Which of the following order is/are correct for the rate of E2 reaction ?

Options

A. 5-Bromocycloheptene > 4-Bromocycloheptene
B. 2-Bromo-1-phenylbutane > 3-Bromo-1-phenylbutane
C. 3-Bromocyclohexene > Bromocyclohexane
D. 3-Bromo-2-methylpentane > 2-Bromo-4-methylpentane

Answer

To determine the correct order for the rate of E2 reactions among the given compounds, we need to analyze the stability of the transition states formed during the E2 elimination process. The stability of the transition state is influenced by the degree of substitution of the resulting alkene. More substituted alkenes are generally more stable, leading to a faster reaction rate.

### Step-by-Step Solution:

1. **Understanding E2 Mechanism**:
- E2 (bimolecular elimination) involves the simultaneous removal of a leaving group (like bromine) and a proton from the β-carbon, forming a double bond.
- The transition state resembles the product alkene, and its stability is crucial for the reaction rate.

2. **Analyzing the Given Compounds**:
- **5-bromo cycloheptane vs. 4-bromo cyclohexane**:
- 5-bromo cycloheptane leads to a non-conjugated alkene, while 4-bromo cyclohexane can lead to a conjugated alkene.
- Conjugated alkenes are more stable, so **4-bromo cyclohexane** will react faster than **5-bromo cycloheptane**.

3. **Comparing 2-bromo-1-phenylbutane and 3-bromo-1-phenylbutane**:
- 2-bromo-1-phenylbutane forms a conjugated alkene upon elimination, while 3-bromo-1-phenylbutane does not.
- Thus, the rate of E2 reaction for **2-bromo-1-phenylbutane** is greater than for **3-bromo-1-phenylbutane**.

4. **Comparing 3-bromo-1-phenylbutane and 3-bromo-cyclohexane**:
- 3-bromo-1-phenylbutane leads to a less stable alkene compared to 3-bromo-cyclohexane, which can form a conjugated product.
- Therefore, **3-bromo-cyclohexane** reacts faster than **3-bromo-1-phenylbutane**.

5. **Comparing 3-bromo-2-methylpentane and 2-bromo-4-methylpentane**:
- 3-bromo-2-methylpentane can form a more substituted alkene compared to 2-bromo-4-methylpentane.
- Hence, the rate of E2 reaction for **3-bromo-2-methylpentane** is greater than for **2-bromo-4-methylpentane**.

6. **Final Order of Rates**:
- From the analysis, we conclude that the correct order for the rate of E2 reactions is:
- 4-bromo cyclohexane > 2-bromo-1-phenylbutane > 3-bromo-cyclohexane > 3-bromo-1-phenylbutane > 3-bromo-2-methylpentane > 2-bromo-4-methylpentane.

### Conclusion:
The correct orders for the rate of E2 reactions are:
- 2-bromo-1-phenylbutane > 3-bromo-1-phenylbutane
- 3-bromo-cyclohexane > 3-bromo-1-phenylbutane
- 3-bromo-2-methylpentane > 2-bromo-4-methylpentane