Question

The decreasing order of rate of reaction is $$\mathrm{R}-\mathrm{OH}+\mathrm{HCl}\stackrel{\mathrm{ZnC}}{⟶}\mathrm{R}-\mathrm{Cl}+{\mathrm{H}}_2\mathrm{O}$$ $(A)1^{\circ }>2^{\circ }>3^{\circ }$ (B) $1^{\circ }<2^{\circ }>3^{\circ }$ (C) $3^{\circ }>2^{\circ }>1^{\circ }<{\mathrm{CH}}_3\mathrm{OH}$ (D) $3^{\circ }>2^{\circ }>1^{\circ }>{\mathrm{CH}}_4\mathrm{OH}$

Short answer

The short answer is: (C) $3^{\circ }>2^{\circ }>1^{\circ }<{\mathrm{CH}}_3\mathrm{OH}$.

Step-by-step solution

Understand the reaction mechanism

For this reaction, the catalyst ZnCl facilitates the formation of a carbocation intermediate by breaking the R-OH bond and forming an R-Cl bond while releasing water (H2O). The stability of the carbocation intermediate plays a crucial role in determining the rate of reaction. In general, more stable carbocations react faster.

Determine carbocation stability for primary, secondary, and tertiary alcohols

The stability of a carbocation increases with the number of alkyl groups attached to the carbon atom: 3° > 2° > 1°. This is because alkyl groups donate electron density to the positively charged carbon, stabilizing the positive charge. Therefore, tertiary carbocations are more stable than secondary carbocations, which are more stable than primary carbocations.

Infer the order of reactivity of alcohols based on carbocation stability

Since more stable carbocations lead to a faster reaction rate, we can infer the decreasing order of reactivity based on the stability of the carbocations formed during the reaction. As discussed earlier, the following order of stability holds: 3° > 2° > 1°. Therefore, the decreasing order of the reaction rate is the same: 3° > 2° > 1°.

Choose the correct answer based on the analysis

From the analysis above, we have concluded that the correct decreasing order of reactivity is 3° > 2° > 1°. This corresponds to the answer choice (C). However, we also need to check if CH3OH or CH4OH fit in this order. Since CH3OH (methanol) is a primary alcohol, CH3OH is less reactive than 3° and 2° alcohols but more reactive than CH4OH (which doesn't exist). Therefore, the correct answer is: (C) $3^{\circ }>2^{\circ }>1^{\circ }<{\mathrm{CH}}_3\mathrm{OH}$

Key concepts

Reaction Mechanism

Understanding the reaction mechanism is essential for grasping the principles of chemical transformations. In the context of the provided reaction, the focus is on the conversion of alcohols to chlorides using ZnCl as a catalyst. The catalyst facilitates the formation of a carbocation intermediate—a positively charged carbon atom resulting from the cleavage of the R-OH bond.

This is a crucial step as it dictates the subsequent formation of the R-Cl bond and the release of water. The key takeaway here is that the stability of the carbocation intermediate is central to the reaction's rate. As a general rule, more stable intermediates lead to faster reactions, a concept that is paramount in predicting the behavior of organic compounds during chemical reactions.

Alcohol Reactivity Order

In the world of organic chemistry, not all alcohols are created equal—particularly when it comes to their reactivity. The reactivity order refers to the tendency of different types of alcohols (primary, secondary, and tertiary) to react. As the step by step solution indicates, a primary (1°) alcohol has one alkyl group attached to the carbon bearing the hydroxyl group, while secondary (2°) and tertiary (3°) alcohols have two and three such groups, correspondingly.

The reactivity pattern, 3° > 2° > 1°, mirrors the increased stability provided by alkyl groups through electron donation. This stabilization effect is known as hyperconjugation or the +I inductive effect. It's beneficial to become familiar with these concepts as they are often the underlying reasons for the observed reactivity order of alcohols and other organic compounds.

Rate of Reaction

Rate of reaction is a term frequently encountered in chemistry that deals with the speed at which reactants turn into products. When considering carbocation stability and alcohol reactivity, it's important to recognize that the rate of reaction is not merely a theoretical concept but has practical implications. Higher carbocation stability results in a faster rate of reaction because the intermediate is more likely to form and less likely to revert back to the starting materials.

In the exercise under discussion, the rate of reaction decreases from tertiary to primary alcohols (3° > 2° > 1°), which is inextricably connected to the stability of the corresponding carbocations. Incorporating this understanding of rate factors, including electronic effects and molecular structure, can significantly improve a student's ability to anticipate and reason through the outcomes of organic reactions.