How would polyethylene have the VSEPR shape of tetrahedral?

To understand why polyethylene can have a tetrahedral shape according to the VSEPR theory, let's first break down the components involved.

Polyethylene is a polymer made up of repeating units called monomers. Each monomer consists of two carbon atoms bonded together, and each carbon atom in the monomer forms single bonds with two hydrogen atoms.

The VSEPR (Valence Shell Electron Pair Repulsion) theory predicts molecular geometries based on the repulsion between electron pairs around the central atom. In this theory, each bonded or lone pair of electrons repels others, resulting in specific molecular shapes.

For polyethylene, we can focus on one monomer as it represents the structural unit for the entire polymer. In the monomer, each carbon atom has four electron groups around it (two single bonds and two lone pairs) due to its tetrahedral arrangement. According to VSEPR, the electron groups are positioned as far apart as possible to minimize repulsion.

Based on this, the monomer unit of polyethylene has a tetrahedral shape around each carbon atom. As these monomers are linked together to form the polymer, the tetrahedral shape is maintained throughout the polyethylene chain.

So, the tetrahedral shape of polyethylene is a result of the VSEPR theory applied to the carbon atoms in the monomer units.

You may be thinking that the double bond makes it a trigonal planar structure but when ethylene (with double bonds) is polymerized the double bond is broken and polyethylene consists of single bonds and that makes it tetrahedral. :-)