The energy required to break 76 gm gaseous fluorine into free gaseous atom is 180 kcal at `25^(@)`C. The bond energy of F - F bond will be

Options

A. 180 kcal
B. 90 kcal
C. 45 kcal
D. 104 kcal

Answer

To find the bond energy of the F-F bond in gaseous fluorine (F2), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We are given that breaking 76 grams of gaseous fluorine (F2) into free gaseous atoms requires 180 kcal of energy at 25°C.

2. **Calculate the Number of Moles of F2**:
- The molar mass of F2 (fluorine gas) is approximately 38 g/mol (since the atomic mass of fluorine is about 19 g/mol).
- To find the number of moles of F2 in 76 grams:
\[ \text{Number of moles of F2} = \frac{\text{mass}}{\text{molar mass}} = \frac{76 \text{ g}}{38 \text{ g/mol}} = 2 \text{ moles} \]

3. **Determine the Energy Required per Mole**:
- We know that breaking 2 moles of F2 requires 180 kcal of energy. Therefore, the energy required for 1 mole of F2 can be calculated as:
\[ \text{Energy per mole} = \frac{180 \text{ kcal}}{2} = 90 \text{ kcal} \]

4. **Identify the Bond Energy**:
- The bond energy of the F-F bond is the energy required to break one mole of F2 into its constituent atoms (2 F atoms). Since we have calculated that breaking 1 mole of F2 requires 90 kcal, we conclude that:
\[ \text{Bond energy of F-F bond} = 90 \text{ kcal/mol} \]

### Final Answer:
The bond energy of the F-F bond is **90 kcal/mol**.