We have obtained the excess chemical potential of methane in water, over a broad range of temperatures, from computer simulation. The methane molecules are described as simple Lennard-Jones interaction sites, while water is modeled by the recently proposed TIP4P/2005 model. We have observed that the experimental values of the chemical potential are not reproduced when using the Lorentz-Berthelot combining rules. However, we also noticed that the deviation is systematic, suggesting that this may be corrected. In fact, by introducing positive deviations from the energetic Lorentz-Berthelot rule to account indirectly for the polarization methane-water energy, we are able to describe accurately the excess chemical potential of methane in water. Thus, by using a model capable of describing accurately the density of pure water in a wide range of temperatures and by deviating from the Lorentz-Berthelot combining rules, it is possible to reproduce the properties of methane in water at infinite dilution. In addition, we have applied this methane-water potential to the study of the solid methane hydrate structure, commonly denoted as sI, and find that the model describes the experimental value of the unit cell of the hydrate with an error of about 0.2%. Moreover, we have considered the effect of the amount of methane contained in the hydrate. In doing so, we determine that the presence of methane increases slightly the value of the unit cell and decreases slightly the compressibility of the structure. We also note that the presence of methane increases greatly the range of pressures where the sI hydrate is mechanically stable.