Single Irreversible Reaction with General Kinetics

a Single Irreversible Reaction with General Kinetics 

First consider the case of a chemical reaction that is very slow with respect to the mass transfer, so that the amount of A that reacts during its transfer through the liquid film is negligible. The rate of transfer of A from the liquid interface to the bulk may then be written  

When the rate of reaction cannot be neglected with respect to the mass transfer, the amount reacted in the film has to be accounted for in an explicit way. Let A be the component of the gas phase reacting with a non-volatile component B in the liquid phase and let the film be isothermal. The reaction considered is  

The bulk concentrations must be determined from an equation for the mass flux through the film-bulk boundary  

Integrating Eq. 6.3.a-l or Eq. 6.3.a-2 with the given boundary conditions and rate equation leads to the concentration profiles of A and B in the liquid film. The rate of the overall phenomenon, as seen from the interface, then follows from the application of Pick s law  

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Similar methods may be used for analysis of selectivity, yield, and concentration maxima in other types of parallel or sequential reaction schemes with either reversible or irreversible steps. However, when the kinetics involve other than first-order rate laws, convenient analytical solutions cannot be obtained, in general, and step-by-step calculations are probably more convenient. Also, the graphical method illustrated in Figure 4.15 is not applicable for parallel or sequential schemes because normally the rate of appearance or consumption of intermediates of interest depends on the concentration of more than one species and representation of rate in a single (—r) versus C relationship is not possible. 

The second prerequisite is that enzyme reaction should be irreversible. In theory, the estimation of prarameters by kinetic analysis of reaction curve is still feasible when reaction reversibility is considered, but the estimated prarameters possess too low rehabihty to have practical roles (data impnbhshed). Generally, a prepraration of a substance with contaminants less than 1% in mass content can be taken as a pure substance. Namely, a reagent leftover in a reaction accoimting for less than 1% of that before reaction can be negligible. For convenience, therefore, an enzyme reaction is considered irreversible when the leftover level of a substrate of interest in equilibrium is much less than l%of its initial one. To promote the consumption of the substrate of interest, the concentrations of other substrates should be preset at levels much over 10 times the initial level of the substrate of interest. In this case, the enzyme reaction is ap>p)arently irreversible and follows kinetics on single substrate. Or else, the use of scavenging reactions to remove products can drive the reaction forward. The concurrent uses of both approaches are usually better. 

Reinmuth has examined chronopotentiometric potential-time curves and proposed diagnostic criteria for their interpretation. His treatment applies to the very limited cases with conditions of semi-infinite linear diffusion to a plane electrode, where only one electrode process is possible and where both oxidized and reduced forms of the electroactive species are soluble in solution. This approach is further restricted in application, in many cases, to electrode processes whose rates are mass-transport controlled. Nicholson and Shain have examined in some detail the theory of stationary electrode polarography for single-scan and cyclic methods applied to reversible and irreversible systems. However, since in kinetic studies it is preferable to avoid diffusion control which obscures the reaction kinetics, such methods are not well suited for the general study of the mechanism of electrochemical organic oxidation. The relatively few studies which have attempted to analyze the mechanisms of electrochemical organic oxidation reactions will be discussed in detail in a following section. 

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