A method is proposed for predicting vapor pressures, liquid densities and vaporization enthalpies of pure compounds in a wide temperature range between the triple point and the critical point. The method relies on the application of a previously proposed multicomponent equation of state which is based on well known properties of pure components and universal behavior of fluids. Simple rules are given for the calculation of all eight constants of the chosen equation of state which requires as input data the critical point and the normal boiling temperature only. The reliability of the new procedure is discussed on the basis of results obtained by predicting the properties of several well studied compounds belonging to the following classes: hydrocarbons, alcohols, acids and polar compounds not strongly associated. The method compares favorably with the Riedel equation for predicting the vapor pressures and with the Rackett equation for predicting the orthobaric densities. However, it only gives semi-quantitative results for the vaporization enthalpies of the C 5+ compounds. The method appears less sensitive to the inaccuracies of the critical values than literature methods.