Perfluoropolymers are a unique class of materials that display anomalous thermodynamic partitioning compared to hydrocarbon polymers and show exceptional separation performance for certain gas pairs. However, the molecular origin by which fluorine affects gas sorption is not well-understood, and the sorption behavior of partially fluorinated polymer analogues is rarely quantified. Here, we synthesized and characterized a series of structurally analogous poly(ether imide)s spanning from fully hydrocarbon to perfluorinated, which involved the synthesis of a perfluorinated dianhydride monomer. Sorption isotherms for multiple temperatures and gases were analyzed using the non-equilibrium lattice fluid model. The lattice fluid parameters were estimated from infinite dilution sorption data. The binary interaction parameter increased with polymer fluorine content for all gases, with CH4 showing the largest increase in unfavorable deviation from ideal mixing. Continuous trends for the enthalpic, entropic, and infinite dilution sorption selectivity with fluorine content were observed, wherein the increase in enthalpic selectivity was greater than the decrease in entropic selectivity, resulting in overall increased sorption selectivity for gas pairs where the less condensable gas is also the faster permeating gas (e.g., N2/CH4). Our findings connect the sorption behavior of hydrocarbon polymers and perfluoropolymers and provide mechanistic insight into the role of fluorine on gas sorption.