Propose a mechanism for the acid-catalyzed hydration of 1 -methylcyclohexene to give 1 -methylcyclohexanol. Which step in your mechanism is rate determining?

The process where the double bond in an alkene molecule accepts a proton, H+, is known as protonation. In an acid-catalyzed hydration reaction, this is often the first and one of the most vital steps.

For clarification, let's visualize 1-methylcyclohexene as two carbon atoms connected by a double bond. When this molecule is introduced to an acid, like sulfuric acid, the highly electron-rich area of the double bond is attracted to the positively charged hydrogen atom (the proton). When the alkene 'grabs' this proton, the double bond 'breaks,' reallocating one of its electrons to form a new bond with the hydrogen. This results in the formation of a carbocation, a species with a positively charged carbon atom that is eager for further reactions.

This step is crucial because the stability of the carbocation formed affects the overall rate of the reaction. More stable carbocations form quicker and with less energy compared to their less stable counterparts. Therefore, certain alkenes with the ability to form more stable carbocations will undergo hydration more readily.

Once the carbocation is formed by protonation, it's primed for the next step: the nucleophilic attack. A nucleophile is a molecule or ion that donates a pair of electrons to form a new chemical bond. In this context, water (H2O) acts as our nucleophile.

Water is considered a nucleophile because the oxygen atom holds a pair of non-bonding electrons. The carbocation created from the protonation is positively charged and thus electron-poor, making it very attractive to electron-rich species. The non-bonding electrons on water's oxygen atom quickly associate with the carbon atom in the carbocation, establishing a new carbon-oxygen bond. This reaction transforms the carbocation into a protonated alcohol, which is, in our example, a protonated 1-methylcyclohexanol.

This step is generally quite fast, as the reactive carbocation is highly willing to accept electrons from the water molecule, making the nucleophilic attack happen readily once the protonated intermediate is in place.

In a multi-step reaction, the rate-determining step (RDS), often referred to as the rate-limiting step, is the slowest phase that determines the speed at which the reaction overall proceeds. It is essentially the 'bottleneck' of the reaction mechanism.

Identifying the RDS is a bit like finding the slowest runner in a relay race. No matter how fast the other runners are, the race progresses at the pace of the slowest runner. In our hydration reaction, the step in which the carbocation is formed is usually the RDS because forming a high-energy, unstable intermediate (the carbocation) requires surmounting a significant energy barrier. This means that the formation of the carbocation from the alkene and the proton will most often be slower than the subsequent nucleophilic attack by water and final deprotonation steps.

Understanding the rate-determining step is critical when developing synthetic processes or studying reaction mechanisms. By knowing which step limits the reaction, chemists can modify conditions or reactant structures to optimize reaction rates and yields, ultimately guiding the efficiency of chemical processes.