Volume change due to reaction

For the case of a sphere, the control volume is given by a thin spherical shell of thickness dr and radius r. If we assume that the complex diffusion process inside the porous structure can be represented by Fick s first law, and we additionally suppose that the volume change due to reaction is negligible (i.e. the total number of moles is constant), we arrive at the following form of the mass conservation law for the reacting species i ... 

Again, we assume isothermal conditions and the absence of a volume change due to reaction. The governing rate equations for the disappearance of reactant A ... 

An inert gas (N2) is assumed to be present in large excess. As a matter of the small partial pressures of the reacting species under these conditions, the adsorption isotherms may be approximated by linear relationships (cq 176) the volume change due to reaction may be neglected. 

Therefore, in this case as well, the number a equals zero and again the intraparticle pressure gradient vanishes. So, no pressure will build up inside the pellet either if there is no volume change due to reaction or if the catalyst pores are very broad. 

Because our concern here is mainly with liquid-phase reactions, any volume change due to reaction can be neglected, so that the material balance of Equation 10.22 continues to be valid. It is convenient, however, to recast this... 

Assume that the reaction is first order in propylene, zero order in oxygen, and irreversible. You may also neglect volume change due to reaction, although this assunqition is not strictly justified. 

FIG. 3.4. The effect of volume change due to reaction on the relationship between conversion and normalized time. 

We feed a stream at a volumetric flow rate of 0.11/s containing A, B, and a diluent solvent, with cao = 0.5 M and varying y = cbo/cao- Assuming isothermal operation, and neglecting any volume change due to reaction, plot the conversion of A as a function of temperature and y. 

For constant volume CSTR with no volume change due to reaction, the mole balances for a volumetric feed rate v are... 

For CVD processes at atmospheric or reduced pressure, the reactants are usually used in low concentration in H2 or some inert carrier gas. Therefore, volume changes due to the change in the number of moles between reactants and products are negligible. In addition, in CVD processes, unlike in combustion systems, energy contributions caused by heats of reaction are... 

It has been shown that the volume change that occurs when Fe3 + (aq) is reduced to Fe2 + (aq) is an increase of + 13.6 cmVmol, of which + 4 cm3/mol is a consequence of a solvational effect and the remaining +9.6 cmVmol arises from intrinsic changes. Hence, the reaction volume change due to the oxidation of promethazine should be about —8 cmVmol. It may be argued from crystallographic data and other information... 

Considering that the enantioselectivity (E) is dependent on high hydrostatic pressure the KM and v value should also be dependent on pressure. In view of the enzyme catalysed reactions volume changes due to conformational changes of the enzymes should expect larger sensitivity of the reaction rates compared to the uncatalysed ones. 

Volume changes due to the reaction may become considerable. This may lead to intraparticle pressure gradients, which will influence the effectiveness factor because ... 

Because of volume changes due to the reaction, pressure gradients may occur inside the catalyst pellet. This can give rise to two effects. First, it influences the effective diffusion coefficients, since the gas-phase diffusion coefficients depend on pressure. Second, the pressure gradients affect the concentrations (or more accurately, chemical activities), which determine the reaction rate. Hence pressure gradients must directly influence the effectiveness factor. 

It is important to be aware of clustering caused by electrostriction in order to understand reactions of ions in supercritical rare gases. If a classical continuum model is used to calculate clustering, the magnitude of the volume change due to electrostriction would be overestimated because such a model ignores the density build-up around the ion. Because of this density augmentation, the compressibility of the fluid near the ion is less and, since electrostriction is proportional to compressibility, the actual electrostriction will be less... 

Solution Because all the substances are dissolved in the same solution, they all have the same volume, and therefore their numbers of moles are proportional to their molarities. Therefore, we can calculate the molarity ratios from the balanced chemical equation. First we write the balanced chemical equation and put under it rows for "Initial concentrations," "Change due to reaction," and "Equilibrium concentrations." We then put the data given in the problem into our table. We assume that there is no C or D present initially, since none was mentioned. 

The reaction is first order in A and irreversible. The tank initially is charged with species A at concentration Cao- At time zero, the feed pump is turned on and delivers constant flowrate, Q/. The feed concentration of A is ca/, which is also constant. The tank volume is Vr. Liquid density change due to reaction may be neglected. 

From now on we shall concentrate on reactions taking place in a well-mixed vessel (test-tube, cell, reactor etc.) of constant volume at constant pressure and temperature. More generally speaking, it is assumed that all the transport processes in the thermodynamic sense (including volume changes due to the reaction) are negligible. Further — at the present tacit — assumptions will be made clear below. The present chapter sets up a framework for the reactions it deals with stoichiometry. 

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