The activity coefficients of the binary mixtures ethanol + 1-butanol, ethanol + octane, and 1-butanol + octane were determined at temperatures of (308.15, 313.15, and 318.15) K. The determination of the vapor phase composition at equilibrium was carried out using headspace gas chromatography analysis. Multiple headspace extraction was used to calibrate the headspace gas chromatograph. Comparison of the phase diagrams produced using standard Legendre orthogonal polynomial techniques with phase diagrams from the literature showed good agreement. The composition of the azeotropes were reported, where applicable.