Effects of intraparticle diffusion on the experimental parameters

In the presence of intraparticle diffusion effects, the observed rate differs from the surface intrinsic rate which is controlled only by the reaction kinetics. Therefore, the rate must be corrected by the effectiveness factor rj. 

Under strong diffusion effects, the effectiveness factor is inversely proportional to Thiele modulus. When the reaction has a generic n-order, one should take care in interpreting the experimental results, since, according to Equation 18.29, the reaction order is not the same as the intrinsic rate. The observed rate is as follows  

Substituting the effectiveness factor as a function of Thiele modulus, the factor is inversely proportional to Thiele modulus in the presence of strong diffusion effects. Therefore, from Equation 18.29, we obtain  

Therefore, we have a measured reaction order w (apparent order) which is obtained by equating Equations 18.34 and 18.35  

Consequently, a zero-order reaction will have an apparent order equals to a first-order reaction will present the same apparent order and a second-order reaction, an apparent order of 3/2. Therefore, the order of reaction is apparent. 

---