In this work, we have measured the thermodiffusion coefficient of different n-alkane binary mixtures at several concentrations using the thermogravitational technique. In particular, we have studied the n-dodecane/n-heptane system as a function of composition and other systems covering a large range of mass differences and concentration at 25 degrees C and 1 atm. The results show that for any concentration the thermodiffusion coefficient of n-alkane mixtures is proportional to the mass difference between the components and to the ratio of the thermal expansion coefficient and viscosity of the mixture. The obtained equation allows us to determine the infinite dilution values of the thermodiffusion coefficient. We compare these values with recent experimental results in dilute polymer solutions and analyze the Brenner theory of thermodiffusion. Finally, it is shown that the thermodiffusion coefficient depends linearly with the mass fraction, and it can be calculated from the viscosity and thermal expansion of the pure components.