Question

In the following benzyl/allyl system ( \(\mathrm{R}\) 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) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \rightarrow\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}->\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\) (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) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}->\mathrm{CH}_{3} \mathrm{CH}_{2}->\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\)

Short answer

Option (a) is correct.

Step-by-step solution

Understand Inductive Effect

The inductive effect is the shift of electron density through sigma bonds due to the electronegativity differences between atoms. Alkyl groups show a +I (positive inductive effect) as they can donate electron density.

Analyze Alkyl Groups

The strength of the +I effect increases with branching of the alkyl group. The order is: - Tertiary > Secondary > PrimarySo, for alkyl groups: \[\left(\mathrm{CH}_{3}\right)_{3}\mathrm{C}- > \left(\mathrm{CH}_{3}\right)_{2}\mathrm{CH}- > \mathrm{CH}_{3}\mathrm{CH}_{2}-\]This order affects the choices given.

Evaluate Given Options

For each option, follow the ranking of the inductive effect:- (a) \(\left(\mathrm{CH}_{3}\right)_{3}\mathrm{C}- > \left(\mathrm{CH}_{3}\right)_{2}\mathrm{CH}- > \mathrm{CH}_{3}\mathrm{CH}_{2}-\) (Matches the order)- (b) \(\mathrm{CH}_{3}\mathrm{CH}_{2}- > \left(\mathrm{CH}_{3}\right)_{2}\mathrm{CH}- > \left(\mathrm{CH}_{3}\right)_{3}\mathrm{C}-\) (Reversed order)- (c) \(\left(\mathrm{CH}_{3}\right)_{2}\mathrm{CH}- > \mathrm{CH}_{3}\mathrm{CH}_{2}- > \left(\mathrm{CH}_{3}\right)_{3}\mathrm{C}-\) (Incorrect order)- (d) \(\left(\mathrm{CH}_{3}\right)_{3}\mathrm{C}- > \mathrm{CH}_{3}\mathrm{CH}_{2}- > \left(\mathrm{CH}_{3}\right)_{2}\mathrm{CH}-\) (Incorrect order and incorrect ranking)

Key concepts

Alkyl Groups

Alkyl groups are important in understanding the inductive effect because they can donate electron density through sigma bonds. This donation happens due to the presence of carbon-hydrogen bonds in the alkyl groups, which are less electronegative compared to other potential substituents in organic molecules.

The capacity of an alkyl group to donate electron density is characterized by its ability to exhibit a +I effect or positive inductive effect. The stronger the +I effect, the better the alkyl group is at pushing electron density towards the rest of the molecule it’s attached to.

To determine the +I effect among different alkyl groups, we look at their structure, specifically the level of branching:

• Tertiary alkyl groups (like \((\text{CH}_3)_3\text{C}-\)) have the highest electron donating ability because they have three alkyl chains branching off centrally positioned carbon, resulting in higher electron density at the carbon center.


• Secondary alkyl groups (such as \((\text{CH}_3)_2\text{CH}-\)) have moderate electron donating capacity with two branching alkyl chains.


• Primary alkyl groups (like \(\text{CH}_3\text{CH}_2-\)) have the least electron donating ability as they possess only one alkyl chain directly attached to the main carbon atom.

This order is crucial when predicting the inductive effect among different molecules or functional groups. It helps chemists predict how these groups will interact in a chemical environment.

Sigma Bonds

Sigma bonds (\(\sigma\) bonds) are a type of covalent bond and play a central role in the context of the inductive effect. These bonds occur when there is a head-on overlap between two atomic orbitals. This overlap is usually the result of interactions between the s orbitals or the axis of p orbitals.

The sigma bond is characterized by its stability and strength, making it one of the critical pillars of molecular structure. Now, when we talk about the inductive effect, sigma bonds become fundamental because they are the connectors through which electron density is transmitted. The electrons in a sigma bond can be slightly shifted between atoms due to electronegativity differences.

The inductive effect is essentially the consequence of this electron density shift through sigma bonds rather than the pi bonds, which are involved in double and triple bond formations. Therefore, understanding sigma bonds is key to understanding how inductive effects propagate and influence molecular property changes. Keep in mind that, unlike pi bonds, sigma bonds allow rotation around the bond axis, which imparts different chemical properties based on the molecule's surroundings and conditions.

Electron Density Shift

An electron density shift is what underpins the inductive effect we frequently encounter in organic chemistry. This movement of electron density within a molecule primarily occurs through sigma bonds. As electrons are negatively charged, they tend toward more electronegative elements within a molecule.

This process results in polarization, where a part of the molecule holds more electron density and another holds less, creating slightly positive and negative regions. This is particularly significant when analyzing a molecule's reactivity and interaction with other substances.

Factors like the electron pushing ability of substituents and comparative electronegativity significantly influence these electron density shifts:

• Substituents like alkyl groups push electron density outward, creating a +I effect.


• Conversely, electronegative elements (like halogens) tend to draw electron density, resulting in a -I effect (negative inductive effect). This contrasts the positive effect seen with most alkyl groups.

Understanding these shifts gives insight into how electron distribution affects molecular characteristics and reactions. This polarization will influence the stability of intermediates and transition states, thus determining reaction pathways and product distributions in chemical processes.