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, we can follow these steps:

### Step 1: Understand the given information
We know that the energy required to break 76 grams of gaseous fluorine (F2) into free gaseous atoms is 180 kcal.

### Step 2: Determine the molar mass of F2
The molar mass of fluorine (F) is approximately 19 g/mol. Therefore, the molar mass of F2 is:
\[ \text{Molar mass of F2} = 2 \times 19 \, \text{g/mol} = 38 \, \text{g/mol} \]

### Step 3: Calculate the number of moles of F2 in 76 grams
To find the number of moles of F2 in 76 grams, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
Substituting the values:
\[ \text{Number of moles of F2} = \frac{76 \, \text{g}}{38 \, \text{g/mol}} = 2 \, \text{moles} \]

### Step 4: Relate the energy to the bond energy
The energy required to break 2 moles of F2 into free atoms is 180 kcal. Since breaking one mole of F2 produces 2 moles of F atoms, the energy required to break one mole of F2 (which contains one F-F bond) is:
\[ \text{Energy per mole of F2} = \frac{180 \, \text{kcal}}{2} = 90 \, \text{kcal} \]

### Step 5: Conclusion
Thus, the bond energy of the F-F bond is 90 kcal.

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

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