Energy required to dissociate `4g` of gaseous hydrogen into free gaseous atoms is `208Kcal` at `25^(@)C`
The bond energy of `H-H` bond will be

Options

A. `104Kcal`
B. `10.4Kcal`
C. `1040Kcal`
D. `1.40Kcal`

Explanation

To find the bond energy of the H-H bond, we can follow these steps:

### Step 1: Understand the given data
We know that the energy required to dissociate 4 grams of gaseous hydrogen (H₂) into free gaseous atoms is 208 Kcal at 25°C.

### Step 2: Calculate the number of moles of hydrogen
The molar mass of hydrogen (H₂) is approximately 2 g/mol. Therefore, the number of moles in 4 grams of hydrogen can be calculated as follows:

\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{4 \text{ g}}{2 \text{ g/mol}} = 2 \text{ moles} \]

### Step 3: Relate the dissociation energy to bond energy
When 4 grams of hydrogen gas dissociates, it breaks 2 moles of H-H bonds. Each mole of H₂ contains Avogadro's number of molecules (approximately \(6.022 \times 10^{23}\)).

### Step 4: Calculate the energy required to break one H-H bond
Since the energy required to dissociate 2 moles of H₂ is 208 Kcal, the energy required to break one mole of H-H bonds (which corresponds to 1 mole of H₂) is:

\[ \text{Energy per mole} = \frac{208 \text{ Kcal}}{2} = 104 \text{ Kcal} \]

### Step 5: Conclusion
Thus, the bond energy of one H-H bond is 104 Kcal.

### Final Answer
The bond energy of the H-H bond is **104 Kcal**.

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