Which of the following alkanes is the least reactive towards free-radical substitution reactions ?

Options

A. (a)`CH_(4)`
B. (b)`(CH_(3))_(3)CH`
C. (c)`CH_(3)CH_(3)`
D. (d)`CH_(3)CH_(2)CH_(3)`

Answer

To determine which alkane is the least reactive towards free-radical substitution reactions, we need to analyze the stability of the free-radical intermediates formed during these reactions. The stability of these intermediates is crucial because more stable intermediates lead to more reactive alkanes.

### Step-by-Step Solution:

1. **Understanding Free-Radical Substitution**:
Free-radical substitution reactions involve the formation of free radicals, which are highly reactive species with unpaired electrons. The stability of these free radicals is a key factor in determining the reactivity of the alkane.

2. **Identifying the Alkanes**:
We need to consider the alkanes provided in the question. Common examples include methane (CH4), ethane (C2H6), propane (C3H8), and butane (C4H10).

3. **Stability of Free-Radical Intermediates**:
The stability of free radicals increases with the number of alkyl groups attached to the carbon bearing the unpaired electron. This is due to the +I (inductive) effect, where alkyl groups donate electron density to the positively charged carbon, stabilizing the radical.

- **Methane (CH4)**: Forms a primary radical (CH3•) with no alkyl groups to stabilize it.
- **Ethane (C2H6)**: Forms a primary radical (C2H5•) with one alkyl group.
- **Propane (C3H8)**: Forms a secondary radical (C3H7•) with two alkyl groups.
- **Butane (C4H10)**: Can form both primary (C4H9•) and secondary radicals, but also has the potential for tertiary radicals if branched.

4. **Comparing Reactivity**:
- Methane, having no alkyl groups, has the least stable radical (CH3•) and thus is the least reactive towards free-radical substitution.
- Ethane is more reactive than methane due to the presence of one alkyl group.
- Propane and butane are even more reactive due to the presence of more alkyl groups, which stabilize their radicals.

5. **Conclusion**:
Based on the stability of the radicals formed, methane (CH4) is the least reactive alkane towards free-radical substitution reactions.

### Final Answer:
The least reactive alkane towards free-radical substitution reactions is **methane (CH4)**.