Arrange the following halides in the decreasing order of \(\mathrm{S}_{\mathrm{N}} 1\) reactivity. 1\. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl}\) 2\. \(\mathrm{CH}_{2}^{3}=\mathrm{CHCH}(\mathrm{Cl}) \mathrm{CH}_{3}\) 3\. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}(\mathrm{Cl}) \mathrm{CH}_{3}\) (a) \(1>2>3\) (b) \(2>3>1\) (c) \(2>1>3\) (d) \(3>2>1\)

Carbocation stability is a fundamental concept in organic chemistry, especially when discussing reaction mechanisms such as the SN1 reaction. A carbocation is a positively charged carbon atom, which is a highly reactive intermediate that can be formed during certain chemical reactions. The stability of a carbocation is crucial because it affects how quickly a reaction will proceed.

In terms of stability, carbocations can be classified as primary (attached to one other carbon), secondary (attached to two other carbons), or tertiary (attached to three other carbons). Typically, the more alkyl groups (carbon-containing groups) a carbocation has attached to the positively charged carbon, the more stable it is. This is due to both inductive effects, where the alkyl groups donate electron density towards the positively charged carbon, and hyperconjugation, where neighbouring sigma bonds share their electron density with the empty p-orbital of the carbocation.

Tertiary carbocations are the most stable, followed by secondary and then primary. This stability affects the rate of SN1 reactions because the formation of a more stable carbocation lowers the energy barrier for the reaction, making it faster. Therefore, when analyzing an SN1 reaction, it's essential to look at the carbon that forms the carbocation; its degree of substitution directly correlates with the reaction's reactivity.

Understanding the reactivity order of halides is key to predicting the outcomes of SN1 reactions. In SN1 reactions, the halide leaving group departs to form a carbocation intermediate, and the reactivity is heavily influenced by how easily the halide can leave. Several factors play into this, including the strength of the carbon-halogen bond, the size of the halide, and its ability to stabilize the negative charge it acquires upon leaving.

The general order of reactivity for halides in SN1 reactions is iodide (I) being the most reactive, followed by bromide (Br), and then chloride (Cl), with fluoride (F) being the least reactive. Larger halide ions, like iodide, form weaker bonds with carbon and can more easily stabilize the negative charge when they leave due to their larger size and corresponding better ability to disperse the negative charge.

For the specific exercise regarding the given compounds, the reactivity order isn't about the type of halide (as they are all chlorides), but rather about the nature of the carbon to which the chloride is attached, directly impacting the carbocation's stability. This is why, in this context, we focus on the classification of the carbon (primary, secondary, tertiary) rather than the halide itself.

The SN1 reaction mechanism is a two-step process important in organic chemistry for creating new carbon-carbon or carbon-heteroatom bonds. The name SN1 stands for 'Substitution, Nucleophilic, Unimolecular,' which describes the key aspects of the mechanism. 'Substitution' refers to the replacement of a group in a molecule; 'Nucleophilic' means that a nucleophile, an electron-rich species, is attacking the electron-deficient carbon; and 'Unimolecular' implies that the rate-determining step involves a single molecular entity.

The SN1 reaction proceeds via a two-step mechanism:

Step 1: Formation of the Carbocation

This is the rate-determining step in which the leaving group, usually a halide, departs from the substrate, resulting in a carbocation. The ease of formation of this carbocation, which is dependent on its stability, is critical for the reaction rate.

Step 2: Nucleophilic Attack

Once the carbocation is formed, it is quickly attacked by the nucleophile. This step is usually fast because the positively charged carbocation is an excellent electrophile and is readily attacked by nucleophiles. Importantly, since the first step is the slowest and involves the formation of the carbocation, the SN1 mechanism is heavily influenced by factors affecting carbocation stability, which were described in previous sections.