•FST has been successfully applied to six binary ionic liquid mixtures.•Only ρ and u have been used to compute a number of useful and important thermodynamic and thermoacoustical properties.•The validity of FST for pure ionic liquids and their binary mixtures has been tested from the theoretical values of σ and u.•The magnitudes of u, Pint, E and ΔHv, ced, δ and n obtained from FST demonstrate the excellent agreements. For the first time, widely employed Flory’s statistical theory of binary liquid mixtures has been successfully applied to six binary ionic liquid mixtures. Only density and sound speed data have been used to compute a number of useful and important thermodynamic and thermoacoustical properties of DEAA + H2O, DEAS + H2O, TEAA + H2O, TEAS + H2O, TMAA + H2O and TMAS + H2O at 298.15 K. Experimental values of density and sound speed were taken from the recent work of Venkatesu et al J P C 118B (2014) 5971. Their data are rare, very precise and accurate. The validity of FST for pure ionic liquids (RTIL’s) and their binary mixtures has been tested from the theoretical values of surface tension and sound speed. The magnitudes of sound speed, internal pressure, energy and heat of vaporization, cohesive energy density, solubility parameter and polarity factor obtained from FST demonstrate the excellent agreement with the available values of the experimental properties.