Volume Change Upon Reaction

Example 2.11 Suppose initially pure A dimerizes, 2A —> B, isothermally in the gas phase at a constant pressure of 1 atm. Find a solution to the batch design equation and compare the results with a hypothetical batch reactor in which the reaction is 2A B - - C so that there is no volume change upon reaction. 

The equations and plots presented in the foregoing sections largely pertain to the diffusion of a single component followed by reaction. There are several other situations of industrial importance on which considerable information is available. They include biomolecular reactions in which the diffusion-reaction problem must be extended to two molecular species, reactions in the liquid phase, reactions in zeolites, reactions in immobilized catalysts, and extension to complex reactions (see Aris, 1975 Doraiswamy, 2001). Several factors influence the effectiveness factor, such as pore shape and constriction, particle size distribution, micro-macro pore structure, flow regime (bulk or Knudsen), transverse diffusion, gross external surface area of catalyst (as distinct from the total pore area), and volume change upon reaction. Table 11.8 lists the major effects of all these situations and factors. 

We developed the equations required to compute the volume of the reactor if there is a significant volume change upon reaction. We require an equation of state for this purpose. Tables 4.1 and 4.2 describe the appropriate balances for a constant-density mixture, an ideal mixture, and a mixture with a general equation of state. 

The space-time yield (column 5) reaches a maximum at about 4 1./ hour/g. cobalt. In column 6 the space-time yield was calculated as indicated in the footnote. The volume change upon reaction to form chiefly hydrocarbons with 5 to 16 carbon atoms is approximately constant over a wide range of variation of molecular weight distribution therefore the partial pressure of the reaction products is approximately directly proportional to the contraction. The figures in column 6 increase more slowly than those of column 5 with increasing throughput, but there is no maximum. It seems probable that the temperature of the catalyst surface increases... 

Most autocatalytic reactions occur in liquid solutions where volume changes upon reaction are usually negligible, so the analysis using the constant-volume case here is reasonable. The normal kinetic formulation for this reaction is then... 

The changes in density with composition may be neglected, but volume changes upon reaction should be considered. The solubility of organics in the acid phase, and water and sulfuric acid in the organic phase, may be... 

As long as gaseous reactions are not under consideration, volume changes upon reaction are very small and justly neglected. 

No (Shimizu 2004). It has long been known that the partial molar volume change upon reaction AV, can be expressed in terms of AAf, and AN, in the following form (Ben-Naim 1992),... 

Currently, the most promising artificial muscles are electrochemomechanical actuators. These devices are designed to transduce electrical energy into mechanical work through electrochemical reactions in conductive polymer films. The most common CPs currently under investigation for this application include PPy and PANI [61,95], utilizing the volume change upon oxidation/reduction accompanied by ions/solvents... 

In this constant-volume SBO, a stirred tank reactor is charged initially with a reactant or reactants (B). One reactant is fed to the reactor at a constant volumetric flow rate Qq, and the product is removed at the same rate. This is a general description of the reactions of scheme 1 in Figure 2.10. In analyzing these schemes, we make the following reasonable assumptions to simplify the equations there is no volume change upon mixing of the two liquids or upon reaction, and the reactor is perfectly mixed. 

Reaction 1 is highly exothermic. The heat of reaction at 25°C and 101.3 kPa (1 atm) is ia the range of 159 kj/mol (38 kcal/mol) of soHd carbamate (9). The excess heat must be removed from the reaction. The rate and the equilibrium of reaction 1 depend gready upon pressure and temperature, because large volume changes take place. This reaction may only occur at a pressure that is below the pressure of ammonium carbamate at which dissociation begias or, conversely, the operating pressure of the reactor must be maintained above the vapor pressure of ammonium carbamate. Reaction 2 is endothermic by ca 31.4 kJ / mol (7.5 kcal/mol) of urea formed. It takes place mainly ia the Hquid phase the rate ia the soHd phase is much slower with minor variations ia volume. 

Solution The obvious way to solve this problem is to choose a pressure, calculate Oq using the ideal gas law, and then conduct a batch reaction at constant T and P. Equation (7.38) gives the reaction rate. Any reasonable values for n and kfCm. be used. Since there is a change in the number of moles upon reaction, a variable-volume reactor is needed. A straightforward but messy approach uses the methodology of Section 2.6 and solves component balances in terms of the number of moles, Na, Nb, and Nc-... 

The character of carbonaceous material s influence on performance of asymmetric EC systems (carbon - NiOx) is more complicated than that of carbon-carbon system. It is determined by the higher operating potential of NiOx electrode, due to which oxidation and volume changes in electrode active mass upon charge-discharge processes are taking place as the reaction of transformation of Ni(OH)2 into NiOOH is occurring. 

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