Problem 178 - A Complete Resource Book in Chemistry for JEE Main

Question

In the following benzyl/allyl system or [R]C=C [R]c1ccccc1 ( \(\mathrm{R}\) is alkyl group) decreasing order of inductive effect is (a) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}->\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}->\mathrm{CH}_{3} \mathrm{CH}_{2}-\) (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2}->\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}->\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\) (c) \(\left.\mathrm{CH}_{3}\right)_{2} \mathrm{CH}->\mathrm{CH}_{3} \mathrm{CH}_{2} \rightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\) (d) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}->\mathrm{CH}_{3} \mathrm{CH}_{2}->\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\)

Step-by-Step Solution

Answer

Option (a) is correct: The order is \(\text{(CH}_3\text{)}_3\text{C} > \text{(CH}_3\text{)}_2\text{CH} > \text{CH}_3\text{CH}_2\).

Step 1: Understanding Inductive Effect

The inductive effect refers to the transmission of charge through a chain of atoms in a molecule by electrostatic induction. Electronegative and electron-withdrawing groups typically reduce electron density (negative inductive effect), whereas alkyl groups often increase electron density (positive inductive effect). The more substituted the alkyl group, the stronger its +I effect.

Step 2: Identify Alkyl Group Strength

For the given alkyl groups, the order from strongest to weakest +I effect is 1. \( ext{(CH}_3 ext{)}_3 ext{C}-\) (tertiary butyl)2. \(\text{(CH}_3\text{)}_2\text{CH}-\) (isopropyl)3. \(\text{CH}_3\text{CH}_2-\) (ethyl)

Step 3: Analyze Each Option

Now analyze the options:- Option (a): \(\text{(CH}_3\text{)}_3\text{C} > \text{(CH}_3\text{)}_2\text{CH} > \text{CH}_3\text{CH}_2\)- Option (b): \(\text{CH}_3\text{CH}_2 > \text{(CH}_3\text{)}_2\text{CH} > \text{(CH}_3\text{)}_3\text{C}\)- Option (c): \(\text{(CH}_3\text{)}_2\text{CH} > \text{CH}_3\text{CH}_2 > \text{(CH}_3\text{)}_3\text{C}\)- Option (d): \(\text{(CH}_3\text{)}_3\text{C} > \text{CH}_3\text{CH}_2 > \text{(CH}_3\text{)}_2\text{CH}\)

Step 4: Select the Correct Order

The correct order for the decreasing inductive effect is option (a): \(\text{(CH}_3\text{)}_3\text{C} > \text{(CH}_3\text{)}_2\text{CH} > \text{CH}_3\text{CH}_2\). This option lists alkyl groups from strongest to weakest positive inductive effect according to their degree of substitution.

Key Concepts

Alkyl groups

Alkyl groups are chains of carbon and hydrogen atoms attached to the rest of a molecule. They are known for their ability to influence the chemistry of a molecule by either donating electrons or creating space around them. This electron-donation is primarily due to their positive inductive effect, which means they push electrons towards more electronegative elements or groups in a molecule.
Consider common alkyl groups such as methyl \(\left(\mathrm{CH}_3^{}\right)\), ethyl \(\left(\mathrm{CH}_3\mathrm{CH}_2-\right)\), and tert-butyl \(\left(\mathrm{CH}_3\right)_3\mathrm{C}-\). Methyl groups are the simplest, with a single carbon bound to three hydrogen atoms. As we move to larger groups, such as ethyl—which has two carbons—the electron-donating ability increases due to the higher number of electrons and enhanced steric bulk.
The power of an alkyl group's inductive effect depends on its substitution degree, with more highly substituted groups (like tert-butyl) generally having stronger inductive effects due to increased electron density leading to a larger electron-pushing capacity from the nucleus.

Electrostatic induction

Electrostatic induction is a phenomenon where charges are redistributed within a molecule due to the influence of nearby charged groups or electronegative atoms. It doesn't require an actual flow of electrons, but rather a shift in how they are distributed across a molecule. This principle is particularly important when understanding the inductive effect.
In chemistry, electrostatic induction is crucial for explaining how molecules can affect each other even when they are not directly connected by chemical bonds. When electronegative atoms or electron-withdrawing groups are present, they pull electron density towards themselves, creating a lower electron density in adjacent atoms. Conversely, electron-donating groups, like alkyl groups, push electron density into nearby atoms or groups.
This effect is essential in understanding reactivity, stability, and many other properties of molecules. For instance, in a molecule with different substitutions on a carbon chain, understanding how electrostatic induction functions helps predict which parts of the molecule might be more reactive or undergo chemical changes faster.

Substitution degree

The substitution degree refers to the number of other carbon or hydrogen atoms that are directly bonded to a carbon atom in a molecule. This concept is fundamental when analyzing the strength of inductive effects in alkyl groups. The substitution degree helps categorize carbon atoms as primary, secondary, tertiary, or quaternary.

• Primary carbon atoms are attached to one other carbon atom.
• Secondary carbon atoms connect to two other carbon atoms.
• Tertiary carbon atoms have three other carbons attached.
• Quaternary carbon atoms have four carbon neighbors.

The more substituted a carbon atom is, the stronger its ability to push electrons through the molecule. This is because the more bonds an alkyl group has to other carbon atoms, the more dense its electron cloud, enhancing its electron-donating (positive inductive) effect.
In practice, tertiary alkyl groups, like in tert-butyl \(\left(\mathrm{CH}_3\right)_3\mathrm{C}-\), have a more substantial inductive effect than secondary groups such as isopropyl \(\left(\mathrm{CH}_3\right)_2\mathrm{CH}-\), which in turn are more influential than primary groups like ethyl \(\mathrm{CH}_3\mathrm{CH}_2-\). This hierarchy is crucial in predicting chemical behavior, such as stability and reactivity, in various organic compounds.