The speed of sound in gaseous 1,1,1-trifluoroethane has been obtained at temperatures between (270 and 370) K from measurements of the resonance frequency of the radial modes of a spherical resonator. Ideal gas heat capacities and acoustic virial coefficients have been calculated from the results. The acoustic data have been used to determine density virial coefficients with a hard-core square-well intermolecular potential equation of state. A Helmholtz energy equation of state is proposed, whose parameters are directly fitted to the present speed of sound data and uses the acoustically determined temperature dependence of the perfect gas heat capacity. The Helmholtz equation so obtained compares favourably with other conventional methods and provides a high accuracy equation specific for the vapour phase of the fluid. The performance of the equation, in terms of the accuracy of the thermodynamic properties derived from it, has been determined by comparison of predicted densities with available experimental data. The equation of state shows very good extrapolation behaviour beyond the range of temperatures and pressures of the experimental data to which it was fitted.