The present study provides a solvent-free organic synthesis of quaternary ammonium salts: bis(2-hydroxyethyl)dimethylammonium taurate ([BHEDMA][Tau]) and bis(2-hydroxyethyl)dimethylammonium acetate ([BHEDMA][OAc]). These ionic compounds are promising materials for carbon dioxide capture processes, as mono sorbents, supplemental components in the conventional process of chemical absorption, and in the combined membrane approach for improving sorption efficiency. The synthesized compounds were characterized by 1H NMR and FT-IR spectroscopies and elemental analysis. Afterward, the sorption properties of the compounds were evaluated using the inverse gas chromatography (IGC) method, and their thermodynamic parameters were calculated in the temperature range of 303.15–333.15 K. The enthalpy change (∆sH) was less than 80 kJ·mol−1, indicated by the physical nature of sorption and also proved by FT-IR. Henry’s law constant in regard to carbon dioxide at 303.15 K was equal to 4.76 MPa for [BHEDMA][Tau], being almost 2.5 lower than for [BHEDMA][OAc] (11.55 MPa). The calculated carbon dioxide sorption capacity for [BHEDMA][Tau] and [BHEDMA][OAc] amounted to 0.58 and 0.30 mmol·g−1, respectively. The obtained parameters are comparable with the known solid sorbents and ionic liquids used for CO2 capture. However, the synthesized compounds, combining the advantages of both alkanolamines and ionic liquids, contain no fluorine in their structure and thus match the principles of environmental care.