The addition polymerization of ethylene to form linear high-density polyethylene is represented by t

Question

The addition polymerization of ethylene to form linear high-density polyethylene is represented by the equation:\ $n	ext{CH}_2=	ext{CH}_2(g) ightarrow -(	ext{CH}_2-	ext{CH}_2)_n-(s)$, where $n$ is a very large integral degree of polymerization. Given that the average bond dissociation enthalpies at $298	ext{ K}$ for $	ext{C=C}$ double bonds and $	ext{C-C}$ single bonds are $+590	ext{ kJ mol}^{-1}$ and $+331	ext{ kJ mol}^{-1}$, respectively, calculate the magnitude of the standard enthalpy of polymerization per mole of ethylene ($|\Delta H^\circ_{	ext{poly}}|$ in $	ext{kJ mol}^{-1}$).

Professor PC Thomas Classes · Answer

During the addition polymerization of ethylene, each monomer unit ($	ext{CH}_2=	ext{CH}_2$) undergoes the breakage of one carbon-carbon double bond ($	ext{C=C}$) and forms two single covalent half-bonds connecting it to adjacent monomer units in the polymer chain. Two half-bonds per monomer are structurally and energetically equivalent to the formation of one full $	ext{C-C}$ single bond per ethylene molecule. However, in the monomer itself, there is no $	ext{C-C}$ single bond, whereas in the repeating unit $-(	ext{CH}_2-	ext{CH}_2)-$, there is one internal $	ext{C-C}$ single bond plus two external half-bonds (totaling two $	ext{C-C}$ single bonds formed per monomer unit). Therefore, per mole of ethylene polymerized: $1	ext{ mole}$ of $	ext{C=C}$ bonds is broken (endothermic) and $2	ext{ moles}$ of $	ext{C-C}$ single bonds are formed (exothermic). The enthalpy of polymerization is: $\Delta H^\circ_{	ext{poly}} = 	ext{BE}(	ext{C=C}) - 2 	imes 	ext{BE}(	ext{C-C}) = 590 - 2(331) = 590 - 662 = -72	ext{ kJ mol}^{-1}$. Thus, the magnitude is $72	ext{ kJ mol}^{-1}$.