Explain the difference in molecular structure between Structure I and Structure II gas hydrates.

Gas hydrates are ice-like crystalline solids formed when water molecules create a cage-like structure around small gas molecules. The primary difference between Structure I (sI) and Structure II (sII) gas hydrates lies in the size and arrangement of these water cages, which dictates the types of gas molecules they can encapsulate. Structure I hydrates have two types of cages: a small cage with 12 pentagonal faces (5^12, meaning each face is a pentagon and there are 12 of them) and a larger cage with 12 pentagonal faces and 2 hexagonal faces (5^126^2). These cages are relatively small, accommodating smaller gas molecules like methane, ethane, carbon dioxide, and hydrogen sulfide. Structure II hydrates, on the other hand, also have two cage types but with different sizes and shapes. They consist of a smaller cage with 12 pentagonal faces (5^12), similar to sI, and a larger, more spacious cage with 12 pentagonal faces and 4 hexagonal faces (5^126^4). The larger cage in sII hydrates can accommodate larger gas molecules that cannot fit into the sI cages, such as propane, isobutane, and nitrogen. In summary, Structure I hydrates are characterized by smaller cages suitable for smaller gas molecules, while Structure II hydrates contain both smaller and larger cages, allowing them to incorporate larger gas molecules. The specific gas composition and thermodynamic conditions determine which hydrate structure will form.