Propose a mechanism for reaction of the first three propylene units in the polymerization of propylene in the presence of a peroxide.

Ozonolysis can be applied selectively to different types of carbon–carbon double bonds. The compound shown below contains two vinyl ether double bonds, which are electron-rich because of the electron-donating alkoxy groups. Ozone reacts more quickly with electron-rich double bonds and more slowly with hindered double bonds. At −78 °C, this compound quickly adds two equivalents of ozone. Immediate reduction of the ozonide gives a good yield of a single product. Show the expected ozonolyis product, and label the functional groups produced, some of which are not typical from ozonolysis of simple alkenes.

When styrene (vinylbenzene) is commercially polymerized, about 1–3% of 1,4-divinylbenzene is often added to the styrene. The incorporation of some divinylbenzene gives a polymer with more strength and better resistance to organic solvents. Explain how a very small amount of divinylbenzene has a marked effect on the properties of the polymer.

The cationic polymerization of isobutylene (2-methylpropene) is shown in Section 8-16A. Isobutylene is often polymerized under free-radical conditions. Propose a mechanism for the free-radical polymerization of isobutylene.

The following cyclization has been observed in the oxymercuration-demercuration of this unsaturated alcohol. Propose a mechanism for this reaction.

Predict the product of formula C₇H₁₃BrO from the reaction of this same unsaturated alcohol with bromine. Propose a mechanism to support your prediction.

A graduate student attempted to form the iodohydrin of the alkene shown below. Her analysis of the products showed a good yield of an unexpected product. Propose a mechanism to explain the formation of this product.