Question

The correct order of rate of dehydrohalogenation for following compound when treated wite alcoholic \(\mathrm{NaOH}\) is (i) Cis-4-iodo-t-butyl cyclohexane (II) Trans-4-iodo-t-butyl cyclohexane (A) I > II (B) \(\mathrm{II}>\mathrm{I}\) (C) \(\mathrm{I}=\mathrm{II}\) (D) Can't compare

Short answer

The correct order of the rate of dehydrohalogenation for the given compounds is Trans-4-iodo-t-butyl cyclohexane (II) > Cis-4-iodo-t-butyl cyclohexane (I), due to the lower steric hindrance in the Trans-isomer compared to the Cis-isomer. Therefore, the correct answer is (B) II > I.

Step-by-step solution

Reaction mechanism and basic concepts

In an E2 dehydrohalogenation reaction, a strong base (such as alcoholic NaOH) attacks the hydrogen of the carbon adjacent to the one that bears the halogen (iodine in this case). The resulting negatively charged ion then moves to the halogen, causing the iodine to leave the molecule, forming a double bond in the process. The rate of the reaction is highly dependent on the steric hindrance around the β-carbon (carbon adjacent to the carbon bearing the halogen). Lower steric hindrance would lead to a faster reaction rate.

Compare steric hindrance in Cis- and Trans-4-iodo-t-butyl cyclohexane

In both Cis- and Trans-4-iodo-t-butyl cyclohexane, the t-butyl group and the iodine atom are at the 4th position of the cyclohexane. The difference lies in the spatial orientation of these groups. In the Cis-isomer (I), both the t-butyl group and the iodine atom are located on the same side of the cyclohexane ring, creating high steric hindrance. In the Trans-isomer (II), the t-butyl group and the iodine atom are located on opposite sides of the cyclohexane ring, leading to less steric hindrance compared to the Cis-isomer.

Determine the correct order of the rate of dehydrohalogenation

Since the steric hindrance in Trans-4-iodo-t-butyl cyclohexane (II) is lower than that in Cis-4-iodo-t-butyl cyclohexane (I), the rate of dehydrohalogenation would be faster for the Trans-isomer (II). Hence, the correct order of rate is: Trans-4-iodo-t-butyl cyclohexane (II) > Cis-4-iodo-t-butyl cyclohexane (I) The correct answer is (B) II > I.

Key concepts

E2 Reaction Mechanism

Understanding the E2 reaction mechanism is crucial for grasping why certain reactions occur more rapidly than others. The E2 mechanism, which stands for bimolecular elimination, is a one-step process where a strong base eliminates a proton from the β-carbon, while simultaneously the leaving group, such as a halide, departs from the alpha carbon. This concerted process results in the formation of a double bond, characteristic of alkenes.

As this occurs, the strong base, in this exercise alcoholic NaOH, helps generate the alkene by removing a proton adjacent to the carbon holding the halogen. The halide's departure and the double bond's formation are synchronous, hinting at the 'concerted' nature of the E2 reaction. The reaction's rate is a product of the base and substrate concentrations, pointing to its bimolecular character.

Importantly, the E2 mechanism has a stereospecific outcome, which means the three-dimensional orientation of the atoms affects the reaction rate. This will tie into the concept of cis-trans isomerism, which influences the steric hindrance, a key factor in the reaction kinetics.

Steric Hindrance

Steric hindrance refers to the resistance faced by a chemical reaction due to the spatial demands of substituents within a molecule. In simpler terms, it's the 'crowdedness' around a reaction site that can slow down a reaction or prevent it entirely. Larger groups close to the reactive site can block the approach of the base needed for the E2 mechanism, thus affecting the reaction rate.

In the example of cis- and trans-4-iodo-t-butyl cyclohexane, the t-butyl group is particularly bulky, and its placement can drastically influence how easily the base can approach and remove the target hydrogen atom. Trans isomers typically experience less steric hindrance—as seen in Compound II—since substituents are opposite each other, allowing for easier access and a faster reaction. Thus, analyzing these spatial factors is key when considering reaction rates in an E2 dehydrohalogenation scenario.

Cis-Trans Isomerism

Cis-trans isomerism is a form of stereoisomerism where molecules with the same formula can have different physical properties due to the arrangements of groups relative to a double bond or, in cyclic compounds like cyclohexane, due to the arrangement around the ring. 'Cis' indicates the two substituents are on the same side while 'trans' denotes they are on opposite sides.

In the context of dehydrohalogenation, this isomerism plays a substantial role. Cis isomers often have higher steric hindrance because the bulky groups are closer together, leading to increased interaction and spatial conflict. Conversely, trans isomers, with their substituents on opposite sides, tend to have lower steric hindrance, resulting in typically faster reaction rates. In the textbook exercise, recognizing this difference aids in predicting that Trans-4-iodo-t-butyl cyclohexane (II) reacts more quickly than its cis-counterpart (I), due to the reduced steric hindrance.