Derivation of Global Rate Equations

Dividing by Ay and taking limits as Ay 0, we get a second-order differential equation 

Y is a dimensionless number called Hatta number. Hatta number is the ratio of resistance to mass transfer to the resistance to reaction. The Hatta number value is larger for a faster reaction compared to that of a slower reaction as the resistance to reaction is lower than the resistance to mass transfer for a faster reaction. Combining Equations 4.75 and 4.81, we rewrite the equation for Hatta number y as 

In general, y 3 for slow reaction, y 3 for fast reaction and y is very large for instantaneous reaction. Substituting the boundary conditions 

Flux N i of A in the liquid film is calculated by evaluating dC /dy at y = 0 and substituting in Equation 4.74. Thus, taking the derivative of with respect to y and substituting y = 0 in the derivative term, we get 

As the steady-state condition is assumed at every location in the reactor, the flux N q of A in the gas phase is equal to the flux Nal of A in the liquid film and this flux value is equal to the overall flux (or rate) N - 

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