Adsorption processes of gaseous molecules are known to be associated with isotopic fractionation, this being supported both experimentally and theoretically, From theoretical considerations [Lasaga, A.C., Otake, T., Watanabe, Y., Ohmoto, H. (2008) Anomalous fractionation of sulfur isotopes during heterogeneous reactions Earth and Planetary Science Letters 268 225-238], this process might also result in a "mass-independent" isotopic fractionation (MIF) of sulfur [i.e. delta S-33 not equal 0.515 X delta S-34] and could bear on our understanding of the sulfur isotope geological record. The anomalous fractionation could find its origin in the difference in the number of vibrational bound states of the adsorption complex (i.e. unbound states are neglected) among the four sulfur isotopes. In the present study, the equilibrium isotopic fractionation of sulfur during adsorption is investigated using a similar 1-dimensional (1-D) Morse potential. We demonstrate that no anomalous fractionation is expected when the contribution of all the accessible states (both bound and unbound) is properly taken into account. These results thus contradict the conclusion of Lasaga et al. [Lasaga, A.C., Otake, T., Watanabe, Y., Ohmoto, H., 2008. Anomalous fractionation of sulfur isotopes during heterogeneous reactions. Earth Planet. Sci. Lett. 268, 225-238.] stating that adsorption reactions would result in anomalous fractionations. Neglecting unbound states in our calculations would actually led to similar anomalous isotope fractionation, showing that the anomalous effect indeed arises from this simplification. Equilibrium adsorption processes are thus not expected to be associated with anomalous fractionation among the four sulfur isotopes.