Chemical Reactions and Rate Equations

When fuel cells are operating, the heat generation rate (the source term needed in the thermal-fluid model) depends on the rates of the various chemical and 

The cathode reaction, on the other hand, has a single stoichiometry  

The heat source is related to the enthalpy change of the reactions, and the free-energy change of reactions (15a) and (15b) combined with (15e) determines the fuel cell Nernst potential. If chemical equilibrium is achieved in the system, the fuel composition, heat generation, and Nernst potential can be determined from thermodynamic theory. However, chemical equilibrium is usually not attained. In such cases, fuel composition and other information cannot be rigorously determined and must be approximated. The details of the reaction mechanism are complicated and usually not well understood, both for electrochemical and chemical reactions. 

Therefore, when equilibrium cannot be plausibly assumed, apparent kinetic parameters (effective rate constants) must be used to express the reaction rate. The parameters that describe the electrochemical reaction rate include the above-mentioned exchange current density, the transfer coefficient, the activation enthalpy, and the pre-exponential factor as well as the reaction order of the species involved. These parameters are not necessarily related to a single rate-determining step, as is often assumed in electrochemical theory. By investigating i-ri curves as functions of electrode potential, temperature, and concentration of the reacting species, insight may be gained into the reaction mechanism and microscopic transport processes (such as surface diffusion) that 

Chemical reactions, too, may be characterised in a similar manner, following a strategy of effective kinetic parameters. When detailed knowledge of the reaction mechanism is lacking, the effective rate constants and other reaction-kinetic parameters can be determined by fitting a simplified kinetic model to the experimental data. For example, the steam-reforming conversion rate of CH4 (reaction (15c)) may be expressed by the following empirical equation [6]  

---