Diffusion and First-Order Heterogeneous Reactions

In addition to these two cases, other very different situations can also be diffusion-controlled. Two more examples are the case of facilitated diffusion across membranes and that of reactions controlled by Brownian motion. In the facihtated-diffusion case, shown schematically in Fig. 16.2-1 (c), one solute quickly reacts with a second carrier solute to form a complex this complex then diffuses across the membrane. The overall transport rate is governed by complex diffusion weighted by the equilibrium constant for complex formation. This case is discussed in Section 18.5. 

Still another diffusion-controlled process is called in chemistry a diffusion-controlled reaction, although it is very different from the other cases. In this case, shown schematically in Fig. 16.2-1(d), the system is an initially homogeneous mixture of two types of molecules. These species react instantaneously whenever they collide, so that then-reaction rate is controlled by their molecular motion, that is, by their diffusion. This process is described in detail in Section 17.4 a similar dispersion-controlled process is described in Section 17.5. 

By this point, we should try to find the common thread through this tweed of diffusion control. The key feature in all these cases is the coupling between chemical kinetics and diffusion. In every case, the overall rate is a function of the diffusion coefficient. Sometimes this rate depends on little else more frequently, it also includes aspects of chemical dynamics. In any case, the idea of diffusion control is obviously indefinite without reference to a more specific situation. Make sure you know which definition is being imphed before trying to understand what is happening. 

After these general concerns, we turn to the analysis of diffusion and heterogeneous chemical reaction. The simplest case is the first-order mechanism shown 

This particular case occurs with surprising frequency. The most common practical example is an electrochemical reaction. For example, anions diffuse to the anode these anions react there, and any produets diffuse away. Because this kind of reaction often takes place in aqueous solution and at moderately high voltage, its rate is often governed by the diffusion steps. 

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