The KLRR perturbation theory has been initially proposed by Kang et al. in order to compute the equation of state (EOS) of a fluid of soft spheres represented by an EXP-6 potential. Victorov and Gubin have recently improved this method and they showed that, compared to other theories (namely HMSA/C and MCRSR), this improved KLRR theory turns out to be more accurate. In the first part of this paper, the comparison is extended to a larger range of temperature and stiffness of potential. Then, in order to use such a perturbation theory in a thermochemical code, the treatment of mixtures has to be handled since the KLRR method is expressed for a pure fluid. Usually, the Van-der-Waals one fluid mixing rule (VdW-1f) is employed. It consists in averaging the mixture by an effective fluid. We also intend here to re-evaluate this well-known and largely used model.