Temperature first-order reversible reactions

Optimum temperature progression for a first order reversible reaction A o R... 

A stirred tank reactor with a pump-around heat exchanger is arranged as on the sketch. The first order reversible reaction, A B, is to be carried to 80% conversion. The reaction temperature is to be kept at the value at which equilibrium conversion would be 90%. Temperature drop across the exchanger is to 60 K. Reaction in the exchanger circuit is neglected. Operating data are shown on the sketch and other data are k = exp(17.2-5800/T), 1/hr... 

A first order reversible reaction, A B, is carried out in a plug flow reactor, starting with pure A. The specific rate and equilibrium constants are functions of temperature, k = A exp (-E/T)... 

A palladium-hydrogen-mordenite catalyst with a 10.8/1 silica/alumina mole ratio was evaluated for the hydroisomerization of cyclohexane. The rate of reaction followed a first-order, reversible reaction between cyclohexane and methylcyclopentane. The energy of activation for this reaction between 400° and 500°F was 35.5 it 2.4 kcal/mole. Cyclohexane isomerization rates decreased with increasing hydrogen and cyclohexane-plus-methylcyclopentane partial pressure. These effects are compatible with a dual-site adsorption model. The change of the model constants with temperature was qualitatively in agreement with the expected physical behavior for the constants. 

Initial variable studies had shown that gas-to-particle mass transfer and intra-particle diffusion were not rate limiting. The reaction mechanism was assumed to follow a first-order reversible reaction. After confirming this assumption, the effect of temperature and pressure on this reaction was investigated by determining the effect on the rate constant. 

If the integral in Eq. (9.6.2) can be worked out explicitly, then it may be possible to obtain an equation for the optimal temperature. For example, consider the first order reversible reaction A B, with rate law r = ka — taking place in an isothermal reactor whose feed is pure A. If the required fractional conversion is Y, then the feed concentration can be written the current concentrations are a = Gq — and 6 = f, and... 

Exercise 9.6.4. Show that if the inlet extent of reaction for a first order reversible reaction is not zero, then Eq. (9.6.5) for the optimal temperature must be modified to read... 

Example 8JJ>-I Optimal Temperature Trajectories for First Order Reversible Reactions... 

A first-order reversible reaction B is carried out in a batch reaction vessel at a constant temperature. The initial concentration of A is AO — 4 kmol/m. The reaction is monitored for 10 min by sampling the reactor fluid every 1 min and measuring the concentration of A. The concentration of A measured at intervals of 1 min is reported below ... 

OPTIMAL TEMPERATURE TRAJECTORIES FOR FIRST-ORDER REVERSIBLE REACTIONS... 

In our opinion, this book demonstrates clearly that the formalism of many-point particle densities based on the Kirkwood superposition approximation for decoupling the three-particle correlation functions is able to treat adequately all possible cases and reaction regimes studied in the book (including immobile/mobile reactants, correlated/random initial particle distributions, concentration decay/accumulation under permanent source, etc.). Results of most of analytical theories are checked by extensive computer simulations. (It should be reminded that many-particle effects under study were observed for the first time namely in computer simulations [22, 23].) Only few experimental evidences exist now for many-particle effects in bimolecular reactions, the two reliable examples are accumulation kinetics of immobile radiation defects at low temperatures in ionic solids (see [24] for experiments and [25] for their theoretical interpretation) and pseudo-first order reversible diffusion-controlled recombination of protons with excited dye molecules [26]. This is one of main reasons why we did not consider in detail some of very refined theories for the kinetics asymptotics as well as peculiarities of reactions on fractal structures ([27-29] and references therein). 

In order to explain the data of Aronowitz et al (12) and previous shock—tube and flame data, Westbrook and Dryer (12) proposed a detailed kinetic mechanism involving 26 chemical species and 84 elementary reactions. Calculations using tnis mechanism were able to accurately reproduce experimental results over a temperature range of 1000—2180 K, for fuel—air equivalence ratios between 0.05 and 3.0 and for pressures between 1 and 5 atmospheres. We have adapted this model to conditions in supercritical water and have used only the first 56 reversible reactions, omitting methyl radical recombinations and subsequent ethane oxidation reactions. These reactions were omitted since reactants in our system are extremely dilute and therefore methyl radical recombination rates, dependent on the methyl radical concentration squared, would be very low. This omission was justified for our model by computing concentrations of all species in the reaction system with the full model and computing all reaction rates. In addition, no ethane was detected in our reaction system and hence its inclusion in the reaction scheme is not warranted. We have made four major modifications to the rate constants for the elementary reactions as reported by Westbrook and Dryer (19) ... 

The optimal temperature policy in a batch reactor, for a first order irreversible reaction was formulated by Szepe and Levenspiel (1968). The optimal situation was found to be either operating at the maximum allowable temperature, or with a rising temperature policy, Chou el al. (1967) have discussed the problem of simple optimal control policies of isothermal tubular reactors with catalyst decay. They found that the optimal policy is to maintain a constant conversion assuming that the decay is dependent on temperature. Ogunye and Ray (1968) found that, for both reversible and irreversible reactions, the simple optimal policies for the maximization of a total yield of a reactor over a period of catalyst decay were not always optimal. The optimal policy can be mixed containing both constrained and unconstrained parts as well as being purely constrained. 

A multicell reaction system consists of a finite number of cells of the same volume and temperature and having the same reaction within them. Transport between the cells can be described by first order (formal) reactions. Show that, if the (common) mechanisms within the cells are of zero deficiency, and are weakly reversible, then the whole multicell reaction system is quasithermodynamic. 

Experimental data on the variation of equilibrium conversion with temperature T for a first-order reversible exothermic reaction are reported below ... 

Consider the reversible first order reaction A R. It is possible to determine the minimum reactor volume at the optimum temperature Tgp( that is required to obtain a fractional conversion X, if the feed is pure A with a volumetric flowrate of u. A material balance for a CESTR is... 

It is of substantial interest to note that, c.s the temperature of the reaction mixture is increased to —33-5°, ion 19 is converted quantitatively back to 18. At that temperature the first-order rate constant for the reversion has been calculated to be 8-0 x 10 sec , which corresponds to a free enthalpy barrier AG ) of 17-4 kcal/mol. 

We have examined the effects of concentration, temperature, solvent and added electrolyte on the kinetics of this structural interconversion. In all instances, the kinetics are well described by the rate law for a reversible first-order reaction [Equation 1] ... 

The initial concentrations of A and B in the feedstream are each 10 moles/m3. The remainder of the stream consists of inerts at a concentration of 30 moles/m3. The reaction is reversible and substantial amounts of all species exist at equilibrium under the pressure and temperature conditions employed. The forward reaction is first-order with respect to A and first-order with respect to B. At 120 °C the rate constant for the forward reaction is 1.4 m3/ mole-ksec. The reverse reaction is first-order in C, first-order in D, and inverse first-order in B. The rate constant for the reverse reaction is 0.6 ksec-1. 

P4.11.01. OPTIMUM TEMPERATURE PROFILE OF REVERSIBLE FIRST AND SECOND ORDER REACTIONS. 

Palmer et al have studied the pyrolysis of C302 at temperatures in the range 900-1100 °K by following the rate of carbon deposition from a He stream containing 0.1-0.5 mole % C302. The reaction was first order in C302 and was inhibited by the addition of CO a substance other than C302 or CO was responsible for carbon deposition at the wall. Reaction (1) and its reverse... 

With the system of Example 9.2 and starting with an R-free solution, kinetic experiments in a batch reactor give 58.1% conversion in 1 min at 65°C, 60% conversion in 10 min at 25°C. Assuming reversible first-order kinetics, find the rate expression for this reaction and prepare the conversion-temperature chart with reaction rate as parameter. 

Surface species in the mechanism are denoted (s) in the species name. In this reaction mechanism, only reaction 7 was written as a reversible reaction all of the rest were specified as irreversible. Formally, reactions 12 and 14 should be third order in the concentration of Pdfs) and O(s), respectively. However, the reaction order has been overridden to make each one first-order with respect to the surface species. In some instances, reactions have been specified with sticking coefficients, such as reactions 1, 3, 11, and 13. The other reactions use the three-parameter modified Arrhenius form to express the temperature-dependent rate constant. 

The isomerizations of n-butenes and n-pentenes over a purified Na-Y-zeolite are first-order reactions in conversion as well as time. Arrhenius plots for the absolute values of the rate constants are linear (Figure 2). Similar plots for the ratio of rate constants (Figure 1), however, are linear at low temperatures but in all cases except one became curved at higher temperatures. This problem has been investigated before (4), and it was concluded that there were no diffusion limitations involved. The curvature could be the result of redistribution of the Ca2+ ions between the Si and Sn positions, or it could be caused by an increase in the number of de-cationated sites by hydrolysis (6). In any case the process appears to be reversible, and it is affected by the nature of the olefin involved. In view of this, the following discussion concerning the mechanism is limited to the low temperature region where the behavior is completely consistent with the Arrhenius law. 

Mutarotation has been shown to be a first-order reaction, the velocity constant being independent of reaction time and concentration of reactants. The rate of mutarotation increases 2.8 times with a 10°C rise in temperature. By applying the law of mass action, equations have been developed to measure the rate of the reversible reaction between the a and (3 forms of lactose. If a dilute lactose solution at constant temperature contain a moles of a and b moles of /3, then the amount of (3 formed (x) per unit of time is... 

The insertion of CO into metal-carbon a bonds has been reviewed.585-590 Carbonylation of alkyl platinum(II) complexes usually requires elevated temperatures, although at higher temperatures the reaction is reversible (equation 211).591 With PtMe2(dppe) insertion occurs into only one of the Pt—Me bonds. For complexes PtX(Ar)L2, carbonylation follows pseudo first-order kinetics. Rates are decreased by addition of L to a maximum value where the carbonylation rate is independent of L. The pathway involves formation of a five-coordinate intermediate PtX(Ar)(CO)L2, followed by dissociation to form PtX(Ar)(CO)L. The migratory step to yield PtX(COAr)L is unaffected by added L. This pathway is outlined in Scheme 6.502... 

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