Problem 23 - Basic Principles of Organic Chemistry

Question

Would you expect the \(S_{\mathrm{N}} 2\) reaction of sodium cyanide with methyl bromide to be faster, slower, or about the same with \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~S}=\mathrm{O}\) or ethanol as solvent? Explain.

Step-by-Step Solution

Answer

The reaction is faster in \((\text{CH}_3)_2\text{SO})\) than in ethanol.

Step 1: Understanding the Reactants and Reaction Type

In an \( S_N2 \) reaction, sodium cyanide (\( ext{NaCN} \)) acts as the nucleophile and attacks methyl bromide (\( ext{CH}_3 ext{Br} \)) resulting in the substitution of the bromide ion with a cyanide group.

Step 2: Role of Solvent in Reaction Rate

The solvent can influence the reaction rate. For \( S_N2 \) reactions, polar aprotic solvents are usually ideal because they do not solvate anions effectively, allowing the nucleophile to react more freely.

Step 3: Solvent Evaluation - Dimethyl Sulfoxide (\(( ext{CH}_3)_2 ext{SO})\)

Dimethyl sulfoxide (\(( ext{CH}_3)_2 ext{SO})\) is a polar aprotic solvent. It does not solvate ions strongly, making it ideal for \( S_N2 \) reactions as it enhances the nucleophilicity of \( ext{CN}^- \) ions, leading to a faster reaction.

Step 4: Solvent Evaluation - Ethanol

Ethanol is a polar protic solvent. It can solvate the \( ext{CN}^- \) ions, reducing their nucleophilicity and making them less effective in attacking the methyl group, slowing down the \( S_N2 \) reaction.

Step 5: Comparing Reaction Speeds by Solvent

Given that \(( ext{CH}_3)_2 ext{SO} \) does not solvate the \( ext{CN}^- \) anion as strongly as ethanol does, the \( S_N2 \) reaction with dimethyl sulfoxide as the solvent will be faster compared to ethanol.

Key Concepts

Nucleophile

A nucleophile is a chemical species that donates an electron pair to form a chemical bond in reaction processes, such as the S_N2 reaction. Nucleophiles are important in substitution reactions because they seek positive or electron-deficient centers to donate their electrons. In the given exercise, sodium cyanide (\( \text{NaCN} \)) acts as the nucleophile. It holds a negatively charged cyanide ion (\( \text{CN}^- \)), which is eager to attack the slightly positive carbon in methyl bromide (\( \text{CH}_3\text{Br} \)). This attack involves the nucleophile pushing out the leaving group, which in this case is the bromide ion (\( \text{Br}^- \)). Key characteristics of nucleophiles include:

• An ability to donate electrons
• Presence of lone pairs or pi electrons
• Higher reactivity with softer, less hindered electrophiles

Understanding the behavior of nucleophiles helps predict how quickly and efficiently a reaction like S_N2 might proceed.

Polar Aprotic Solvent

Solvents have a critical influence on the S_N2 reaction mechanism, primarily through their interaction with the nucleophile. A polar aprotic solvent is particularly effective in these reactions because it does not form hydrogen bonds with anions. Aprotic solvents like dimethyl sulfoxide (\((\text{CH}_3)_2\text{SO}\)), mentioned in the exercise, are polar enough to dissolve the nucleophile but do not stabilize the charged species, allowing them to remain potent. Features of polar aprotic solvents include:

• High polarity to dissolve reactants
• Lack of hydrogen-bonding capacity with nucleophiles
• Ability to increase the reaction rate by not hindering nucleophiles

Polar aprotic solvents are advantageous in S_N2 reactions, as seen with dimethyl sulfoxide enhancing the reactivity of \( \text{CN}^- \) compared to ethanol, a polar protic solvent.

Reaction Rate

The rate of an S_N2 reaction depends heavily on the nature of the nucleophile, the solvent used, and the structure of the substrate. In the given S_N2 reaction involving sodium cyanide and methyl bromide, the speed at which these reactants convert to products is a direct reflection of these factors. The important determinants of an S_N2 reaction rate are:

• Strength and concentration of the nucleophile
• Polar aprotic solvents providing less hindrance to nucleophiles
• The structure and size of the electrophile or substrate

When dimethyl sulfoxide is used, the \( \text{CN}^- \) ions are more reactive, thereby increasing the rate of the reaction compared to when ethanol is the solvent. Ethanol's ability to solvate and stabilize \( \text{CN}^- \) ions reduces their effectiveness as a nucleophile, thus slowing down the reaction.