Is an ice-cream tub made of a single molecule?

Question

Background

In my answer to another question, I repeated a claim made to my class by my high school chemistry teacher. I didn't reference it, because the relevant FAQ suggests high school science can generally be assumed. However, the claim was, to my surprise, pooh-poohed. This is a follow-up question to allow it to be properly scrutinised.

Claims

• Plastic ice-cream tubs are typically made of low-density polyethylene (LPDE). [Ref]

• Polyethylene has a lot of cross-branching between the chains. Wikipedia states:

As with any polymer, the structure of the resulting substance defies molecular description due to cross branching of the chains

• The key claim: There is so much cross-branching, that a typical ice-cream tub (excluding the separate lid) consists of one single molecule of plastic. [Reference: My Year 11 Chemistry Teacher, whose name I have shamefully forgotten.]

I never had any reason to doubt these claims until recently. Are they true?

Answer 1

This is a very good question but one where it isn't the principle that's wrong just the detail.

Polymerization reactions typically produce very large molecules but not so large that a single molecule would make up as much material as a whole ice cream tub. One data sheet on LDPE tells us that the typical molecular weight of the industrial product is 90,000 (some polymers are much bigger than this). (see here for an illuminating description relevant to LDPE).

For non-chemists molecular weights are (simplifying slightly) the weight relative to a single hydrogen atom. Carbon is 12 on this scale and ethylene (the monomer from which the plastic is made which consists of 2 carbons and 4 hydrogens) is 32. This mean that a typical molecule of the plastic is (crudely) made from a little under 3,000 ethylene molecules. The other fact you need to know is that there are about 6 x 10^23 hydrogen atoms in a gramme of hydrogen (see the wikipedia definition of Avogadro's number). Simple mathematics tells us that a gramme of LDPE will contain roughly 6.7 x 10^18 molecules so that is the order of the number in a tub for ice cream which, I expect, weighs a few grammes.