The given question describes a polymer 'X' that consists of linear molecules, is closely packed, and is prepared in the presence of triethylaluminium and titanium tetrachloride under low pressure. To identify this polymer, let's analyze the information provided step-by-step:
- Tacticity and Linear Structure: The description mentions that the polymer consists of linear molecules, which are closely packed. This indicates high crystallinity and density, typical of certain types of polyethylene.
- Synthesis Method: The polymer is prepared using triethylaluminium and titanium tetrachloride. This is a classic Ziegler-Natta catalyst system used for synthesizing high-density polyethylene (HDPE). This process is typically conducted under low pressures, contributing to linear, closely packed polymer chains.
- Ruling Out Other Options:
- \(\text{Polyacrylonitrile}\): Predominantly used to make acrylic fibers, it does not use the described catalyst or reaction conditions.
- \(\text{Polyterephthalate}\): Commonly known as polyethylene terephthalate (PET), it is not produced using Ziegler-Natta catalysts. It is typically formed through polycondensation reactions.
- \(\text{Low density polyethylene (LDPE)}\): LDPE is produced at high pressures using free radical polymerization, resulting in branched polymers. Thus, it does not match the description.
- Correct Answer: Based on the synthesis method and linear, closely packed structure, the polymer described is \(\text{High-density polyethylene (HDPE)}\).
Therefore, the correct answer is High Density Polyethylene.