In this work, a model for the thermal conductivity of nonpolar and polar substances is developed based on the geometric similitude concept between the P-v (molar volume)- -T and T-k (thermal conductivity)- -P plots. The Redlich-Kwong equation of state is used to perform the geometric similitude. The parameters of the model are estimated by fitting experimental data of saturated liquid and saturated vapor. Generalized expressions in terms of the normal boiling point are proposed for the parameters of n-alkanes and n-alcohols. The calculated average absolute deviations are 7.63 and 8.55%, respectively, for the n-alkanes and the n-alcohols used to develop the generalized expressions. Also, some predictive calculations are performed, and deviations below 10.62 and 9.42% are obtained for n-alkanes and n-alcohols, respectively. In total, 2412 experimental data (952 correlated data and 1460 predicted data) in the temperature range of 95- to 645.5 K and pressures below 906.4 bar have been considered. The empirical model has been extended to binary and ternary mixtures using several approaches. In total, 16 mixtures in the temperature range between 287.55 and 345.48 K at 1.01 bar are evaluated. The deviations are below 4.63% when one binary interaction parameter is used. In general, the results indicate that the empirical model is simpler than the other models reported in the literature and generates adequate results.