# Calculating the enthalpy of polymerisation of ethylene given the bond strengths

Given the average bond dissociation enthalpies of a $\ce{C-C}$ bond (say $x$) and a $\ce{C=C}$ bond (say $y$), find the enthalpy of the following polymerisation reaction (per mole of ethylene):

$$\ce{nCH_2=CH_2 -> [-CH2-CH2 -]_n}$$

where $n$ is a large integer and $x, y$ are in $\pu{kJ/mol}$.

According to me, this should simply be $y-x$ as for every double bond broken, a single bond is formed. But the source book of this problem states the answer to be $y-2x$ claiming that for every double bond broken, 2 single bonds are formed.

How is this possible?

Thus, the enthalpy is in fact $y-2x$