Question

The order of rate of dehydration of following alcohols is (A) \(I>I I>I I I\) (B) II > III > I (C) II > I > III (D) III \(>\mathrm{II}>\mathrm{I}\)

Short answer

Unfortunately, the alcohols are not mentioned in the problem statement. Please provide the structure of the alcohols to proceed with the problem.

Step-by-step solution

Identify the given alcohols

Unfortunately, the alcohols are not mentioned in the problem statement. Please provide the structure of the alcohols to proceed with the problem.

Predict the carbocations formed during dehydration

Once the alcohols are given, analyze the structures and predict the carbocations that would form during dehydration. Remember, dehydration occurs by losing the hydroxyl group from the alcohol and forming a double bond. Consider the intermediates that could be formed from all the given alcohols.

Compare the stability of carbocations

Based on the carbocations formed in Step 2, compare their stability using hyperconjugation and inductive effect principles. A more substituted carbocation (higher number of alkyl groups) would be more stable due to greater hyperconjugation. Also, the carbocations with electron-donating groups would be more stable than those with electron-withdrawing groups due to inductive effects.

Establish the order of rate of dehydration

Based on the stability of the carbocations determined in Step 3, establish the order of rate of dehydration for the given alcohols. The alcohol with the most stable carbocation will have the highest rate of dehydration, followed by the second and third most stable carbocations, respectively.

Select the correct option

Finally, compare the established order of rate of dehydration with the given options and select the option that matches the determined order.

Key concepts

Carbocation Stability

Carbocation stability is a crucial concept in understanding the dehydration process of alcohols. During dehydration, alcohols lose a hydroxyl group, forming a carbocation intermediate. The stability of this carbocation significantly affects the rate of the dehydration reaction. A more stable carbocation leads to a faster reaction because it requires less energy to form.
In carbocations, the positively charged carbon atom is electron-deficient, making the carbocation unstable. To stabilize, it needs to attract electrons or disperse the positive charge. Various factors can influence this, with one being the number of carbon atoms (or alkyl groups) attached to the carbocation.
More substituted carbocations, such as tertiary carbocations with three alkyl groups, are more stable than secondary or primary carbocations. The additional alkyl groups can donate electron density through hyperconjugation or inductive effects, stabilizing the positive charge. Always consider the degree of substitution when predicting carbocation stability, as it directly impacts reaction rates.

Hyperconjugation

Hyperconjugation is an essential concept that explains the stability of carbocations through structural resonance. It occurs when the electrons in a sigma bond (often C-H or C-C) interact with an adjacent empty p-orbital of the positively charged carbon atom in the carbocation. This interaction leads to the dispersion of the positive charge over the surrounding alkyl groups.
This effect explains why more alkyl substituted carbocations are more stable. Each additional alkyl group can potentially offer more hyperconjugative structures, distributing the charge more evenly and relieving the electron deficiency of the carbocation.
For example, a tertiary carbocation has more possibilities for hyperconjugation due to the presence of three alkyl groups compared to a primary carbocation, which might have only one or none. This effect is often visible when you write out the contributing structures of hyperconjugation, showing how the charge can "spread out" over the molecule, leading to increased stability.

Inductive Effect

The inductive effect is another key factor in determining the stability of carbocations during the dehydration of alcohols. It refers to the transmission of charge through a chain of atoms in a molecule, influenced by the attraction or repulsion of electrons.
In carbocations, inductive effects help stabilize the positively charged carbon atom. Electron-donating groups, like alkyl chains, push electron density towards the carbocation, stabilizing the positive charge. This effect is primarily due to the overlapping of electrons from the alkyl group with the vacant p-orbital of the carbocation. Conversely, electron-withdrawing groups would destabilize the carbocation by pulling electron density away.
The cumulative inductive effects of multiple alkyl groups can significantly enhance carbocation stability, making a tertiary carbocation generally more stable than a secondary or primary one. Understanding these effects can help predict the order of dehydration rates: the more stable the carbocation, the faster the alcohol will dehydrate.