Metal organic frameworks(MOFs) are a class of crystalline materials utilized in gas storage, chemicalsensing, and other engineering applications. Recently chemists have begun synthesizing MOFs withmoving parts in order to further these applications. A wide array of dynamic MOFs have been created andtheorized. Among them is the interlocking of a ring shaped molecule on the dumbbell like strut of a metalorganic framework called a rotaxane molecular shuttle. Recently a rotaxane molecular shuttle(RMS) MOFwas synthesized for the first time. This RMS-MOF is called UWDM-4 and is a proof of concept materialfor a mechanically interlocked molecule MOF with a moving shuttle harbored in its pores. In order tomotivate further synthesization and experimentation with RMS-MOFs we pose a statistical mechanicalmodel based on the langmuir model of gas adsorption that models the potential for both the shuttle-gascompetition for binding sites and the entropic effects of the moving shuttle to affect gas adsorption.Our model is advantageous in that it can be solved analytically while allowing the two aforementionedeffects to be explored. We defined a usable space of parameters for our model we termed material space,consisting of the bonding energies of the gas at two discrete stations on the strut of the MOF, and anenergetic penalty for the rotaxane to occupy one of the binding sites(this allows us to model the shuttlefavoring one side). We then compared adsorption properties to a single site MOF with the same expectedgas occupancy at a given temperature. We found that an RMS-MOF located properly in material spaceto be less temperature sensitive to adsorption and to have a smaller heating effect from gas adsorption.Both allow for more efficacious gas storage.