The dissociation energies of `H_2and O_2` are 104 and `118 " kcal mol"^(-1)` respectively. The heat of reaction `1/2H_2(g) +1/2O_2(g) rarrO-H(g) ` is 10 kcal. The bond energy of O - H bond is

Options

A. 101 kcal/mol
B. 111 kcal/mol
C. 10.1 kcal/mol
D. 11.1 kcal/mol

Answer

To find the bond energy of the O-H bond, we can use the given dissociation energies and the heat of reaction. Here’s a step-by-step solution:

### Step 1: Write the Reaction
The reaction is given as:
\[ \frac{1}{2} H_2(g) + \frac{1}{2} O_2(g) \rightarrow OH(g) \]

### Step 2: Identify Given Values
- Dissociation energy of \( H_2 \) = 104 kcal/mol
- Dissociation energy of \( O_2 \) = 118 kcal/mol
- Heat of reaction (\( \Delta H \)) = 10 kcal

### Step 3: Calculate the Energy Required to Break Bonds
The energy required to break the bonds in the reactants can be calculated as follows:
- For \( H_2 \): Since we have \( \frac{1}{2} H_2 \), the energy required is:
\[ \frac{1}{2} \times 104 \text{ kcal/mol} = 52 \text{ kcal/mol} \]
- For \( O_2 \): Since we have \( \frac{1}{2} O_2 \), the energy required is:
\[ \frac{1}{2} \times 118 \text{ kcal/mol} = 59 \text{ kcal/mol} \]

### Step 4: Total Energy of Reactants
Now, we can sum the energies from both reactants:
\[ \text{Total Energy of Reactants} = 52 \text{ kcal/mol} + 59 \text{ kcal/mol} = 111 \text{ kcal/mol} \]

### Step 5: Use the Heat of Reaction to Find the Bond Energy
The heat of reaction is defined as:
\[ \Delta H = \text{Energy of Reactants} - \text{Bond Energy of Products} \]
Rearranging gives us:
\[ \text{Bond Energy of Products} = \text{Energy of Reactants} - \Delta H \]
Substituting the values we have:
\[ \text{Bond Energy of Products} = 111 \text{ kcal/mol} - 10 \text{ kcal/mol} = 101 \text{ kcal/mol} \]

### Step 6: Conclusion
The bond energy of the O-H bond is:
\[ \text{Bond Energy of O-H} = 101 \text{ kcal/mol} \]

### Final Answer
The bond energy of the O-H bond is **101 kcal/mol**.

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