Question

Consider the polymerization of ethylene to polyethylene. (Section 12.6) (a) What would you predict for the sign of the entropy change during polymerization ( \(\Delta S_{\text {poly }}\) )? Explain your reasoning. (b) The polymerization of ethylene is a spontaneous process at room temperature. What can you conclude about the enthalpy change during polymerization \(\left(\Delta H_{\text {poly }}\right)\) ? (c) Use average bond enthalpies (Table 8.4) to estimate the value of \(\Delta H_{\text {poly per ethylene }}\) monomer added. (d) Polyethylene is an addition polymer. By comparison, Nylon 66 is a condensation polymer. How would you expect \(\Delta S_{\text {poly }}\) for a condensation polymer to compare to that for an addition polymer? Explain.

Short answer

In the polymerization of ethylene to polyethylene, the entropy change \(\Delta{S}_{\text{poly}}\) is negative as the system becomes more ordered and the degrees of freedom decrease. The enthalpy change during polymerization (\(\Delta H_{\text {poly }}\)) is also negative (exothermic) since the process is spontaneous at room temperature. The estimated value of \(\Delta H_{\text {poly per ethylene }}\) per ethylene monomer added is 331 kJ/mol. Comparing the entropy change for addition and condensation polymers, the magnitude of the negative entropy change for a condensation polymer like Nylon 66 is less than that for an addition polymer like polyethylene, as the release of a small molecule during the condensation polymerization process increases the overall entropy of the system.

Step-by-step solution

(a) Prediction of the Sign of Entropy Change #

In the polymerization of ethylene to polyethylene, individual ethylene molecules combine to form a long-chain polyethylene molecule. To predict the sign of the entropy change \(\Delta{S}_{\text{poly}}\), we should consider the change in the number of molecules and their arrangements (degrees of freedom). Initially, there are many small ethylene molecules (C2H4) freely moving in the system. After polymerization, these molecules form a single large polyethylene molecule that occupies less space. The degrees of freedom for the large polyethylene molecule are significantly less compared to the smaller individual ethylene molecules. Since the system becomes more ordered during this process, the entropy change should be negative (Δ𝑆poly < 0).

(b) Enthalpy Change during Polymerization #

The polymerization of ethylene is a spontaneous process at room temperature. According to the Gibbs free energy equation: ΔG = ΔH - TΔS For a spontaneous process, ΔG is negative. Also, we already determined that ΔS is negative. If ΔG must be negative for the process to occur spontaneously, and TΔS is positive (due to the negative Sign of entropy change and the positive T), this means that ΔH should also be negative to ensure that ΔG remains negative. Therefore, the enthalpy change during polymerization (Δ𝐻poly) is negative (exothermic).

(c) Estimation of Δ𝐻poly per Ethylene Monomer Added #

To estimate the value of \(\Delta H_{\text {poly per ethylene }}\), we will use the average bond enthalpies (from Table 8.4) of the bonds that are broken and formed during the polymerization process: 1. C=C double bond in each ethylene molecule is broken: average bond enthalpy = +612 kJ/mol 2. C-H bond in each ethylene molecule is broken: average bond enthalpy = +413 kJ/mol 3. Two new C-C single bonds are formed in the polymer: average bond enthalpy = -347 kJ/mol (multiply by 2 for both bonds) Note that each C=C bond is replaced by two C-C bonds. Summing up all the bond enthalpy changes: Δ𝐻poly per ethylene monomer added = (+612 + 413 - 2 × 347) kJ/mol = 331 kJ/mol

(d) Comparison of ΔS for Addition and Condensation Polymers #

In the case of addition polymers like polyethylene, individual monomers are directly combined to form the polymer chains. In condensation polymers like Nylon 66, two different monomers react together to form the polymer, and a small molecule (e.g., water) is released as a byproduct. Considering the entropy change during polymerization, ΔS for both addition and condensation polymers will be negative because the system becomes more ordered as monomers combine to form a polymer. However, the release of the small molecule during the condensation polymerization process partially compensates for the reduction in entropy. The degrees of freedom for this small molecule increase the overall entropy of the system. Thus, the magnitude of the negative entropy change for a condensation polymer like Nylon 66 will likely be less than that for an addition polymer like polyethylene. In other words, Δ𝑆poly (condensation polymer) > Δ𝑆poly (addition polymer), with both values being negative.

Key concepts

Entropy Change

During the process of polymerization, entropy changes are crucial to understanding how molecular order is affected. When ethylene transforms into polyethylene, individual ethylene molecules come together to form a much larger, more organized polyethylene chain. This means that the system transitions from a state with many free-moving individual molecules, to a state where those molecules are part of one large structure. This transition leads to a decrease in the degrees of freedom, as the large molecule is more ordered and less flexible.
The decreased movement and higher organization cause a reduction in entropy, indicating a negative entropy change (\(\Delta S_{\text{poly}} < 0\)). This is because the increase in order from individual, freely moving molecules to a structured polymer chain results in a reduction in randomness and disorder, which is what entropy measures.

Enthalpy Change

In polymerization, especially when considering spontaneous processes like the transformation of ethylene to polyethylene, enthalpy changes offer insight into the energy flow of the reaction. Because the polymerization of ethylene is spontaneous at room temperature, we use the Gibbs free energy equation to analyze enthalpy: \( \Delta G = \Delta H - T \Delta S \).
For a reaction to be spontaneous, \( \Delta G \) must be negative. Since the entropy change \( \Delta S \) is negative, the term \( T \Delta S \) is positive, meaning that \( \Delta H \) needs to be negative as well for \( \Delta G \) to remain negative. This results in the polymerization being exothermic, where energy is released, making \( \Delta H_{\text{poly}} < 0 \).
The conclusion is that the energetically favorable nature of the polymerization, as indicated by a negative enthalpy change, results in heat being released into the surroundings.

Addition vs. Condensation Polymers

Polymerization involves distinct types mainly categorized as addition and condensation. In addition polymers, like polyethylene, monomers join without the loss of any atoms, directly forming long chains. However, in condensation polymers, exemplified by Nylon 66, monomers come together, and a small molecule, such as water, is eliminated as a byproduct.
The removal of a molecule during condensation affects the overall entropy differently compared to addition polymerization. While both processes result in a more ordered structure (\(\Delta S_{\text{poly}}\) is negative for both), the small byproduct adds some disorder.
Thus, the absolute value of the entropy decrease is reduced slightly in condensation polymerizations due to the formation of smaller molecules, making the negative change in entropy less pronounced than in addition polymerization. Therefore, \(\Delta S_{\text{poly}}\) for condensation polymers tends to be larger (less negative) than that for addition polymers.

Spontaneous Process at Room Temperature

The term spontaneous describes a process that occurs without any external influence, and in the case of polymerization at room temperature, it is an important consideration. For ethylene’s polymerization into polyethylene to be spontaneous, specific thermodynamic conditions must be met.
The Gibbs free energy (\(\Delta G\)) provides insight into whether a process is spontaneous. If \(\Delta G\) is negative, the process will proceed without external help. As discussed, \(\Delta S_{\text{poly}}\) is negative, which increases the \(\text{T} \Delta S\) term positively, and because \(\Delta H_{\text{poly}}\) is also negative, \(\Delta G\) becomes negative.
This combination of a negative enthalpy change and the effect of temperature on the entropy change ensures that polymerization is spontaneous at room temperature, leading to the natural formation of polyethylene from ethylene.