Question

Which of the following is the correct order of decreasing \(\mathrm{SN}^{2}\) reactivity? (a) \(\mathrm{RCH}_{2} \mathrm{X}>\mathrm{R}_{2} \mathrm{CHX}>\mathrm{R}_{3} \mathrm{CX}\) (b) \(\mathrm{R}_{3} \mathrm{CX}>\mathrm{R}_{2} \mathrm{CHX}>\mathrm{RCH}_{2} \mathrm{X}\) (c) \(\mathrm{R}_{2} \mathrm{CHX}>\mathrm{R}_{3} \mathrm{CX}>\mathrm{RCH}_{2} \mathrm{X}\) (d) \(\mathrm{RCH}_{2} \mathrm{X}>\mathrm{R}_{3} \mathrm{CX}>\mathrm{R}_{2} \mathrm{CHX}\)

Short answer

(a) is the correct order: \(RCH_2X > R_2CHX > R_3CX\).

Step-by-step solution

Review SN2 Reaction Mechanism

The SN2 reaction involves a backside attack by a nucleophile, leading to inversion of configuration. The rate of the SN2 reaction is affected by steric hindrance; therefore, less hindered substrates react faster.

Analyze Each Alkyl Halide

Consider each of the alkyl halide types: - Primary ( ext{RCH}_2X ext{)} is least hindered, thus more reactive. - Secondary ( ext{R}_2 ext{CHX} ext{)} has moderate hindrance and reactivity. - Tertiary ( ext{R}_3 ext{CX} ext{)} is most hindered, hence least reactive in SN2 reactions.

Determine Reactivity Order

Based on steric hindrance, the order of decreasing SN2 reactivity is primary ( ext{RCH}_2X ext{)}, secondary ( ext{R}_2 ext{CHX ext{)}}), and then tertiary ( ext{R}_3 ext{CX} ext{)}).

Choose the Correct Option

Referring to each choice: (a)  ext{RCH}_2X > ext{R}_2 ext{CHX} > ext{R}_3 ext{CX} ext{) matches the determined order. (b), (c), and (d) do not match the determined order. Hence, (a) is the correct choice.

Key concepts

Nucleophilic Substitution

Nucleophilic substitution reactions are fundamental in organic chemistry, as they involve the replacement of a leaving group by a nucleophile. In these reactions, a nucleophile, which is an electron-rich species, attacks an electrophilic center, typically a carbon atom. This leads to the displacement of another group called the leaving group. SN2, an abbreviation for bimolecular nucleophilic substitution, is one type of mechanism where this occurs. In SN2 reactions, the reaction happens in a single concerted step. The nucleophile attacks the substrate from the opposite side of the leaving group, resulting in an inversion of stereochemistry. This type of reaction is heavily influenced by various factors, such as steric hindrance and the nature of the nucleophile and substrate.

Steric Hindrance

Steric hindrance is a crucial concept in understanding SN2 reaction dynamics. It refers to the prevention of chemical reactions by the spatial arrangement of atoms within a molecule. In the context of SN2 reactions, large bulky groups attached to the electrophilic center can significantly hinder the approach of the nucleophile.

• Primary substrates are the least hindered, allowing more accessible attacks by nucleophiles.
• Secondary substrates have increased steric hindrance due to more substituents.
• Tertiary substrates are highly hindered, making them poor choices for SN2 reactions.

This hindrance directly affects the rate of the reaction, as bulky groups slow down the nucleophilic attack.

Reactivity Order

The reactivity order in SN2 reactions decreases from primary to tertiary substrates. This order is dictated by the steric hindrance discussed earlier. In a typical SN2 reaction, a primary substrate (\(\mathrm{RCH}_2\mathrm{X}\)), which has only one substituent attached to the primary carbon, exhibits the highest reactivity. This is because there is minimal steric hindrance, allowing the nucleophile to attack freely. As we move to secondary substrates (\(\mathrm{R}_2\mathrm{CHX}\)), with two groups attached, the reactivity decreases due to a moderate increase in steric hindrance.Tertiary substrates (\(\mathrm{R}_3\mathrm{CX}\)), with three groups attached, show the least reactivity in SN2 reactions because the nucleophile struggles to approach the carbon center due to the high steric demands.

Primary, Secondary, Tertiary Substrates

Substrate structure significantly impacts the outcomes of SN2 reactions. These substrates can be classified as primary, secondary, or tertiary based on the number of carbon-containing groups attached to the carbon bearing the leaving group.

• Primary substrates: These compounds have only one carbon group attached, making them optimal for SN2 reactions due to minimal steric hindrance.
• Secondary substrates: With two carbon groups attached, these substrates have moderate reactivity in SN2 processes.
• Tertiary substrates: These have three carbon groups attached. Because of high steric hindrance, SN2 reactions are unfavorable.

Understanding these classifications can help predict the outcome and feasibility of nucleophilic substitution reactions.