Previous theories correlate RTIL-membrane performance with the RTIL's viscosity, molar volume, or chemical interactions with the faster fluxing chemical. However, we improved membrane performance by selecting RTILs that hindered the transport of the slower fluxing chemical. Theoretically, increasing the RTIL's hydrogen-bond acceptor ability lowers the solubility of the non-polar methane gas. Membranes fabricated from RTILs with high Kamlet-Taft hydrogen-bond accepting parameters,beta, had significantly better performance (2600 GPU-water and water/methane selectivity of 100,000) compared to previous RTIL-membranes. We report a strong correlation (exponential fit, R-2 = 0.97, N = 6) between the selectivities and beta's. Using high-beta RTILs did produced RTIL-membranes competitive with polymer membranes and introduced new research pathways for improving RTIL gas separations that focuses on decreasing the solubility of non-polar gases.