Question

Polymerization. Consider a polymerization reaction in the gas phase in which \(n\) moles of identical monomers are in equilibrium with one mole of chains of \(n\)-mers: $$ n(0) \stackrel{\frac{k}{\longrightarrow}}{\underbrace{0-0-0-0}_{n \text { monomers }}} $$ (a) Do you expect typical polymerization processes to be driven or opposed by enthalpy? By entropy? What are the physical origins of these enthalpies and entropies? (b) Do you expect polymerizations to be exothermic (giving off heat) or endothermic (taking up heat)? Explain the explosions in some polymerization processes. (c) Are polymerization equilibrium constants for long chains more or less sensitive to temperature than those for shorter chains?

Short answer

Polymerizations tend to be driven by exothermic enthalpy changes and opposed by entropy decreases. Explosions result from rapid heat release. Equilibrium constants are more sensitive to temperature for long chains.

Step-by-step solution

Analyzing Enthalpies and Entropies in Polymerization

Enthalpy (∆H) typically relates to bond formation and breakage during polymerization. Polymerization processes usually involve breaking weaker intermolecular forces in monomers and forming stronger covalent bonds in the polymer chain, which releases energy, suggesting an exothermic process (negative ∆H). Entropy (∆S) denotes the disorder of the system. In polymerization, the system’s disorder decreases as individual monomers form an ordered polymer chain, suggesting a decrease in entropy (negative ∆S).

Determining the Exothermic or Endothermic Nature

Polymerizations are often exothermic as the formation of stable chemical bonds in polymers releases energy. Exothermic reactions release heat to the surroundings, which can sometimes lead to explosions if heat is not properly dissipated, especially in bulk polymerizations where the reaction rate is high, resulting in rapid heat generation.

Temperature Sensitivity of Polymerization Equilibrium Constants

The equilibrium constant (K) is influenced by temperature changes. For long chains, the process involves more bond formations and breaking of intermolecular forces compared to shorter chains. Hence, the equilibrium constant for long chains is more sensitive to temperature changes because of the larger change in enthalpy and entropy terms involved in forming longer chains.

Key concepts

enthalpy in polymerization

In the context of polymerization, enthalpy (∆H) represents the heat content associated with the bond formation and bond breakage in the reaction. When individual monomers polymerize to form a longer polymer chain, weaker intermolecular bonds in the monomers are replaced by stronger covalent bonds in the polymer chain. This bond formation generally releases energy.

This results in an exothermic process, where ∆H is negative, indicating that polymerization releases heat. The physical origin of this exothermic behavior comes from the energy dynamics when transitioning from weaker bonds in monomers to stronger covalent bonds in the polymer. Exothermic reactions release heat to the surroundings, which if not dissipated properly, especially in bulk polymerizations, might lead to rapid heat buildup and potential explosions.

Hence, typical polymerization processes are driven by a decrease in enthalpy.

entropy in polymerization

Entropy (∆S) is a measure of randomness or disorder in a system. During polymerization, many individual monomer units join to form a single, ordered polymer chain. This process reduces the overall entropy of the system, making ∆S negative.

The physical origin of this entropy change is the transition from many dispersed, freely moving monomers to one relatively ordered polymer chain. This ordering reduces the randomness in the system. Thus, polymerization is typically opposed by entropy because the system moves from a higher entropy state (many individual monomers) to a lower entropy state (one polymer chain).

Therefore, polymerization processes typically exhibit a decrease in entropy.

temperature sensitivity of equilibrium constants

The equilibrium constant (K) of polymerization reactions is influenced by changes in temperature. According to the van 't Hoff equation, the sensitivity of K to temperature is related to the changes in enthalpy and entropy.

For long polymer chains, the polymerization process involves more extensive bond formations and the breakdown of intermolecular forces compared to shorter chains. This larger involvement of enthalpy and entropy changes makes K more sensitive to temperature changes for long chains.

In essence, temperature fluctuations have a more pronounced effect on the equilibrium constants of long-chain polymerizations compared to shorter chains, due to the different magnitudes in ∆H and ∆S involved.