Pressure reaction rate expressions

Fig. 7 Dependence of IR band intensities on H2 partial pressure during ethene hydrogenation catalyzed by Ir4/y-Al203 at 288 K and 760 Torr (40 Torr C2H4, 50-300 Torr H2, and the balance He). The bands at 2990 (diamonds) and 2981 cnr (squares) were chosen to represent di-cr-bonded ethene and that at 1635 cnr (circles) to represent water on the y-AbOs support. These IR bands were chosen as the best ones to minimize error caused by overlap with other bands. The triangles represent the reaction rate expressed as a turnover frequency (TOF), the rate of reaction in units of molecules of ethene converted per Ir atom per second. The data indicate a correlation of the band intensities with the TOF, consistent with the suggestion that the ligands represented by the bands are reaction intermediates (but the data are not sufficient to identify the reaction intermediates) [39]...

As the system pressure is decreased at constant temperature, the time between collisions will increase, thereby providing greater opportunity for unimolecular decomposition to occur. Consequently, one expects the reaction rate expression to shift from first-order to second-order at low pressures. Experimental observations of this transition and other evidence support Linde-mann s theory. It provides a satisfactory qualitative interpretation of unimolecular reactions, but it is not completely satisfactory from a... 

Studies of the effect of pressure on initial rates limit the possible Hougen-Watson rate expressions to certain classes. Subsequent studies using nonstoichiometric feeds and inerts and product species in the feed mixture further serve to determine the exact form of the reaction rate expression. 

It is particularly convenient to choose the reference conditions at which the volumetric flow rate is measured as the temperature and pressure prevailing at the reactor inlet, because this choice leads to a convenient physical interpretation of the parameters and CA0 and, in many cases, one finds that the latter quantity cancels a similar term appearing in the reaction rate expression. Unless otherwise specified, this choice of reference conditions is used throughout the remainder of this text. For constant density systems and this choice of reference conditions, the space time t then becomes numerically equal to the average residence time of the fluid in the reactor. 

The CO oxidation reaction occurs rapidly at room temperature and below. As an example, on a Au(lll) surface at 250 K with onear unity exposed to a constant CO pressure of Pco = 2 x 10 Torr, the reaction rate expressed as turn-over frequency (TOF [molecules CO2 (Au atom s)" )/ is approximately 2.5 x 10-3 immediately after the reaction has been initiated and then declines at a relatively constant rate reaching a value of 3 x 10" after the reaction has proceeded approximately 800 seconds. Reaction order... 

By choosing a suitable solvent and suitable conditions (concentrations, temperatures, and pressures), the solvent, the substrate, the product, and the hydrogen can form a single phase. When such a single phase is fed to a fixed-bed reactor, extremely high reaction rates have been achieved for very large molecules [28 - 30]. These reaction rates, expressed on a molar basis, are the same as those achieved in gas-phase reactors for small molecules [30]. 

The situation when the gas is isotopically scrambled, however, is very different and indeed the experimentally observed measured quantity is also very different. When the gas is isotopically scrambled, one does not measure these specific ratios of rate constants. Instead, a statistical steady-state, such as Q -F OO QOO QO + O and in the above example O + QQ OQQ OQ + Q, exists at all energies, and now the energy distribution of the vibrationally excited intermediates is that which is dictated by the steady-state equations for the above reactions, and not by that of a vibrationally hot intermediate formed solely via one channel. Under such conditions all energies of the intermediate are statistically accessible, if not from one side of the reaction intermediate then from the other. Phrased differently, the isotopic composition of the collisionally stabilized product Q3 or QO2 or will typically differ from that of the vibrationally excited species Q or QO2, since the intrinsic lifetime of the latter is isotope-dependent, as discussed in [15]. The usual RRKM-type pressure-dependent rate expression and conventional isotope effect results, modified by the nonstatistical effect discussed earlier [15]. 

P4C-1 In the article desaibing the liquid reaction of isoprene and maleic anhydride under pressure [AIChE J., 16(5), 766 (1970)], the authors show the reaction rate to be greatly accelerated by the application of pressure. For an equimolar feed they wri te the second-order reaction rate expression in terms of the mole fraction y. 

On the far right of the numerator we have two parameters that may be difficult to obtain independently. They are the adsorption equilibrium constant for B and the surface equilibrium constant for the reaction Asurf Bsurf- Our goal is to clear these by reexpressing them in terms of something that is unchanging. After all both of these may be strong functions of the catalyst structure and composition. The overall reaction A B is, however, one which is fixed at any temperature and pressure by the overall equilibrium constant. This is independent of the catalyst. Therefore we want to use this in the reaction rate expression. Here is how we do it ... 

Total pressure analysis of the initial reactant product conversion rate can distinguish between these two mechanisms, provided that rates of conversion can be measured at sufficiently high pressure. The rate expressions given by equations (14-188) and (14-191) have units of mol/area-time for surface-catalyzed chemical reactions. However, rate data obtained from heterogeneous catalytic reactors are typically reported in units of mol/time per mass of catalyst. One obtains these units simply by multiplying the kinetic rate law (i.e., mol/area-time) by the internal surface area per mass of catalyst (i.e., S ), which is usually on the order of 100 m /g. If the feed stream to a packed catalytic reactor contains pure ethanol, then the initial reactant product conversion rate for the four-step mechanism is... 

Pressure measurements can be accomplished by a number of different types of devices without disturbing the system being observed. Another type of reaction system that can be monitored by pressure measurements is one in which one of the products can be quantitatively removed by a solid or liquid reagent that does not otherwise affect the reaction. For example, acids formed by reactions in the gas phase can be removed by absorption in basic solutions. From knowledge of the reaction stoichiometry and measurements of the total pressure as a function of time, one can determine the corresponding extents of reaction and partial pressures or concentrations of the various reactant and product species. An example of how pressure measurements can be used to determine a reaction rate expression is provided in Illustration 3.3. 

Homogeneous gas and catalyst in the bed is a continuum so that temperature, pressure, and concentrations do not distinguish whether they are inside the catalyst or in the gas phase. The kinetic rate expressions are so-called effective or pellet kinetic rates, where the catalyst effectiveness factors have been included in the reaction rate expressions. 

Solution. Note that this is a variable volume reactor since it operates at a constant temperature and pressure. The rate expression for the reaction, r, is... 

The question to be answered is what can be adjusted, other than tenderature, that will affect the reaction rate and/or the conversion. In the reaction rate expression, the primary temperature effect is in the Arrhenius expression. For gas-phase reactions, assuming ideal gas behavior, the concentrations c,- = P/i r. The increase in tenperature discussed in Exanple 19.1 will actually reduce the concentrations however, the exponential increase in the reaction rate constant is the primary effect. It is also observed that increasing the pressure increases the concentration, thereby increasing the reaction rate. There is an additional effect. This can be seen from the equation of a plug flow reactor. 

From a typical reaction rate expression such as Equation f20.91. as the pressure increases, so do the concentration and the reaction rate. Therefore, the same trends are observed as with temperature. However, the quantitative effect is not as great, because the concentration dependence on pressure is not exponential. 

It is always preferable to use models which have a stronger content of our knowledge about the physics and chemistry of the process. We normally do that by breaking up M into a kinetic model M that relates local reaction rates to local concentrations, temperature, pressure and catalyst conditions, and a reactor model that quantitatively describes the transport processes and heat and mass balances in the reactor. While in many cases we have the tools to derive an approximation for M. from first principles we can very seldom do that for M. Aside from a few cases of gaseous reactions, we cannot predict ML. For the reactor modeling we have to accept the fact that reaction rate expressions are empirical correlations. What the study of reaction mechanisms has contributed to us is some a priori information as to what form M might have. 

Low temperatures strongly favor the formation of nitrogen dioxide. Below 150°C equiUbrium is almost totally in favor of NO2 formation. This is a slow reaction, but the rate constant for NO2 formation rapidly increases with reductions in temperature. Process temperatures are typically low enough to neglect the reverse reaction and determine changes in NO partial pressure by the rate expression (40—42) (eq. 13). The rate of reaction, and therefore the... 

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