Steady-state mass diffusion with homogeneous chemical reaction

6 Steady-state mass diffusion with homogeneous chemical reaction 

According to (2.338), for steady-state, geometric one-dimensional diffusion with chemical reaction we have 

We will now assume that substance A and the products created by the chemical reaction are only present in very small amounts in substance B. So, this is approximately c = N/V = const. In addition we will set I) = const. 

If substance B is a porous solid the molecular diffusion coefficient D has to be replaced by the effective diffusion coefficient DeB. This is smaller than the molecular diffusion coefficient because the movement of the molecules is impeded by the pores. It is common practice to define a diffusion resistance factor 

A porous solid of volume V consists of the volume Vg of the solid material and VG = V — Vs the volume of the solid-free spaces. We call p = VG/V the void fraction. The resistance factor depends on the voidage of the porous body and on a diversion or winding factor /j,p such that the relationships 

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A to products by considering mass transfer across the external surface of the catalyst. In the presence of multiple chemical reactions, where each iRy depends only on Ca, stoichiometry is not required. Furthermore, the thermal energy balance is not required when = 0 for each chemical reaction. In the presence of multiple chemical reactions where thermal energy effects must be considered becanse each AH j is not insignificant, methodologies beyond those discussed in this chapter must be employed to generate temperature and molar density profiles within catalytic pellets (see Aris, 1975, Chap. 5). In the absence of any complications associated with 0, one manipulates the steady-state mass transfer equation for reactant A with pseudo-homogeneous one-dimensional diffusion and multiple chemical reactions under isothermal conditions (see equation 27-14) ... 

In these electrode processes, the use of macroelectrodes is recommended when the homogeneous kinetics is slow in order to achieve a commitment between the diffusive and chemical rates. When the chemical kinetics is very fast with respect to the mass transport and macroelectrodes are employed, the electrochemical response is insensitive to the homogeneous kinetics of the chemical reactions—except for first-order catalytic reactions and irreversible chemical reactions follow up the electron transfer—because the reaction layer becomes negligible compared with the diffusion layer. Under the above conditions, the equilibria behave as fully labile and it can be supposed that they are maintained at any point in the solution at any time and at any applied potential pulse. This means an independent of time (stationary) response cannot be obtained at planar electrodes except in the case of a first-order catalytic mechanism. Under these conditions, the use of microelectrodes is recommended to determine large rate constants. However, there is a range of microelectrode radii with which a kinetic-dependent stationary response is obtained beyond the upper limit, a transient response is recorded, whereas beyond the lower limit, the steady-state response is insensitive to the chemical kinetics because the kinetic contribution is masked by the diffusion mass transport. In the case of spherical microelectrodes, the lower limit corresponds to the situation where the reaction layer thickness does not exceed 80 % of the diffusion layer thickness. 

In this form of voltammetry, the concentration distributions of each species in the electrode reaction mechanism are temporally invariant at each applied potential. This condition applies to a good approximation despite various processes still occurring such as mass transport (e.g. diffusion), heterogeneous electron transfer and homogeneous chemical processes. Theoretically it takes an infinite time to reach the steady state. Thus, in a practical sense steady-state voltammetric experiments are conducted under conditions that approach sufficiently close to the true steady state that the experimental uncertainty of the steady-state value of the parameter being probed (e.g. electrode current) is greater than that associated with not fully reaching the steady state. The... 

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