The study of clathrates as a solution for CO₂ capture and treatment has received significant scientific attention, as has their use in water desalination, a critical issue in many countries due to the scarcity of potable water. This work proposes a thermodynamic modeling approach compared with experimental data for the treatment of clathrate hydrates with N₂–CO₂ gas mixtures, using cyclopentane as an effective promoter. The binary equilibria among the considered substances were studied using the PPR78 model as an alternative to the simple Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) models. Thanks to the modifications introduced to the PR model, using PPR78 results in absolute standard deviations below 2%, making it an optimal model for the considered binary equilibria.