  We show that most of the empirical or semi-empirical isotherms proposed to
extend the Langmuir formula to sorption (adsorption, chimisorption and
biosorption) on heterogeneous surfaces in the gaseous and liquid phase belong
to the family and subfamily of the Burr_{XII} cumulative distribution
functions. As a consequence they obey relatively simple differential equations
which describe birth and death phenomena resulting from mesoscopic and
microscopic physicochemical processes. Using the probability theory, it is thus
possible to give a physical meaning to their empirical coefficients, to
calculate well defined quantities and to compare the results obtained from
different isotherms. Another interesting consequence of this finding is that it
is possible to relate the shape of the isotherm to the distribution of sorption
energies which we have calculated for each isotherm. In particular, we show
that the energy distribution corresponding to the Brouers-Sotolongo (BS)
isotherm [1] is the Gumbel extreme value distribution Finally we propose a
generalized GBS isotherm, calculate its relevant statistical properties and
recover all the previous results by giving well defined values to its
coefficients. In the course of the discussion we make contact with the Tsallis
nonextensive theory [2] and the noninteger order reaction and fractal kinetics
theory [3]. In the spirits of the present and previous publications, we propose
an alternative formula to include fractality in the Michealis-Menten enzyme
catalysis theory. Finally we suggest that the stochastic cluster model
introduced by K.Weron [4] to account for the universal character of relaxation
in disordered systems should be relevant for other phenomena in particular for
heterogeneous sorption
