Depending on the synthesis and/or post-treatment method, MXenes become covered by surface terminations. Here, via calculations based on density functional theory, we investigate how suitable the Ti2C MXene, with nine different termination possibilities (none, Br, Cl, F, H, NH, O, OH, or S), is for adsorbing 12 flue gas molecules, namely, CH4, CO, CO2, H2, H2O, H2S, N2, NH3, NO, O2, SO2, and SO3. According to our results, a general rule is that stronger adsorption is associated to more charge transferred between the adsorbent and the adsorbate. The clean Ti2C MXene is very reactive and spontaneously dissociates nearly half the species considered. H and F surface terminations are locally replaced by O in the presence of O2 since its dissociation on Ti2CH2 or Ti2CF2 is energetically cheap and exothermic. The Ti2C(OH)2 surface is damaged by the adsorption of NO, O2, SO2, or SO3 because they bind the H atoms of hydroxyl groups and locally create O terminations. Ti2CO2 and Ti2CS2 are selective toward the chemisorption of NH3 and NO, respectively, with adsorption energies suitable for adsorption/separation applications. The Ti2CBr2, Ti2CCl2, and Ti2C(NH)2 surfaces physisorb all the investigated molecules, with binding energies that qualitatively correlate with their van der Waals volumes, thus having potential for application in reusable gas storage.