Degree of polymerisation

This page walks through degree of polymerisation for SPM Chemistry, step by step: the formula you need, the units to watch, and a worked example.

When you use this

A polymer is a long chain of repeating units. The degree of polymerisation counts how many of those units are joined in one molecule, and SPM Chemistry tests it as a short calculation on addition polymers such as poly(ethene) and PVC.

The formula and units

n = relative molecular mass of the polymer / relative molecular mass of the repeating unit

• n is the degree of polymerisation, a pure number with no unit.
• For an addition polymer the repeating unit has the same relative molecular mass as the monomer, because forming the chain only opens the carbon-carbon double bond and loses no atoms.

Units. Relative molecular masses have no unit, so n has no unit either. Work out the monomer’s relative molecular mass from its formula using the relative atomic masses (C = 12, H = 1, Cl = 35.5).

Worked example 1 (easy)

Poly(ethene) is made from ethene, C₂H₄. A poly(ethene) molecule has a relative molecular mass of 28000. Find its degree of polymerisation. (C = 12, H = 1)

• Relative molecular mass of ethene = (12 x 2) + (1 x 4) = 28.
• n = 28000 / 28 = 1000.

Worked example 2 (medium)

PVC is made from chloroethene, C₂H₃Cl. A PVC molecule has a relative molecular mass of 125000. Find its degree of polymerisation. (C = 12, H = 1, Cl = 35.5)

• Relative molecular mass of chloroethene = (12 x 2) + (1 x 3) + 35.5 = 62.5.
• n = 125000 / 62.5 = 2000.

Worked example 3 (SPM level)

A sample of poly(propene) has a degree of polymerisation of 3000. Its monomer is propene, C₃H₆. Find the relative molecular mass of the poly(propene) molecule. (C = 12, H = 1)

• Relative molecular mass of propene = (12 x 3) + (1 x 6) = 42.
• relative molecular mass of polymer = n x monomer mass = 3000 x 42 = 126000.

This reverse calculation is common in the exam: given the degree of polymerisation, multiply by the repeating-unit mass to find the polymer’s relative molecular mass.

Why the repeating unit equals the monomer here

For an addition polymer the repeating unit and the monomer have the same relative molecular mass. When monomers add together, the only change is that a carbon-carbon double bond opens to form new single bonds along the chain; no atoms are added or removed. So you can use the monomer’s relative molecular mass directly as the mass of the repeating unit. This is a defining feature of addition polymerisation and is exactly what the calculation relies on.

Counting units, not bonds

The degree of polymerisation is a count of repeating units, so a value of 1000 means one thousand monomer units are joined in that chain. Real samples contain chains of different lengths, so the figure is an average for the sample rather than an exact count for every molecule. In the SPM syllabus you meet this idea for addition polymers, where each unit contributes the same mass, which keeps the arithmetic to the one clean division above. Understanding it also helps you answer questions that ask what the degree of polymerisation actually means, not just how to work out its value.

Common traps

• Using the wrong monomer formula. Get the relative molecular mass of the correct repeating unit; chloroethene is 62.5, not 28.
• Thinking the mass changes on polymerising. For an addition polymer it does not; the repeating unit mass equals the monomer mass.
• Dividing the wrong way. Degree of polymerisation is the large polymer mass divided by the small unit mass, so the answer is a large whole number.
• Adding a unit. The degree of polymerisation is just a count and carries no unit.

Our teachers have students first write the repeating unit and its relative molecular mass, then decide whether the question wants the degree of polymerisation or the polymer mass, so the single division goes the right way every time.