Initial rates total pressure dependence

Hougen and Watson [42] suggested analysis of the rate dependency on the partial reactant or the total pressure at low conversion levels, where the product concentrations can be neglected and so-called initial rates are measured. Depending on the assumed rate determining step in the kinetic model a different pressure dependency is predicted, as exemplified in Fig. 13. This allows a direct discrimmination between possible rate expressions of different models. 

If the overall gas-phase chemical reaction isA- -B-o-C- -D, then the total pressure dependence of the initial reactant product conversion rate is exactly the same for the following two mechanisms ... 

Hence, the method of initial rates cannot distinguish between these two mechanisms to determine whether surface coverage by an intermediate reactive species is important. However, the total pressure dependence of initial rates can distinguish between either of the mechanisms outlined above and the following scenario ... 

When the six-step mechanism given by (14-71) provides a reasonable description of the chemical kinetics and the second of two possible dual-site reactions on the catalytic surface is rate limiting, the total pressure dependence of the initial... 

In Section 14-8, we illustrate how a differential plug-flow mass balance near the inlet of a tubular reactor packed with porous catalytic pellets provides experimental data for quantitative evaluation of (i Hougen-watsonimitiai via equation (14-199). Hence, the data pairs include the total pressure dependence of this initial conversion rate. As illustrated by (14-96), a second-order polynomial model is appropriate. Hence,... 

If the feed stream to a tubular reactor packed with porous catalysts is stoichiometric in reactants A2 and B, then the total pressure dependence of the initial rate of conversion of reactants to products is... 

This initial rate approaches zero at both low and high total pressure. Quantitative analysis of the total pressure dependence of this initial rate is achieved via algebraic manipulation of (14-109), as follows ... 

The initial reactant product conversion rate should increase at higher temperature because kinetic rate constants for elementary steps, particularly the desorption of gas D, increase at higher temperature. In summary, there is no total pressure dependence of the initial reactant product conversion rate when (1) A -h B C -h D, (2) single-site adsorption is appropriate for each component, and (3) desorption of one of the products controls the Hougen-Watson kinetic rate law. 

Consider the six-step mechanism described by (14-138) in which dualsite adsorption of reactant A2 is rate controUing. A stoichiometric feed of reactants A2 and B is present at the inlet to a packed catalytic tubular reactor. Perform linear least-squares analysis of the total pressure dependence of the initial rate of conversion of reactants to products. Your solution to this problem should contain five or six answers. 

This reaction occurs in a packed catalytic tubular reactor and data have been obtained near the inlet to characterize the total pressure dependence of the initial rate, when a stoichiometric feed (i.e., 1 2) of reactants A2 and B is present. At constant temperature T, experiments were performed such that all total pressures ptotai exist in a narrow range near the critical point of this ternary mixture. Hence, forward exhibits a significant dependence on total pressure. Employ a linear least-squares procedure and analyze the experimental data (i.e., 381hw, initial vs. ptotai) which have been measured. Hint Identify the dependent (y) and independent (x) variables, and the slope (aO and intercept (ao) for the following polynomial model y = ao+ Uix. 

Later, Yang and Hougen [33] proposed to discriminate on the basis of the total pressure dependence of the initial rate. Initial rates are measured, for example, with a feed consisting of only A when no products have yet been formed (i.e., when = 0). Nowadays this method is only one of the so-called... 

Total pressure dependence of the initial rate should be in agreement with (1) and (2). 

Figure 2.4 Total pressure dependence of initial rates for the reaction A— B + C. (Source Froment [17]. Reproduced with permission of John Wiley Sons.)...

There are also other ways of checking the consistency of L H kinetics. As Yang and Hougen (1950) first proposed, various rate-controlling steps can be discriminated on the basis of the total pressure dependence of the initial rate. Experimental kinetic data can also be used in a variety of ways (Kittrell and Mezaki 1967) to check the proposed mechanism and controlling step. Some of the rate constants associated with individual steps can be checked by independent experiments or compared with theoretical values. For example, adsorption constants determined by correlation of kinetic data can be compared with those constants obtained directly from adsorption experiments (Kabel and Johanson 1962). The magnitude of rate constant can also be compared with the theoretical value obtained from transition state theory (Sinfelt et al. 1960). Spectroscopic studies can lead to information on individual steps. 

Here Wx represents the initial rate of heat production for some process (or processes) that is dependent on the partial pressure of the water vapor in the calorimetric system and gives a positive contribution to the initial rate of heat production by wet oxidation (unlike the steam distillation process envisaged for wet oxidation at 225°C, which aids in the retardation of the initial rate of heat production). If this relationship were valid, then a plot of the logarithm of the initial rate Wx against the logarithm of the ratio of the partial pressure of water vapor in the system to the total pressure in the system would be linear. However, as demonstrated by Figure 3, no such simple relationship is found. 

Effect of Concentration and CO Pressures on the Ruthenium Carbonyl-Trimethylamine WGSR System. As shown in Figure 1, the RU3(CO) 2/NMe3 WGSR system demonstrates a nearly first-order rate dependence on CO pressure at 0.5 mM Ru3(CO) 2 concentration. (Throughout this discussion, the total ruthenium carbonyl concentration is expressed as moles Ru3(00) 2 added per liter of solution this should not be construed to be the actual solution concentration of the trimer under operating conditions.) Here the initial rates of H2 production are 14.6 mmol /hr at 415 psi CO and 46.0 mmol /hr at 1200 psi. Thus, within experimental uncertainty, a threefold increase in CO pressure leads to a threefold increase in rate. 

An often useful discriminant is initial rate data as a function of total pressure. The equations are simpler because terms for the products are absent. Depending on the results of initial rate analysis, the number of complete equations that may need to be investigated could be narrowed. For instance it may be determined initially if a reactant is adsorbed with or without dissociation. Since the number of possible mechanisms sometimes can be 15 or 20 or more, every bit of preliminary assistance is desirable. Typical initial... 

Show how the initial rates depend on the total pressure. 

Fig. 1. Initial rate dependence on total pressure for S02 oxidation (M3).

The examination of the initial rate dependence upon total pressure is by far the most common means of examining the various classes of rival models in terms of their ability to fit the observed data. Yang and Hougen (Yl) have presented a classification of a multitude of possible models in terms of the dependence of the predicted rate upon total pressure. Generally speaking, the... 

In every case in which a kinetic model is selected to represent adequately a reaction, the rate surface predicted by the model must be compared to the surface observed in the data. In the methods discussed in Section II, only one section through the entire rate surface was examined for example, the dependence of initial rate on total pressure could be investigated when in fact the total rate surface constituted the dependence of rate on several component partial pressures and temperature. The misleading results obtain-... 

Figure 2. Dependence of the extrapolated initial rate of benzene ethylation on aromatic olefin mole ratio at 57S°K and one atmosphere total pressure...

The temporal resolution of both methods is limited by the risetime of the IR detectors and preamplifiers, rather than the delay generators (for CS work) or transient recorders (SS) used to acquire the data, and is typically a few hundred nanoseconds. For experiments at low total pressure the time between gas-kinetic collisions is considerably longer, for example, approximately 8 /is for self-collisions of HF at lOmTorr. Nascent rotational and vibrational distributions of excited fragments following photodissociation can thus be obtained from spectra taken at several microseconds delay, subject to adequate SNR at the low pressures used. For products of chemical reactions, the risetime of the IR emission will depend upon the rate constant, and even for a reaction that proceeds at the gas-kinetic rate the intensity may not reach its maximum for tens of microseconds. Although the products may only have suffered one or two collisions, and the vibrational distribution is still the initial one, rotational distributions may be partially relaxed. 

Two years later Thompson and Hinshelwood (40) after studying the kinetics of the oxidation of ethylene in silica vessels at temperatures between 400° and 500° and finding that the rate is affected by the total pressure approximately in a reaction of the third order, the effects depending very much more on the partial pressure of the ethvlenes than on that of oxygen, suggested as a via media that while there is no doubt that Bone s interpretation of the course of the oxidation as a process of successive hydroxylations is essentially correct... the first stage in the reaction is the formation of an unstable peroxide if this reacts with more oxygen the chain ends but if it reacts with ethylene, unstable hydroxylated molecules are formed which continues the chain. It should be noted, however, that they adduced no experimental proof of the actual initial formation of the assumed peroxide. 

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