Modification of the Thiele Modulus for a Reversible Reaction

The total molal concentration of A and B is constant, as for every 1 mole of A reacted 1 mole of B is formed. Thus 

Substituting this specific reaction rate Equation 4.188 into the molal balance Equation 4.155 derived for a spherical catalyst pellet, we get 

Substituting the equilibrium concentration Ca — Ae into Equation 4.189, we have 

we find that Equations 4.191 and 4.193 are analogous to the corresponding Equations 4.157 and 4.158 derived for an irreversible reaction in the spherical catalyst pellet except that is replaced by Ca and the rate constant fc is replaced by + K/K). So, the equation for Thiele modulus O defined for an irreversible reaction will hold good for a reversible reaction with the rate constant fc in O replaced by ki(l + K/K). Thus, the Thiele modulus O for a reversible reaction in a spherical catalyst pellet is 

In general, the modified Thiele modulus O for the reversible reaction in a pellet of any regular shape is 

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