The correct order for homolytic bond dissociation energies (`Delta H` in kcal/mol) for `CH_(4)(A), C_(2)H_(6)(B)` and `CH_(3)Br(C)` is

Options

A. `C gt B gt A`
B. `B gt A gt C`
C. `C gt A gt B`
D. `A gt B gt C`

Answer

To determine the correct order for the homolytic bond dissociation energies (ΔH in kcal/mol) for CH₄ (A), C₂H₆ (B), and CH₃Br (C), we will analyze the number of carbon-hydrogen bonds in each compound and the influence of the surrounding atoms on these bonds.

### Step-by-Step Solution:

1. **Identify the Structures**:
- **CH₄ (Methane)**: Contains one carbon atom bonded to four hydrogen atoms.
- **C₂H₆ (Ethane)**: Contains two carbon atoms, each bonded to hydrogen atoms. The structure has a total of six carbon-hydrogen bonds.
- **CH₃Br (Bromomethane)**: Contains one carbon atom bonded to three hydrogen atoms and one bromine atom.

2. **Count the Carbon-Hydrogen Bonds**:
- For **CH₄**: There are 4 C-H bonds.
- For **C₂H₆**: There are 6 C-H bonds.
- For **CH₃Br**: There are 3 C-H bonds.

3. **Consider the Influence of Other Atoms**:
- In **CH₄** and **C₂H₆**, the presence of only hydrogen atoms means that the C-H bonds are relatively strong due to the lack of electronegative atoms.
- In **CH₃Br**, the presence of bromine (a more electronegative atom) can weaken the C-H bonds due to the inductive effect, making them easier to break compared to the bonds in methane and ethane.

4. **Evaluate the Bond Dissociation Energies**:
- The bond dissociation energy is generally higher when there are more strong bonds. Thus, the order of bond dissociation energies will be influenced by the number of C-H bonds and the nature of surrounding atoms.
- **C₂H₆ (B)** has the highest number of C-H bonds (6), which contributes to a higher bond dissociation energy.
- **CH₄ (A)** has 4 C-H bonds, which is less than ethane but more than bromomethane.
- **CH₃Br (C)** has the least number of C-H bonds (3) and the presence of bromine weakens these bonds, resulting in the lowest bond dissociation energy.

5. **Final Order**:
- Therefore, the correct order for the homolytic bond dissociation energies is:
- **C₂H₆ (B) > CH₄ (A) > CH₃Br (C)**

### Conclusion:
The correct order for homolytic bond dissociation energies is:
**C₂H₆ (B) > CH₄ (A) > CH₃Br (C)**.