In this paper a generalized attraction term is investigated with respect to the resulting phase behaviour in pure substances and binary mixtures. For the calculation of phase equilibria the attraction term is combined with the van der Waals (vdW)-repulsion and the Carnahan-Starling (CS)-repulsion. The chosen parametrization of the attraction term allows a general discussion of the mathematical structure of an attraction term including a wide range of attractive virial coefficients. In the investigation of the pure substance properties it is focused on the values of the critical compressibility factor, the critical packing fraction and the close packing fraction. These properties together determine the shape of the liquid-gas coexistence curve. The performance of the attraction term for modeling binary mixtures has been traced by the liquid-liquid closed-loop immiscibility area in the global phase diagram. This phenomenon is very sensitive to changes in the equation of state and a suitable property for characterizing an equation of state with respect to its binary phase behaviour.