Reaction zero-order volume

The dashed line in Figure 5.2 correspond to a zero-order volume reaction. The mean Sherwood number is a monotone decreasing function of the rate order n. Therefore, for 0 < n < 1 the curves describing the limit Sherwood number as Pe = oo lie between the dashed line and the upper continuous line. As the rate order n decreases, the curves corresponding to the Sherwood number for Pe = 0 and Pe = oo gradually come closer to each other and rise to the dashed line. In the limit case n = 0, all three curves merge into a single curve, i.e., the mean Sherwood number does not depend on the Peclet number at all. 

The inetabolism of ethyl alcohol may be considered to occur via a zero-order reaction (i.e., its elimination occurs linearly w ith time.) If a person is able to metabolize appro.ximately 10 inL of the alcohol per hour, how long a time period is required to elimimite 8 pints of beer containing 3.2% alcohol Assume that tlie volume of a pint of beer is 530 mL. 

This form assumes that the effect of pressure on the molar volume of the solvent, which accelerates reactions of order > 1 by increasing the concentrations when they are expressed on the molar scale, has been allowed for. This effect is usually small, ignored but in the most precise work. Equation (7-41) shows that In k will vary linearly with pressure. We shall refer to this graph as the pressure profile. The value of A V is easily calculated from its slope. The values of A V may be nearly zero, positive, or negative. In the first case, the reaction rate shows little if any pressure dependence in the second and third, the applied hydrostatic pressure will cause k to decrease or increase, respectively. A positive value of the volume of activation means that the molar volume of the transition state is larger than the combined molar volume of the reactant(s), and vice versa. 

One may use the same general approach when the reaction kinetics are other than first-order. However, except in the case of zero-order kinetics, it is not possible to obtain simple closed form expressions for CAN, particularly if unequal reactor volumes are used. However, the numerical calculations for other reaction orders are not difficult to make for the relatively small number of stages likely to be encountered in industrial practice. The results for zero-order kinetics may be determined from equation... 

The decomposition reaction A -> B + C occurs in the liquid phase. It has been suggested that your company produce C from a stream containing equimolar concentrations of A and B by using two continuous stirred tank reactors in series. Both reactors have the same volume. The reaction is first-order with respect to A and zero-order with respect to B and C. Each reactor... 

A zero order gas reaction, A = rR, proceeds in a constant volume bomb with 20% inerts, and the pressure rises from 1.0 to 1.3 atm in 2 min. When the same reaction proceeds at constant pressure of 3 atm and with 40% inerts, what is the fractional change of volume in 4 minutes ... 

A gas phase reaction has a zero order rate equation in the concentration range of interest. Given the additional data following, find the space velocity, cuft of feed/(hr)(cuft of catalyst bed), needed for 95% conversion. C0 = 0.005 lbmol/cuft, inlet concentration k = 5 lbmol/(hr)(cuft of catalyst), specific rate D = 0.1 ft2/hr, diffusivity c = 0.40, fractional free volume... 

The simplest case of compositional dependence is the zero-order reaction, in which the concentration gradient is not affected by concentration. Denoting the molar concentration of the ith element (or component) as c, (and neglecting surface area and volume of solution effects), we have... 

Figure 3.21 Test for a homogeneous zero-order reaction, Eq. 69, in a constant-pressure, varying volume reactor.

For example, for a zero-order reaction and a vaiiable-volume system,... 

Figure 17.6. Generalized chart of catalyst effectiveness for reactions of order n in particles with external surface Ap and volume Vp. The upper curve applies exactly to zero-order reaction in spheres, and the lower one closely for first- and second-order reactions in spheres.

The work of Sihvonen is complicated not only by its tremendous volume but also by its rather limited accessibility. He has given a review of his work with a fairly complete bibliography (68) another review contains a considerable number of experimental curves (66). At very high temperatures (> 1400° C.) both Meyer and Sihvonen independently observed effects that have not been observed by any other workers. The C + H20 reaction becomes zero-order with respect to water vapor pressure and the activation energy has a value of about 90 keal. per mole (52, 65, 66). Meyer reports identical Arrhenius plots for C + C02 and C -f H20 in this region. The C + 02 reaction... 

These results illustrate the general conclusion that, as the number of tanks is increased, the total volume required diminishes and tends in the limit to the volume of the equivalent plug-flow reactor. The only exception is in the case of a zero order reaction for which the total volume is constant and equal to that of the plug flow reactor for all configurations. 

A catalytic hydrogenation is performed at constant pressure in a semi-batch reactor. The reaction temperature is 80 °C. Under these conditions, the reaction rate is lOmmolT s-1 and the reaction may be considered to follow a zero-order rate law. The enthalpy of the reaction is 540 kj moT1. The charge volume is 5 m3 and the heat exchange area of the reactor 10 m2. The specific heat capacity of water is 4.2kJkg 1K 1. 

The reaction model assumed is one in which free-radical polymerisation is compartmentalised within a fixed number of reaction loci, all of which have similar volumes. As has been pointed out above, new radicals are generated in the external phase only. No nucleation of new reaction loci occurs as polymerisation proceeds, and the number of loci is not reduced by processes such as particle agglomeration. Radicals enter reaction loci from the external phase at a constant rate (which in certain cases may be zero), and thus the rate of acquisition of radicals by a single locus is kinetic-ally of zero order with respect to the concentration of radicals within the locus. Once a radical enters a reaction locus, it initiates a chain polymerisation reaction which continues until the activity of the radical within the locus is lost. Polymerisation is assumed to occur almost exclusively within the reaction loci, because the solubility of the monomer in the external phase is assumed to be low. The volumes of the reaction loci are presumed not to increase greatly as a consequence of polymerisation. Two classes of mechanism are in general available whereby the activity of radicals can be lost from reaction loci ... 

The fact that a plot of H2 volumes initially generated vs. time gave a straight line is indicative of pseudo zero order kinetics. For borohydride hydrolysis, Kaufman and Sen3 and Holbrook and Twist4 also found zero order kinetics. Zero order kinetics for Reaction [1] imply that hydrolysis is independent of the concentrations of the reacting chemical species. This can be explained by assuming that the initial reaction step probably involves a surface catalyzed reaction, most likely BH" adsorption on the catalyst. Since the number... 

I have chosen to make the comparison using a zero-order reaction only. Tables I and II indicate that this is conservative for the two ideal reactor types, and it seems plausible to assume that it is also so for real reactors. The degree of conservatism is little more than a few percent in reactor volume. This restriction is thus a useful way to keep the ultimate results in a simple form without compromising their utility. 

Example 8-3 (taken from Bolton et al, 2001a) A solar collector of an area of 4 m is used to treat a water containing 500 mg of 1,4-dioxane (C4Hg02) at an average solar irradiance of 850 W m . The total volume V of the batch system was 300 L and the substrate was degraded within 1.5 h by a zero order reaction kinetics to a final concentration of [C4Hg02] = 200 mg Calculate the appropriate design parameter. 

P is the number of polymer molecules of degree of polymerization n, R is the number of radicals found in a volume V, R is the number of polymer radicals with degree of polymerization n found in a volume, V. For other definitions, please use the nomenclature associated with Table 15.2. Noting equation 15.14, the kinetics of polymer degradation are very complex. Only the most simple mechanisms have been thoroughly researched. These simplified reactions presented in Table 15.2 are sometimes zero order, more frequently first order, and infiiequently second order in polymer mass. These simplified rate expressions are typically used to model binder burnout. 

Surface Initiation or Termination, The surface acts to initiate or terminate radicals or ions which diffuse out into the homogeneous phase, gas or liquid, where a chain reaction lakes place. The behavior is certainly characteristic of the activity of glass and quartz surfaces in a great many chain reactions, particularly gas-phase oxidations such as H2 + O2. When initiation takes place rapidly at the surface, it is likely that termination is also effective there. Such systems can be recognized by the fact that they react at specific rates which are nearly independent of the surface/volume ratio, i.e., zero order with respect to surface or catalyst. 

A plot of the concentration of A as a function of time will be linear (Figure 5-3) with slope (-t) for a zero-order reaction carried out in a constant-volume batch reactor. 

For the same flow rate fhe plug-flow reactor requires a smalJer volume than the CSTR to achieve a conversion of 60%. Utis comparison can be seen in Figure E2-4.1. For isothermal reactions of greater than zero order, the PFR will always require a smaller volume than the CSTR to achieve the same conversion. 

For this evaluation it is a very fortunate fact that the shape of the 77 versus

reaction order (except when approaching zero order), nor to effects of molar volume change, nor to particle geometry. This makes it possible to determine 771 and 772 by the triangle method and, consequently, with considerable independence of the variables mentioned. 

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