In the description of the kinetic data of sorption processes, equation in the form:

r = k(Xe - X)2, (#)

and the equation obtained on the basis of mass balance of the batch process:

dX/dt = r, X(0) = 0, -> X=Xe2kt/(1+Xekt), (##)

(which is mathematically hyperbolic function) are often used.

For the irreversible reaction of the second order: A -> products , we use the kinetic equation and mass balance (batch process):

r = kcA2; dα/dt = kcAo(1-α)2, α(0)=0 (V = const).

But this is not the same, and moreover in the equations (#) and (##) there is no initial substrate (adsorbate) concentration. Thus, equation (##) can only be used to approximate a single kinetic curve, not a set of curves obtained at different initial concentrations, as is the case of chemical reactions. I do not know the thesis on which the equation (#) is based, apart from intuitive premises. Maybe someone knows? Regards,