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 information about the dissociation energies of hydrogen (H₂) and oxygen (O₂), as well as the heat of the reaction. Here’s a step-by-step solution:

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

### Step 2: Understand the Heat of Reaction
The heat of reaction (\( \Delta H \)) can be expressed in terms of the bond energies of the reactants and products:
\[ \Delta H = \text{(Bond energies of reactants)} - \text{(Bond energies of products)} \]

### Step 3: Identify Bond Energies
The bond energies are given as:
- Dissociation energy of \( H_2 \) = 104 kcal/mol
- Dissociation energy of \( O_2 \) = 118 kcal/mol

### Step 4: Write the Equation for Heat of Reaction
Substituting the bond energies into the heat of reaction equation:
\[ 10 \text{ kcal} = \left( \frac{1}{2} \times 104 \text{ kcal/mol} + \frac{1}{2} \times 118 \text{ kcal/mol} \right) - \text{Bond energy of } O-H \]

### Step 5: Simplify the Equation
Calculating the left side:
\[ 10 \text{ kcal} = \left( \frac{104}{2} + \frac{118}{2} \right) - \text{Bond energy of } O-H \]
\[ 10 \text{ kcal} = (52 + 59) - \text{Bond energy of } O-H \]
\[ 10 \text{ kcal} = 111 - \text{Bond energy of } O-H \]

### Step 6: Solve for Bond Energy of O-H
Rearranging the equation to find the bond energy of O-H:
\[ \text{Bond energy of } O-H = 111 - 10 \]
\[ \text{Bond energy of } O-H = 101 \text{ kcal/mol} \]

### Conclusion
The bond energy of the O-H bond is:
\[ \boxed{101 \text{ kcal/mol}} \]