Question

Which isomer of 1 -bromo-3-isopropylcyclohexane reacts faster when refluxed with potassium tert-butoxide, the cis isomer or the trans isomer? Draw the structure of the expected product from the faster-reacting compound.

Short answer

The cis isomer of 1-bromo-3-isopropylcyclohexane reacts faster when refluxed with potassium tert-butoxide. This is due to the more stable transition state in the cis isomer, with both the base and the leaving group being on the same side. The expected product will be a 1,2-substituted cyclohexene with the isopropyl group on the same side as the double bond.

Step-by-step solution

Understand the difference between cis and trans isomers

In the case of 1-bromo-3-isopropylcyclohexane, the cis isomer has both the bromine and isopropyl groups on the same side of the cyclohexane ring (either both up or both down), while the trans isomer has these groups on opposite sides (one up and one down). This difference in molecular structure has an impact on the reactivity of the isomers.

Understand the reaction mechanism

The reaction mentioned in the problem is an elimination reaction between the given isomer and potassium tert-butoxide, which acts as a strong base. The base removes a beta-hydrogen from the molecule, and as a result, bromide ion, a good leaving group, leaves the molecule. This leads to the formation of a double bond. In this case, there are two possible locations for the double bond, leading to different products.

Compare the stability and reactivity of the cis and trans isomers

To determine which isomer reacts faster with potassium tert-butoxide, we need to consider the stability of the transition state of these isomers. In general, the more stable the transition state, the faster the reaction will proceed. For the reaction to occur in trans isomer, the base would have to approach the molecule from one side while the bromide ion leaves from the other side. In the case of the cis isomer, both the base and the leaving group are on the same side, giving a more stable transition state. Therefore, the cis isomer is expected to react faster than the trans isomer.

Draw the structure of the expected product

As the cis isomer has a more stable transition state and reacts faster, so the product will be formed from the cis isomer. The potassium tert-butoxide will remove a beta-hydrogen from the cis isomer, leading to the elimination of bromide ion and the formation of a double bond. The expected product's structure will be a 1,2-substituted cyclohexene with the isopropyl group on the same side as the double bond.

Key concepts

Cis and Trans Isomers

In organic chemistry, cis and trans isomers refer to molecules with similar molecular formulas but different spatial arrangements of atoms. This spatial difference is crucial in determining the molecule's physical and chemical properties. Applying this concept to 1-bromo-3-isopropylcyclohexane, we can visualize that the cis isomer has the bromine and isopropyl groups on the same side of the cyclohexane ring. This proximity can influence the molecule's reactivity by making certain reactions more or less favorable.

Conversely, the trans isomer positions the groups on opposite sides, resulting in a different shape and potentially different reactivity. These isomers can have markedly different behaviors when exposed to reagents like potassium tert-butoxide, which preferentially reacts with the more accessible hydrogen atoms. In essence, the arrangement of groups in cis and trans isomers can significantly affect how they engage in chemical reactions.

Reaction Mechanism

The reaction mechanism is the step-by-step sequence of elementary reactions by which overall chemical change occurs. In the case of 1-bromo-3-isopropylcyclohexane and potassium tert-butoxide, we are dealing with an elimination reaction. Here, the strong base (potassium tert-butoxide) abstracts a beta-hydrogen, and concurrently, the bromide ion leaves, resulting in the formation of a double bond in the cyclohexane ring.

An important aspect of reaction mechanisms is the formation of transition states—high-energy, unstable arrangements of atoms that occur between the reactants and the products. In steps where such states are lower in energy, the reaction will generally proceed more quickly. Understanding the reaction's mechanism helps predict not only the outcome but also the speed and conditions under which the reaction will occur.

Stability of Transition State

The stability of the transition state plays a pivotal role in determining the reaction rate. A more stable transition state correlates to a lower energy barrier, thereby speeding up the reaction. In the context of elimination reactions with 1-bromo-3-isopropylcyclohexane, the cis isomer has both the base and leaving group in closer proximity, which can lead to a more stable transition state. This proximity provides a degree of steric favorability, minimizing the energy required to reach the transition state.

Additionally, this stability can be analyzed by considering factors such as steric hindrance and the electronic environment of the molecule. By comparing these factors in the cis versus trans isomers, it becomes evident why the cis isomer tends to have a more stable transition state and, thus, reacts more quickly when refluxed with potassium tert-butoxide.

Potassium Tert-Butoxide Reactivity

Potassium tert-butoxide is known for its high reactivity as a strong, sterically hindered base. In elimination reactions, this reagent targets the beta-hydrogen of a substrate, facilitating a reaction by giving rise to an alkene. Its reactivity is significantly influenced by the nature of the substrate, including whether it's a cis or trans arrangement.

In the case of 1-bromo-3-isopropylcyclohexane, potassium tert-butoxide reacts more readily with the cis isomer, as discussed. The steric hindrance associated with this base also means that it is less likely to participate in substitution reactions and favor elimination instead, leading to the creation of double bonds. Understanding the reactivity of potassium tert-butoxide is essential for predicting the course and outcome of reactions involving this potent base.