The correct increasing order of electron donating effect of \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-,\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\) and \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\) groups when attached to benzene or unsaturated system is (a) \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-<\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-<\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\) (b) \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-<\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-<\mathrm{CH}_{3}-\mathrm{CH}_{2}-\) (c) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-<\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-<\mathrm{CH}_{3}-\mathrm{CH}_{2}-\) (d) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}<\mathrm{CH}_{3}-\mathrm{CH}_{2}-<\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\)

Step by step solution

01

List and Analyze the Alkyl Groups

Three alkyl groups are given: 1. \((\mathrm{CH}_{3})_{3} \mathrm{C}-\) 2. \((\mathrm{CH}_{3})_{2} \mathrm{CH}-\) 3. \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\) The electron donating ability of these groups depends on their inductive and hyperconjugative effects.

02

Inductive Effect

The inductive effect arises due to the transmission of a small charge from one carbon atom to another through the sigma bonds. Alkyl groups have a weak +I effect, which means they can transmit a positive charge towards the benzene or unsaturated system. This effect depends on the number of alkyl groups attached to the carbon; the bigger the alkyl group, the stronger the +I effect. So, the order of inductive effect should be: \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-<(\mathrm{CH}_{3})_{2}\mathrm{CH}-<(\mathrm{CH}_{3})_{3}\mathrm{C}-\)

03

Hyperconjugative Effect

The hyperconjugative effect is the overlap of bonding orbitals with the antibonding orbitals of the adjacent bond in a molecule. This effect strengthens the bond between the carbon atom and the benzene ring. A higher number of alpha hydrogens (on the carbon directly connected to the benzene ring) will result in a stronger electron donating effect. In our case, the number of alpha hydrogens in each group are: 1. \((\mathrm{CH}_{3})_{3} \mathrm{C}-\) has 9 alpha hydrogens 2. \((\mathrm{CH}_{3})_{2} \mathrm{CH}-\) has 6 alpha hydrogens 3. \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-\) has 2 alpha hydrogens As a result, the order of the hyperconjugative effect should be: \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-<(\mathrm{CH}_{3})_{2}\mathrm{CH}-<(\mathrm{CH}_{3})_{3}\mathrm{C}-\)

04

Determine the Overall Electron Donating Effect

As both inductive and hyperconjugative effects have an impact on the electron donating ability, the overall order will be the same as found individually for inductive and hyperconjugative effects. The correct increasing order of electron donating effect is: \(\mathrm{CH}_{3}-\mathrm{CH}_{2}-<(\mathrm{CH}_{3})_{2}\mathrm{CH}-<(\mathrm{CH}_{3})_{3}\mathrm{C}-\) So, the correct answer is option (a).

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