Assuming that I understood correctly, I am answering this question. You have to do experiments exactly like how you do the adsorption experiment with your adsorbent only that you will not have your adsorbent in the blank experiment.
If the blank experiment should be carried out without an adsorbent, then it is no longer adsorption studies.
I suggest:
1. You should note the possible heterogeneous reactions that can occur on the adsorbent surface (taking the adsorbate as reactant and the glass as heterogeneous catalyst).
2. Search for other good adsorbents that cannot catalyze any of the identified reactions.
3. Finally, replace the original adsorbent with equal BET surface amount of any of the adsorbent materials identified in (2).
The extent of adsorption achieved with the inert adsorbent of equal BET surface, when compared to that of the original adsorbent should give you what you want.