mechanisms on a microscopic level. The typically small particle densities in the gas phase mean that reactions occur in well defined elementary steps, usually not involving more than three particles. 

In the case of bunolecular gas-phase reactions, encounters are simply collisions between two molecules in the framework of the general collision theory of gas-phase reactions (section A3,4,5,2 ). For a random thennal distribution of positions and momenta in an ideal gas reaction, the probabilistic reasoning has an exact foundation. Flowever, as noted in the case of unimolecular reactions, in principle one must allow for deviations from this ideal behaviour and, thus, from the simple rate law, although in practice such deviations are rarely taken into account theoretically or established empirically. 

Trimoleciilar reactions require the simultaneous encounter of tliree particles. At the usually low particle densities of gas phase reactions they are relatively unlikely. Examples for trimoleciilar reactions are atom recombination reactions... 

The foundations of the modem tireory of elementary gas-phase reactions lie in the time-dependent molecular quantum dynamics and molecular scattering theory, which provides the link between time-dependent quantum dynamics and chemical kinetics (see also chapter A3.11). A brief outline of the steps hr the development is as follows [27],... 

The simplest possible gas-phase reaction mechanisms consist of an elementary reaction and its back reaction. 

An important example for the application of general first-order kinetics in gas-phase reactions is the master equation treatment of the fall-off range of themial unimolecular reactions to describe non-equilibrium effects in the weak collision limit when activation and deactivation cross sections (equation (A3.4.125)) are to be retained in detail [ ]. 

The importance of numerical treatments, however, caimot be overemphasized in this context. Over the decades enonnous progress has been made in the numerical treatment of differential equations of complex gas-phase reactions [8, 70, 71], Complex reaction systems can also be seen in the context of nonlinear and self-organizing reactions, which are separate subjects in this encyclopedia (see chapter A3,14. chapter C3.6). 

Johnston Fi S 1966 Gas Phase Reaction Rate Theory (Ronaid)... 

Grote R F and Hynes J T 1980 The stable states picture of chemical reactions. II. Rate constants for condensed and gas phase reaction models J. Chem. Phys. 73 2715-32... 

In most of gas phase reaction dynamics, the fundamental reactions of interest are bimolecular reactions. 

The field of gas phase reaction dynamics has been extensively reviewed elsewhere [1, 2 and 3] in considerably greater detail than is appropriate for this chapter. Here, we begin by simnnarizing the key theoretical concepts and experimental teclmiques used in reaction dynamics, followed by a case study , the reaction F + H2 HF + H, which serves as an illustrative example of these ideas. 

Instead of shifting the detector position, as indicated in figure B2.5.1 one often varies the location of the reactant mixing region using moveable injectors. This allows complex, possibly slow, but powerfril, analytical teclmiques to be used for monitoring gas-phase reactions. In combination with mass-spectrometric detection. 

One of the most important teclmiques for the study of gas-phase reactions is flash photolysis [8, ]. A reaction is initiated by absorption of an intense light pulse, originally generated from flash lamps (duration a=lp.s). Nowadays these have frequently been replaced by pulsed laser sources, with the shortest pulses of the order of a few femtoseconds [22, 64]. 

Fleming GR 1986 Chemical Applications of Ultrafast Spectroscopy (Oxford Oxford University Press) Jolmston Ft S 1966 Gas Phase Reaction Rate Theory (Ronald)... 

RIchtsmeler S C, Parks E K, Liu K, Polo L G and Riley S J 1985 Gas phase reaction of Iron clusters with hydrogen. I. Kinetics J. Chem. Rhys. 82 3659... 

There are many ingenious and successful routes now developed for nanocry stalline syntliesis some rely on gas phase reactions followed by product dispersal into solvents [7, 9,13,14 and 15]. Otliers are adaptations of classic colloidal syntlieses [16,17,18 and 19]. Electrochemical and related template metliods can also be used to fomi nanostmctures, especially tliose witli anisotropic shapes [20, 21, 22 and 23]. Ratlier tlian outline all of tlie available metliods, this section will focus on two different techniques of nanocrystal syntliesis which together demonstrate tlie general strategies. 

MetallorganicMBE (MOMBE). tire solid source Knudsen cells in conventional MBE are replaced witli gaseous beams of organometallic precursors, directed toward a heated substrate in UHV. Compared to MOCVD, MOMBE eliminates gas phase reactions tliat may complicate tire deposition surface reactions, and provides lower growtli temperatures. 

These expressions are modified in the case of non-unimolecular gas phase reactions to... 

Compounds are transformed into each other by chemical reactions that can be run under a variety of conditions from gas-phase reactions in refineries that produce basic chemicals on a large scale, through parallel transformations of sets of compounds on well-plates in combinatorial chemistry, all the way to the transformation of a substrate by an enzyme in a biochemical pathway. This wide range of reaction conditions underlines the complicated task of imderstanding and predicting chemical reaction events. 

Fundamental enthalpies of gas-phase reactions such as proton affinities or gas-phase acidities can be correlated with the values of the Inductive and the polarizability effect. 

This is illustrated in Figure 17.1. The energies of the van der Waals complexes are a better description of the separated species for describing liquid-phase reactions. The energies of the products separated by large distances are generally more relevant to gas-phase reactions. 

POLYRATE can be used for computing reaction rates from either the output of electronic structure calculations or using an analytic potential energy surface. If an analytic potential energy surface is used, the user must create subroutines to evaluate the potential energy and its derivatives then relink the program. POLYRATE can be used for unimolecular gas-phase reactions, bimolecular gas-phase reactions, or the reaction of a gas-phase molecule or adsorbed molecule on a solid surface. 

With higher alkenes, three kinds of products, namely alkenyl acetates, allylic acetates and dioxygenated products are obtained[142]. The reaction of propylene gives two propenyl acetates (119 and 120) and allyl acetate (121) by the nucleophilic substitution and allylic oxidation. The chemoselective formation of allyl acetate takes place by the gas-phase reaction with the supported Pd(II) and Cu(II) catalyst. Allyl acetate (121) is produced commercially by this method[143]. Methallyl acetate (122) and 2-methylene-1,3-diacetoxypropane (123) are obtained in good yields by the gas-phase oxidation of isobutylene with the supported Pd catalyst[144]. 

Unsaturated nitriles are formed by the reaction of ethylene or propylene with Pd(CN)2[252]. The synthesis of unsaturated nitriles by a gas-phase reaction of alkenes. HCN, and oxygen was carried out by use of a Pd catalyst supported on active carbon. Acrylonitrile is formed from ethylene. Methacrylonitrile and crotononitrile are obtained from propylene[253]. Vinyl chloride is obtained in a high yield from ethylene and PdCl2 using highly polar solvents such as DMF. The reaction can be made catalytic by the use of chloranil[254]. 

Like the chlorination of methane chlorination of ethane is carried out on an industrial scale as a high temperature gas phase reaction... 

Increasing or decreasing the partial pressure of a gas is the same as increasing or decreasing its concentration. The effect on a reaction s equilibrium position can be analyzed as described in the preceding example for aqueous solutes. Since the concentration of a gas depends on its partial pressure, and not on the total pressure of the system, adding or removing an inert gas has no effect on the equilibrium position of a gas-phase reaction. 

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