The energy of activation is lowest for which reaction?

Options

A. `RCH_(2) O^(o+)H_(2) rarr R C^(o+)H_(2)`
B. `R_(2)CHO^(o+)H_(2) rarr R_(2)C^(o+)H`
C. `R_(3)C - O^(o+)H_(2) rarr R_(3)C^(o+)`
D. All have the same energy of activation.

Explanation

To determine which reaction has the lowest energy of activation, we need to analyze the stability of the carbocations formed in each reaction. Here’s a step-by-step solution:

### Step 1: Understand Activation Energy
Activation energy is the minimum energy required for a reaction to occur. It is particularly relevant when considering reactions that form intermediates, such as carbocations.

**Hint:** Activation energy is related to the stability of the intermediates formed during the reaction.

### Step 2: Identify the Type of Carbocations
In the reactions mentioned, we need to identify the type of carbocations formed:
- **Primary Carbocation**: Formed when the positively charged carbon is attached to one alkyl group.
- **Secondary Carbocation**: Formed when the positively charged carbon is attached to two alkyl groups.
- **Tertiary Carbocation**: Formed when the positively charged carbon is attached to three alkyl groups.

**Hint:** The more alkyl groups attached to the positively charged carbon, the more stable the carbocation.

### Step 3: Stability of Carbocations
The stability of carbocations increases with the number of alkyl groups attached:
- **Tertiary (3°) Carbocation**: Most stable due to hyperconjugation and inductive effects from three alkyl groups.
- **Secondary (2°) Carbocation**: Moderately stable with two alkyl groups.
- **Primary (1°) Carbocation**: Least stable with only one alkyl group.

**Hint:** Remember that stability is key to determining activation energy; more stable intermediates require less energy to form.

### Step 4: Relate Stability to Activation Energy
Since the activation energy is inversely related to the stability of the intermediate, the reaction that forms the most stable carbocation (tertiary) will have the lowest activation energy.

**Hint:** Look for the reaction that produces a tertiary carbocation to find the lowest activation energy.

### Step 5: Conclusion
Based on the analysis, the reaction that forms a tertiary carbocation will have the lowest activation energy. Therefore, the answer to the question is that the energy of activation is lowest for the reaction that produces a tertiary carbocation.

**Final Answer:** The reaction with the lowest activation energy is the one that forms a tertiary carbocation (option C).