Given that `Deltah_(f)(H)=218 kJ//mol`. Express the `H-H` bond energy in `K cal//mol`

Options

A. 52.15
B. 911
C. 104
D. 52153

Answer

To solve the problem of converting the heat of formation of hydrogen from kJ/mol to kcal/mol, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
The heat of formation of hydrogen (ΔH_f(H)) is given as 218 kJ/mol.

2. **Understand the Reaction:**
The formation of hydrogen can be represented as:
\[ \frac{1}{2} H_2 \rightarrow H \]
This indicates that breaking one mole of H-H bond (in H2) produces two moles of hydrogen atoms (H).

3. **Calculate the Bond Energy:**
The bond energy of the H-H bond can be calculated by recognizing that breaking one mole of H-H bonds yields two moles of hydrogen atoms. Therefore, the energy required to break one mole of H-H bonds is:
\[ \text{Bond Energy} = 2 \times \Delta H_f(H) = 2 \times 218 \text{ kJ/mol} = 436 \text{ kJ/mol} \]

4. **Convert kJ to kcal:**
To convert the bond energy from kJ to kcal, we use the conversion factor:
\[ 1 \text{ kcal} = 4.2 \text{ kJ} \]
Therefore, we convert 436 kJ/mol to kcal/mol:
\[ \text{Bond Energy in kcal/mol} = \frac{436 \text{ kJ/mol}}{4.2 \text{ kJ/kcal}} \approx 103.81 \text{ kcal/mol} \]
Rounding this gives approximately:
\[ \text{Bond Energy} \approx 104 \text{ kcal/mol} \]

5. **Final Answer:**
The hydrogen-hydrogen bond energy is approximately 104 kcal/mol.