Polymers: Numerical Problems Set (1)

Question

A sample of polyethylene has number-average molecular weight $\bar{M}_n = 28000$ g/mol. The repeating unit ($-\text{CH}_2-\text{CH}_2-$) has molar mass $28$ g/mol. Find the degree of polymerisation.

Solution — Step by Step

Why This Works

The polymer chain is built by stringing together monomer units. The total molecular weight is approximately $n \times M_{\text{monomer}}$ (small end-group corrections matter for short chains but are negligible for $n = 1000$).

For polyethylene, each $-\text{CH}_2-\text{CH}_2-$ comes from one ethylene molecule ($\text{CH}_2=\text{CH}_2$, $M = 28$). So $n$ also equals the number of ethylene molecules incorporated.

Alternative Method

If given the mass average $\bar{M}_w$ instead, divide by the same monomer mass to get the weight-average degree of polymerisation. The two are related by the polydispersity index $\bar{M}_w / \bar{M}_n \geq 1$.

Common Mistake

Students sometimes use molecular weight of ethylene gas including a leading $\text{CH}_2=\text{CH}_2$ formula but compute it as $14$ instead of $28$. Each ethylene contributes 2 carbons and 4 hydrogens, total $24 + 4 = 28$ g/mol. Don’t undercount.