Is the Reaction Heterogeneous or Homogeneous

We first want to discuss the difference between heterogeneous and homogeneous reactions. On first inspection, this difference seems obvious. Heterogeneous reactions must involve two different phases, with the chemical reactions occurring at the interface. Homogeneous reactions take place in a single phase, and the reaction occurs throughout. 

In practice, this distinction is less obvious. As an example, imagine a spherical coal particle burning in a fluidized bed. All the reaction initially takes place on the sphere s surface. This initial reaction is best modeled as heterogeneous. If it were first-order in, for example, oxygen, then the rate equation might be 

However, as the combustion proceeds, the particle may become porous, and the chemical reaction may occur not only at the surface but on all pore walls throughout the particle. In some cases, the pore area may far exceed the particle s superficial surface area. The combustion is now occurring throughout the particle as if the reaction were homogeneous its rate is best modeled as 

The oxygen concentration can be defined either per pore volume or per particle volume. In either case, the homogeneous rate constant has units of reciprocal time. Such constants are fixtures of elementary chemistry textbooks. 

Thus combustion of the coal particle can be modeled as heterogeneous or homogeneous, depending on how the coal is burning. The choice of a model for the reaction is usually subjective, but rarely explicitly stated in the research literature. Instead, it must be inferred. The key for inference is the continuity equation. If this equation has the form 

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