First-order reactions partial pressure

Id) What would be the volume efficiency for two CSTRs in series with the sum of the two CSTR volumes being the same as the PFR volume P5-24u The irreversible first-order (wrt partial pressure of A) gas-phase reaction... 

When a unimolecular reaction occurs with an initial product partial pressure of the reactant A, to yield an amount of die product, jc, the first-order reaction rate equation reads... 

Rate = kPx for a first-order reaction of a gas X. What are the units for the rate constants when partial pressures are expressed in torr and time is expressed in seconds for (a) zero-order reactions (b) first-order reactions (c) second-order reactions ... 

Pyruvic acid is an intermediate in the fermentation of grains. During fermentation the enzyme pyruvate carboxylase causes the pyruvate ion to release carbon dioxide. In one experiment a 200.-mL aqueous solution of the pyruvate in a sealed, rigid 500.-mL flask at 293 K had an initial concentration of 3.23 mmol-L -l. Because the concentration of the enzyme was kept constant, the reaction was pseudo-first order in pyruvate ion. The elimination of CU2 by the reaction was monitored by measuring the partial pressure of the C02 gas. The pressure of the gas was found to rise from zero to 100. Pa in 522 s. What is the rate constant of the pseudo-first order reaction ... 

In the above example, the concentration of copper remains constant (pure copper) so that the reaction rate could be expected to depend on the partial pressure of oxygen in the atmosphere ( Po2)- This would be a first order reaction, but experimental determination of the dependence of the rate on Po2 shows that the rate is approximately proportional to Pq7 implying a fractional order. 

The decomposition of ammonia to the elements is a first-order reaction with a half-life of 200 s at a certain temperature. How long will it take the partial pressure of ammonia to decrease from 0.100 atm to 0.00625 atm ... 

Two important ways in which heterogeneously catalyzed reactions differ from homogeneous counterparts are the definition of the rate constant k and the form of its dependence on temperature T. The heterogeneous rate equation relates the rate of decline of the concentration (or partial pressure) c of a reactant to the fraction / of the catalytic surface area that it covers when adsorbed. Thus, for a first-order reaction,... 

We will consider a dispersed plug-flow reactor in which a homogeneous irreversible first order reaction takes place, the rate equation being 2ft = k, C. The reaction is assumed to be confined to the reaction vessel itself, i.e. it does not occur in the feed and outlet pipes. The temperature, pressure and density of the reaction mixture will be considered uniform throughout. We will also assume that the flow is steady and that sufficient time has elapsed for conditions in the reactor to have reached a steady state. This means that in the general equation for the dispersed plug-flow model (equation 2.13) there is no change in concentration with time i.e. dC/dt = 0. The equation then becomes an ordinary rather than a partial differential equation and, for a reaction of the first order ... 

In order to determine whether a substance will condense or not, one first determines the partial pressure without assuming condensation. If this partial pressure is greater than the vapor pressure, then in an equilibrium situation condensation must have taken place. Because most equilibrium reactions have their K p f s referenced to the elements in the standard states as, for example, carbon cftscussed above, it is difficult to determine the partial pressure of the carbon since the K Pj f s, when carbon is not condensed are not readily available. Say, then, one has carbon as a product and he wishes to determine the physical state. First he calculates the number of moles of carbon as condensed. Then, taking the same number of moles as gaseous, he determines the hypothetical partial pressure these number of moles of gas would exert. This partial pressure must be greater than the vapor pressure for the initial assumption that condensed phase is present to be... 

Such nuances notwithstanding, the symptom of a network with parallel first-order reactions to all three products emerges quite clearly from this single experiment. Even so, however, the question remains open where exactly the reaction path branches and how the rate depends on the partial pressures of CO and H2. We shall return to this interesting type of reaction in later examples (Examples 5.3, 6.5, 7.5, 11.2, 12.1, and 12.2). 

Integration of this equation results in a first order reaction expression in terms of the hydrogen-free mole fraction of MCP ( m) and the corresponding equilibrium value (Ye), rg the molar density of reactor gases, M the molecular weight of MCP, p the partial pressure of CH, P the total pressure, and W the weight of feed per hour per weight of catalyst ... 

Data obtained in fixed-bed reactors and in continuous high-velocity coil-t ype reactors (fluid catalyst) indicate that the catalytic cracking of gas oils is approximately a first-order reaction, but that the apparent order approaches two because of the effect of nonhomogeneity of the feed and because of the increasing dilution of reactant with cracked products as conversion increases at constant total pressure (73). The extent of reaction is determined by the intrinsic activity of the catalyst surface, reaction time at the surface, temperature, and susceptibility of the feed to cracking. Superficial contact time in the reactor is of little consequence. The effective time of reaction is the time spent by oil on the active surface of the catalyst. For a given extent of adsorption, the reaction time should be inversely proportional to weight space velocity and should also be a function of the reactant partial pressure. Results of experiments with... 

Use of Halide Ions to Improve Selectivity. Earlier work has claimed that enhanced selectivities for alkene oxidation can be achieved by the inclusion of electronegative elements such as S, Se, or halogens. This has been reviewed elsewhere. " More recent work has demonstrated substantial improvements in selectivity for propene (25—70%) and isobutene (35—80%) oxidation when either chloride or bromide is present. Both elements are added to the catalyst in the form of trace levels of organo-halide in the process gas stream. The selectivity increase is the result of a decrease in the rate of complete oxidation rather than an increase in the partial oxidation rate. Since the reaction is first order in oxygen pressure and zero order with respect to alkene in the presence and absence of halide, the reaction mechanism is probably similar in both cases. In the light of Anshits recent work, the effect of the halide is presumably to reduce the relative number and/or reactivity of surface lattice oxygen species and thus reduce the amount of irreversibly adsorbed alkene. 

Since chemical adsorption is an exothermic process, the surface coverage decreases with an increase in temperature. The rate of a heterogeneous reaction is proportional to the coverage. As a result the reaction can be treated as a first-order reaction for weakly adsorbed gaseous species. For the strongly adsorbed cases the reaction is the zeroth order because the reaction rate is independent of the partial pressure. For the intermediate case the reaction rate may be a fraction. 

Exercise 6.7.2. A first order reaction A —> B is taking place in spheres of radius in. X is a gas with partial pressure of about I atm and at room temperature outside the pellet. The observed reaction rate is about 10" mole/sec per unit volume of packed reactor. Would you consider diffusion to be an important limiting factor ... 

It has been shown above, that k2 > > kj, when the partial pressure of H2S is normal". In this situation, the importance of the sequential scheme is limited to the top of the reactor, and the HDV reaction for the entire plug flow reactor can therefore be approximated by an irreversible first order reaction with a rate constant for HDV equal to klH (eq 5). 

The model for an enzyme-catalyzed reaction is similar to that for a first-order reaction of a gaseous molecule adsorbed on a solid catalyst, which has a certain number of sites (uniformly active) per unit mass. The surface reaction goes from approximately first order at low partial pressure, when a small fraction of sites are covered, to nearly zero order at high partial pressure and high coverage. Derivations and examples for more complex surface reactions are given in Chapter 2. 

Kinetic data on olefin polymerization by polymer-immobilized zirconocene are scarce. It is generally accepted that homogeneous metallocene catalysts contain uniform active sites however, if they are immobilized on a polymer support, the MWD polymer production becomes broader compared with a homogeneous catalyst [103]. Kinetic analysis of gas-phase ethylene polymerization catalyzed by (CH3)2[Ind]2ZrCl2 bound at a hydroxylated copolymer of styrene with divinylbenzene and previously activated with MAO (0.17 wt.% Zr) has been carried out [104]. The influence of temperature (333 to 353 K), ethylene partial pressure (2 to 6 atm) and MAO level (molar ratio of MAO to zirconium from 2600 to 10,700) were studied. The activity of the catalyst in the gas-phase process changed from 5 to 32 kg PE (g of Zr atm h)It is possible that there are two types of active site. They are stable to temperature and deactivated by the same mechanism. A first-order reaction takes place. The propagation rate constants of two active sites show a similar dependence on temperature. 

A linear relation ln(p/po) vs. x for the change in PH3 partial pressures in flow systems (x = residence time in the hot zone) indicated that decomposition was first order in PH3 [17]. Most published activation energies, however, simply rely on the assumption of a first-order reaction. The following activation energies were measured for the individual surfaces quartz 150 kJ/mol above 670 K [27], 153 kJ/mol above 850 K [14], 245 kJ/mol [18], 18 kJ/mol below 1070 K and 290 kJ/mol above 1170 K [8] glass 185 kJ/mol [28] silicon 231 kJ/mol [28] InP 150 kJ/mol [17], ca. 50 kJ/mol at lower temperatures and less than 21 kJ/mol at higher temperatures [9] (see Fig. 10). The scatter in these data illustrates the unsettled debate on the mechanism of surface-catalyzed PH3 decomposition. 

With low naphthalene partial pressure, oxidation follows first-order reaction kinetics, while with relatively high partial pressures, as used in industrial applications, the reaction becomes zero-order. 

For gas-phase reactions, we can replace the concentration terms in Eqnations 14.5 and 14.6 with the partial pressures of the gaseous reactant. Consider the first-order reaction... 

The simultaneous absorption of two gases that react with the solvent at different rates has been studied by Ouwerkerk. The specific system which he selected for analysis was the selective absorption of HjS in the presence of CO2 into amine solutions. This operation is a feature of several commercially important gas purification processes. Bench scale experiments were conducted to collect the necessary pi sico-chemical data. An absorption rate equation was developed for H2S based on the assumption of instantaneous reaction. For CO2 it was found that the rate of absorption into diisopropanolamine (DIPA) solution at low CO2 partial pressures can best be correlated on the l is of a fast pseudo-first-order reaction. A computer program was developed which took into account the competition between H2S and CC>2 when absorbed simultaneously, and the computer predictions were verified by experiments in a pilot scale absorber. Finally, the methodology was employed successfully to design a large commercial plant absorber. 

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