Chemistry

Chemistry

Problem

Polymerization of ethene to poly(ethylene) can be approximated by the simplified reaction n C2_2H4_4(g) → (–C2_2H4_4–)n_n(s). The process is characterized by ΔH<0\Delta H < 0 and ΔS<0\Delta S < 0; precise numerical values are omitted here for simplicity. (a) Without performing numerical calculations, predict whether the polymerization is thermodynamically favorable at very low temperatures. Justify your prediction in terms of the signs of ΔH\Delta H and ΔS\Delta S. (b) Predict how increasing the reaction temperature affects the spontaneity of the polymerization. Explain your reasoning using appropriate thermodynamic arguments. (c) Industrial polymerizations are often carried out under conditions of elevated pressure as well as moderate temperature. Discuss qualitatively how high pressure can influence the Gibbs free energy change for this gas-to-solid transformation and thereby affect the extent of reaction.
Intuitive explanation

This problem tests your understanding of how entropy and enthalpy compete to determine spontaneity. Even though the reaction releases heat (ΔH<0\Delta H < 0, favorable), polymerization decreases disorder dramatically—many gas molecules become locked into one solid (ΔS<0\Delta S < 0, unfavorable). The key insight is recognizing that ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S, so at low temperatures the negative enthalpy dominates, making the reaction spontaneous, but at high temperatures the −TΔS-T\Delta S term grows and could overcome it. This is why polymers are typically made at lower temperatures.

Intuitive explanation

This problem tests your understanding of how entropy and enthalpy compete to determine spontaneity. Even though the reaction releases heat (ΔH<0\Delta H < 0, favorable), polymerization decreases disorder dramatically—many gas molecules become locked into one solid (ΔS<0\Delta S < 0, unfavorable). The key insight is recognizing that ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S, so at low temperatures the negative enthalpy dominates, making the reaction spontaneous, but at high temperatures the −TΔS-T\Delta S term grows and could overcome it. This is why polymers are typically made at lower temperatures.

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