Hougen-Watson equation

Of particular value in kinetic studies are residual plots using the linearized form of the Hougen-Watson equation. For the model of Eq. (18), for example, we obtain... 

The particular cases of the K.P. are the well-known Langmuir-dependence that is completely corresponding to the linear approximation of K.P. and, obviously, the classical mass-action-law equations. Also it is possible to show that some semi-empirical equations, for example Hougen-Watson equations are the particular cases of the K.P. 

The pre-exponentials and the apparent activation energies corresponding to the rate coefficients ki, k2 and ks had to be estimated from the experimental data sets from fovir batch reactor and ten CSTR experiments. The initial concentration of reactant A and the temperature were varied. The kinetic rate equations of the catalytic reactions can be described by using the following so-called Langmuir-Hinshelwood Hougen-Watson equations. 

This equation, the Langmuir-Hinshelwood equation, was first proposed by Langmuir and Hinshelwood in the 1920-30s for solid-catalyzed gas-phase reactions under the assumption that adsorption and desorption rates are high compared with rates of other chemical transformations on the catalyst surface. In this model, adsorption-desorption steps are considered to be at equilibrium. Later, Hougen, and Watson proposed a similar equation, the Hougen-Watson equation, for a reversible catalytic reaction, again under the assumption that the adsorption-desorption steps are at equilibrium. 

Notice that the rate equations for the steps on the acid sites do not differ in structure from that dealt with in Chapter 1. They do not have the shape of the Hougen-Watson equations dealt with in the present Chapter 2 because the rate equations are written in terms of carbenium ions linked to the catalyst sites, so as to take advantage of the single event approach. As shown here they are not explicitly related to the fluid phase around the site, be it gaseous or liquid. 

The analyses developed in this section are readily extended to reactions with different stoichiometries. Regardless of whether an adsorption or a desorption process is rate limiting, the resulting rate expressions may be written in the typical Hougen-Watson fashion represented by equation 6.3.30. A comprehensive summary of such relations has been developed by Yang... 

I. Derive equations relating the initial reaction rate (7 0) to the total pressure (71) for each of the above cases when the sulfur dioxide and oxygen are initially present in equimolar amounts. Do this using the Hougen-Watson mechanistic models. Show your derivations. 

Hydrogenation of octenes occurs with surface reaction controlling (Hougen Watson, Chemical Process Principles, p 943, 1947). The rate equation is... 

From a consideration of either Eqs. (113) or (114) (K3), it is evident that a saddle point is predicted from the fitted rate equation. This could eliminate from consideration any kinetic models not capable of exhibiting such a saddle point, such as the generalized power function model of Eq. (1) and the several Hougen-Watson models so denoted in Table XVI. 

Such rate expressions are often termed Langmuir-Hinshelwood-Hougen-Watson (LHHW) equations and are widely used in chemical engineering [see Froment and BischofT (79)]. The usual procedure is to postulate plausible mechanisms without considering cycles, as in Example 1. In such cases it may be desirable to develop the complete list of possible direct mechanisms even if further considerations can rule out some as being unlikely. The following example illustrates a typical case. 

In general, the use of Langmuir-Hinshelwood-Hougen-Watson (LHHW)-type of rate equation for representing the hydrogenation kinetics of industrial feedstocks is complicated, and there are too many coefficients that are difficult to determine. Therefore, simple power law models have been used by most researchers to fit kinetic data and to obtain kinetic parameters. 

Further investigations showed significant disadvantages of the above assumptions. Nevertheless, Hinshelwood, Schwab, Hougen, Watson and others derived equations which adequately described a particular kinetic experiment within a certain range of parameters. 

Steps 3-5 are strictly chemical and consecutive to each other Hougen-Watson-Langmuir-Hinshelwood rate equations describing the rate of the purely chemical phenomenon consisting of steps (3)-(5) have been derived in the chapter on the... 

Although the key equations are transcendental, they are readily solvable with hand calculators, particularly those with rootsolving provisions. Several charts to ease the solutions before the age of calculators have been devised M.B. Powley, Can. J. Chem. Eng., 241-245 (Dec. 1958) C.E. Lapple, reproduced in Perry s Chemical Engineers Handbook, McGraw-Hill, New York, 1973, p. 5.27 O. Levenspiel, reproduced in Perry s Chemical Engineers Handbook, 7th ed., p. 6-24 Hougen, Watson, and Ragatz, Thermodynamics, Wiley, New York, 1959, pp. 710-711. 

Steps 3-5 are strictly chemical and consecutive to each other Hougen-Watson-Langmuir-Hinshelwood rate equations describing the rate of the purely chemical phenomenon consisting of steps 3-5 have been derived in Chapter 3 on the kinetics of catalysed reactions. In the transport-limited situation the supply of reactant and/or the removal of reaction product will not be sufficiently fast to keep pace with the potential intrinsic rate, and the concentrations of A and B inside the pores will be different from the corresponding concentrations in the bulk of the fluid phase. 

For nonideal gases this equation must be modified by the introduction of a compressibility factor Zj to be determined from the available tables. Consult, for example, Hougen, Watson, and Ragatz or Hall and Ibele among many sources (see references to Chap. 3). In this case... 

A higher form of interpretation of the effect of solvents on the rate of heterogeneously catalyzed reactions was represented by the Langmuir-Hinshelwood kinetics (7), in the form published by Hougen and Watson (2), where the effect of the solvent on the reaction course was characterized by the adsorption term in the kinetic equation. In catalytic hydrogenations in the liquid state kinetic equations of the Hougen-Watson type very frequently degrade to equations of pseudo-zero order with respect to the concentration of the substrate (the catalyst surface is saturated with the substrate), so that such an interpretation is not possible. At the same time, of course, also in these cases the solvent may considerably affect the reaction. As is shown below, this influence is very adequately described by relations of the LFER type. 

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