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

Draw the structure of the expected product from the faster reacting compound. Answer: The trans isomer of 1-bromo-3-isopropylcyclohexane reacts faster with potassium tert-butoxide when refluxed. The expected product from the faster reacting trans isomer is 1-isopropyl-1-methylcyclohexene.

Step-by-step solution

Draw the structures of cis and trans isomers of 1-bromo-3-isopropylcyclohexane

To begin, let's draw the structures of the cis and trans isomers of 1-bromo-3-isopropylcyclohexane. For the cis isomer, the bromine atom and the isopropyl group are on the same side of the cyclohexane ring. In the trans isomer, the bromine atom and the isopropyl group are on opposite sides of the cyclohexane ring.

Analyze the E2 elimination reaction mechanism

In this reaction, potassium tert-butoxide (KOtBu) acts as a strong base, promoting an E2 elimination mechanism. This means that the base will abstract a β-hydrogen atom from the carbon next to the bromine-bearing carbon (the α-carbon), followed by the simultaneous formation of a C=C double bond and loss of the bromide ion (Br-). The stereochemistry of the reaction requires that the β-hydrogen and the leaving group (Br) be in an anti-periplanar orientation for the reaction to proceed.

Check the stability and accessibility of transition states

The rate of the E2 elimination reaction is directly affected by the stability and accessibility of the transition states. The more stable and easily accessible the transition state, the faster the reaction rate. For the trans isomer, the anti-periplanar β-hydrogen and the leaving group are easily accessible in the chair conformation, allowing for an unhindered E2 elimination reaction. In the case of the cis isomer, the β-hydrogen and the leaving group are not anti-periplanar in the chair conformation, necessitating a ring flip. This leads to a higher energy transition state, making the reaction slower compared to the trans isomer.

Identify the faster reacting isomer and draw the product

Since the trans isomer has a more stable and accessible transition state, it reacts faster in this E2 elimination reaction. The expected product from the faster reacting trans isomer will be formed via the abstraction of the β-hydrogen and the loss of the bromide ion, resulting in the formation of a C=C double bond. The product from the trans isomer is 1-isopropyl-1-methylcyclohexene.

Key concepts

cis-trans isomers

In chemistry, cis-trans isomers are examples of stereoisomers where the orientation of substituent groups attached to a carbon ring or double bond differentiates them. **Cis isomers** have substituents on the same side, while **trans isomers** have them on opposite sides.
Understanding these configurations helps predict the behavior of molecules in different reactions. In the case of 1-bromo-3-isopropylcyclohexane, analyzing the isomers involves looking at the positions of bromine and isopropyl groups. For the **cis isomer**, both these groups appear on the same side of the cyclohexane ring. For the **trans isomer**, however, they are on opposite sides.
This spatial arrangement directly impacts the likelihood and speed of chemical reactions like E2 eliminations, in which the position of groups affect the anti-periplanar orientation, leading to different reaction rates.

anti-periplanar orientation

The concept of **anti-periplanar orientation** is essential in E2 elimination reactions. It refers to the spatial arrangement where a hydrogen atom (that the base abstracts) and the leaving group (like a bromine atom) are situated 180 degrees apart on a plane in a molecule.
This alignment is optimal for the elimination reaction to occur successfully. For E2 reactions, an anti-periplanar arrangement is necessary because it minimizes steric hindrance and allows for proper orbital overlap. This results in the simultaneous formation of a double bond and the removal of a leaving group.
- In the **trans isomer** of 1-bromo-3-isopropylcyclohexane, the chair conformation naturally allows for an anti-periplanar arrangement, facilitating a quicker elimination reaction. - The **cis isomer**, however, may require additional molecular reconfigurations, such as a ring flip, to achieve this orientation, which may slow down the reaction.

transition state stability

The stability of the **transition state** in a chemical reaction significantly affects the overall reaction rate. In an E2 elimination reaction, the transition state is a high-energy intermediate where bonds are simultaneously breaking and forming.
The more stable this state is, the lower the activation energy required, leading to a faster reaction process. Factors contributing to transition state stability include: - **Steric Hindrance**: Less crowded transition states are generally more stable. - **Orbital Overlap**: Optimal overlapping of orbitals during bond formation increases stability. In the given exercise, the **trans isomer** possesses a more stable transition state due to its naturally favorable anti-periplanar orientation in the chair conformation. This accessibility reduces the energy barrier needed for the base to abstract the β-hydrogen and lose the bromide ion.
As a result, the trans isomer reacts faster in the E2 elimination, highlighting the integral correlation between transition state stability and reaction speed.