Which of the following (if any) shall produce the largest percentage of tertiary halide on monohalogenation at 400K

Options

A. `H_(3)C -underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)-H overset(Cl_(2))to`
B. `H_(3)C -underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)-H overset(F_(2))to`
C. `H_(3)C-underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)-H overset(Br_(2))to`
D. All produce same percentage

Answer

To determine which halogen will produce the largest percentage of tertiary halide on monohalogenation at 400 K, we need to analyze the reactivity and selectivity of different halogens in the halogenation process.

### Step-by-Step Solution:

1. **Understanding Monohalogenation**:
- Monohalogenation involves the substitution of one hydrogen atom in an alkane with a halogen atom. This process can lead to the formation of primary, secondary, or tertiary halides depending on the structure of the alkane and the halogen used.

2. **Free Radical Mechanism**:
- The mechanism of monohalogenation involves the formation of free radicals. For example, when Cl2 is used, it dissociates into two Cl radicals:
\[ \text{Cl}_2 \rightarrow 2 \text{Cl}^\cdot \]
- These Cl radicals can then abstract hydrogen atoms from the alkane, forming alkyl radicals.

3. **Stability of Alkyl Radicals**:
- The stability of the alkyl radicals formed during the reaction is crucial. Tertiary radicals are more stable than secondary and primary radicals due to hyperconjugation and the inductive effect of alkyl groups.
- The order of stability is:
\[ \text{Tertiary} > \text{Secondary} > \text{Primary} \]

4. **Selectivity of Halogens**:
- Different halogens have different selectivities for forming tertiary halides. The order of reactivity and selectivity for halogens is:
\[ \text{I}_2 > \text{Br}_2 > \text{Cl}_2 > \text{F}_2 \]
- While iodine is the most selective, it is also less reactive, which leads to the formation of primary and secondary halides. Bromine, on the other hand, is less reactive than chlorine but more selective, making it favorable for the formation of tertiary halides.

5. **Conclusion**:
- At 400 K, bromine (Br2) will produce the largest percentage of tertiary halide due to its balance of reactivity and selectivity. Chlorine (Cl2) is more reactive but less selective, and fluorine (F2) is too reactive, leading to a mixture of products without preference for tertiary halides.

### Final Answer:
The halogen that will produce the largest percentage of tertiary halide on monohalogenation at 400 K is **Bromine (Br2)**.