The full second-order perturbation expansion of the convex molecule fluid, involving new approximations for the radial distribution function of hard spheres and for the surface-to-surface correlation function of the hard convex bodies, has been developed. Parameters of the Kihara generalized pair potential have been determined for n-alkanes in a series from methane up to hexadecane (modeled as hard rods) by fitting the expressions for the residual thermodynamic functions obtained within the theory to the phase equilibrium-data of the individual real compounds along their vapor-liquid coexistence curve. All the Kihara pair potential parameters, i.e., the particle size parameter, the potential depth, the rod length, characterizing the hard core of the model convex molecule, and (for the lower alkanes) also the parallel hard body thickness, were expressed in a general and simple way as functions of the number of carbon atoms in a molecule over the entire range of n-alkanes investigated. The results represent a successful correlation scheme making it possible to represent the bulk thermodynamic data of pure real. substances on the basis of molecular parameters.