Different Definitions of the Mass-Transfer Coefficient

All of the discussion so far has involved kc, the mass-transfer coefficient based on a concentration driving force. However, the mass-transfer coefficient may be based on other driving forces, notably mole fraction and partial pressure (p). Thus, we can write 

Relationships between the various mass-transfer coefficients can be derived by equating the fluxes. For example. 

If differences in temperature and total pressure across the boundary layer are ignored, then the total mixture concentration C is the same at the catalyst surface as it is in the bulk, and C can be divided into both sides of the above equation. 

For an ideal gas, an exactly equivalent procedure can be used to relate the mass-transfer coefficient based on partial pressure to those based on mole fraction and concentration. If P is the total pressure 

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