Second-order reactions mean conversion

Example 1.6 Apply Equation (1.54) to calculate the mean residence time needed to achieve 90% conversion in a CSTR for (a) a first-order reaction, (b) a second-order reaction of the type A - - B — Products. The rate constant... 

Note that the rates of product formation and reactant conversion indeed have the dimensions of mol per unit of time, and that these rates are proportional to the number of sites, or, in fact, the amount of catalyst present in the reactor. Also, in the case of a second order reaction, e.g. betv een adsorbed species A and B, we write the rate in the form r = Nk0j 0 by applying the mean-field approximation. Here the rate is proportional to both the total number of sites on the surface and the probability of finding a species A adjacent to a species B on the surface, the latter being proportional to the coverages of A and B. In the mean-field approximation A and B are distributed randomly over the N available sites this only tends to be valid when the adsorbents repel each other. Thus the rate is not r= k(N0/ )(N02,) since the reactants need to be on adjacent sites. Another important consideration is that we want the rate to be linearly proportional to the amount of catalyst in the reactor, in accordance with r = Nk0A0B for a second order surface reaction. 

A second order reaction has kC0 = 0.0303. Obtain values of the ratios of fractional conversions along a stream line to the mean values over the cross section as a function of mean residence time over the range of 8 = r/R. At particular values of 0, Eq (3) of problem P4.08.01 can be written... 

Apply Equation 1.53 to calculate the mean residence time needed to achieve 90% conversion in a CSTR for (a) a first-order reaction and (h) a second-order reaction of the type A -I- B - products. The rate constant for a first-order reaction has units of reciprocal time. For the current example, assume k = 0.1 s. The rate constant for a second-order reaction has units of reciprocal time and reciprocal concentration. It is common practice to multiply a second-order rate constant by the initial or inlet concentration of the stoichiometrically limiting coefficient. This gives a rate constant with units of reciprocal time. For the second-order reaction suppose ajnk = 0.1 s . ... 

For the second-order reaction, Equation 7.101 show s that varies with the molar flow, which means and r vary along the length of the reactor as Na decreases. We are asked to estimate the catalyst mass needed to achieve a conversion of A equal to 7S%. So for this particular example, 4> decreases from 6.49 to 3.24. As shown in Figure 7,9, we can approximate the effectiveness factor for the second-order reaction using the analytical result for the first-order reaction, Equation 7.42,... 

An endothermic irreversible second-order reaction 2A-tor. The reaction mixture is heated to an initial temperature of 450°C. The reaction then proceeds adiabatically. Calculate the time required to reach a conversion of 80%. The initial concentration of A is kmol/m. The fluid density is p = 995 kg/m. The mean... 

As selectivity is a factor of importance in commercial production, we will deal here only with reaction schemes which are of practical interest. This means that when a product C is made on a commercial scale according to the reaction A — C, where a second reaction C — W may destroy the product C, this second reaction generally will be of a lower rate than the main reaction. Otherwise this reaction scheme would have no commercial value. This means that we may restrict ourselves to those cases for which the second reaction C — W is of an order (order of drop conversion) higher than or the same as that of the first reaction A — C, since this first reaction is more likely to be limited by mass transfer than the slower second reaction. 

It had been established several decades ago that the reaction of 1-chloro-l-ni-troethane with sodium nitrite in aqueous-alcohol medium is second order overall and first order in each reactant (Hawthorne 1956). 1-Deutero-l-chloro-l-nitroethane reacts more slowly than its lighter isotopomer. This means that the kinetic isotopic effect is observed. The reaction proceeds only in moderately alkaline media in strongly alkaline media it does not take place. Only those geminal halo nitro compounds, which carry hydrogen in the geminal position, can undergo the conversion. Based on these facts, Hawthorne (1956) suggested the Sn2 substitution preceded by the isomerization of the initial substrate into the aci-nitro form ... 

Two prototype reaction examples (reversible first-order and irreversible second-order kinetics) were discussed to address issues of rounding when switching from deterministic variables to stochastic (i.e., conversion of real numbers to integers), as well as the thresholds of population sizes and transition probabilities to control accuracy in the first two moments of the population (mean and variance). Other more complex examples were also mentioned. The... 

Another first-order reaction is to be studied at the same flow rate in the vessel characterized in Prob. 6-12. Measurements for this reaction in a plug-flow reactor, operating at the same mean residence time, gave a conversion of 75.2%. (a) Calculate the value of the rate constant for this reaction. (6) Calculate the conversion expected for this reaction in the reactor of Prob. 6-12. (c) Are any assumptions made in obtaining the answer to part (b)l If the reaction were second order, would additional assumptions be necessary to use the same procedure for part (6) ... 

Because an elementary reaction occurs on a molecular level exactly as it is written, its rate expression can be determined by inspection. A unimolecular reaction is a first-order process, bimolecular reactions are second-order, and termolecular processes are third-order. However, the converse statement is not true. Second-order rate expressions are not necessarily the result of an elementary bimolecular reaction. While a stoichiometric chemical equation remains valid when multiplied by an arbitrary factor, a mechanistic eqnation loses its meaning when multiplied by an arbitrary factor. Whereas stoichiometric coefficients and reaction orders may be integers or nonintegers, the molecularity of a reaction is always an integer. The following examples indicate the types of rate expressions associated with various molecularities. Unimolecular ... 

A second-order irreversible reaction A B with rate equation (-r, ) = fcCi and rate constant k = 0.1 m /kmol/min is carried out in a laminar flow reactor. The concentration of A in the feed solution is 5 kmol/m. The mean residence time of fluid in the reactor is 5.9 min. Calculate the conversion of A. 

Hughes and Ingold first demonstrated that the reaction is second order first order in 2-iodooctane and first order in iodide ion. Therefore, the reaction proceeds by an Sj 2 mechanism. They observed further that the rate of racemization of enantio-merically pure 2-iodooctane is exactly twice the rate of incorporation of iodine-131. This observation must mean, they reasoned, that each displacement of iodine-127 by iodine-131 proceeds with inversion of configuration, as illustrated in the following equation. Note that the reaction was run to only a low percent conversion... 

The rate of a reaction and its dependency on the concentrations of the reactants can be measured in several ways. A simple method involves the measurement of the rate at zero to low conversion at different concentrations of one of the substrates, keeping the concentration of other substrates constant. The latter can be done by using an excess of the other substrates (e.g. tenfold excess), which means that we can assume that the concentrations of the latter ones are constant under so-called pseudo-first-order conditions. Secondly we can monitor the reaction rate over a longer period of time taking into account the change in concentration for this one substrate. Alternatively, one can monitor the concentrations of all species and analyse the results numerically. 

Case iii. First Reaction of Order One-Half, Second Reaction of First-Order Drop Conversion. By means of the result S = 1/(1 + k2r) the selectivity as function of the conversion can now be easily calculated for the case of complete segregation and no segregation. The result is shown in Fig. 6, where the parameter now is Ah/fc2ai/2. 

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