Mathematics encountered in kinetics

The mathematical difficulty increases from homogeneous reactions, to mass transfer, and to heterogeneous reactions. To quantify the kinetics of homogeneous reactions, ordinary differential equations must be solved. To quantify diffusion, the diffusion equation (a partial differential equation) must be solved. To quantify mass transport including both convection and diffusion, the combined equation of flow and diffusion (a more complicated partial differential equation than the simple diffusion equation) must be solved. To understand kinetics of heterogeneous reactions, the equations for mass or heat transfer must be solved under other constraints (such as interface equilibrium or reaction), often with very complicated boundary conditions because of many particles. 

the following chapters will start from homogeneous reactions and proceed to diffusion and mass transfer, and then to heterogeneous reactions. 

2 Demystifying some processes that seem to vioiate thermodynamics 

At room temperatures, crystalline quartz is thermod3mamically more stable than silica glass. From ancient times, humans have converted quartz to silica 

The most famous example of nature manipulating thermodynamics is probably the photosynthesis reaction, without which most life forms would not be present on the Earth. Thermodynamically, CO2 + H2O are much more stable than carbohydrate + O2. However, nature can convert CO2 + H2O to carbohydrate + O2 through the photosynthesis reaction  

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