For the linear alkanes from methane to dodecane, make a table of the number of nuclei, the number of independent stretching motions between bonded nuclei (i.e. the number of unique pairs of bonded nuclei) and the number of through-space van der Waals interactions. Use the criterion of three or more nuclei bonded between the nuclei undergoing vdW interactions (total of five nuclei, including the interacting nuclei). Use this data to make a log-log plot of the number of stretches and vdW interactions as a function of number of constituent atoms in the molecule. Use this plot to estimate the scaling of each with respect to the number of constituent atoms, using the power function form of the trendline. Which one will become very large with molecular size the fastest, and why? Determine the sequential pattern for increase in #of stretches and #vdW with N, and use this to extend the data to N=40. Redo the plots and see how the power dependences change. Does this change your conclusion at all about which will increase faster?