The enthalpy of combustion of `H_(2)` , cyclohexene `(C_(6)H_(10))` and cyclohexane `(C_(6)H_(12))` are `-241` , `-3800` and `-3920KJ` per mol respectively. Heat of hydrogenation of cyclohexene is

Options

A. `-121` KJ per mol
B. `+121` KJ per mol
C. `+242` KJ per mol
D. `-242` KJ per mol

Explanation

To find the heat of hydrogenation of cyclohexene (C₆H₁₀), we can use the enthalpy of combustion values provided for hydrogen (H₂), cyclohexene (C₆H₁₀), and cyclohexane (C₆H₁₂). The heat of hydrogenation can be calculated using Hess's law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps.

### Step-by-Step Solution:

1. **Write the combustion equations:**
- For hydrogen:
\[ \text{H}_2 + \frac{1}{2} \text{O}_2 \rightarrow \text{H}_2\text{O} \quad \Delta H = -241 \, \text{kJ/mol} \quad \text{(Equation 1)} \]
- For cyclohexene:
\[ \text{C}_6\text{H}_{10} + \frac{17}{2} \text{O}_2 \rightarrow 6 \text{CO}_2 + 5 \text{H}_2\text{O} \quad \Delta H = -3800 \, \text{kJ/mol} \quad \text{(Equation 2)} \]
- For cyclohexane:
\[ \text{C}_6\text{H}_{12} + 9 \text{O}_2 \rightarrow 6 \text{CO}_2 + 6 \text{H}_2\text{O} \quad \Delta H = -3920 \, \text{kJ/mol} \quad \text{(Equation 3)} \]

2. **Add Equations 1 and 2:**
- When we add the combustion of hydrogen and cyclohexene:
\[ \text{H}_2 + \frac{1}{2} \text{O}_2 + \text{C}_6\text{H}_{10} + \frac{17}{2} \text{O}_2 \rightarrow 6 \text{CO}_2 + 5 \text{H}_2\text{O} \]
- This simplifies to:
\[ \text{C}_6\text{H}_{10} + \text{H}_2 + 9 \text{O}_2 \rightarrow 6 \text{CO}_2 + 6 \text{H}_2\text{O} \quad \text{(Equation 4)} \]

3. **Subtract Equation 3 from Equation 4:**
- We subtract the combustion of cyclohexane (Equation 3) from the combined equation (Equation 4):
\[ \left(\text{C}_6\text{H}_{10} + \text{H}_2 + 9 \text{O}_2 \rightarrow 6 \text{CO}_2 + 6 \text{H}_2\text{O}\right) - \left(\text{C}_6\text{H}_{12} + 9 \text{O}_2 \rightarrow 6 \text{CO}_2 + 6 \text{H}_2\text{O}\right) \]
- This results in:
\[ \text{C}_6\text{H}_{10} + \text{H}_2 \rightarrow \text{C}_6\text{H}_{12} \quad \text{(Equation 5)} \]

4. **Calculate the enthalpy of hydrogenation:**
- The enthalpy change for this reaction (hydrogenation of cyclohexene) is given by:
\[ \Delta H_{\text{hydrogenation}} = \Delta H_{\text{combustion of H}_2} + \Delta H_{\text{combustion of C}_6\text{H}_{10}} - \Delta H_{\text{combustion of C}_6\text{H}_{12}} \]
- Substituting the values:
\[ \Delta H_{\text{hydrogenation}} = (-241) + (-3800) - (-3920) \]
- Simplifying this:
\[ \Delta H_{\text{hydrogenation}} = -241 - 3800 + 3920 = -121 \, \text{kJ/mol} \]

### Final Answer:
The heat of hydrogenation of cyclohexene (C₆H₁₀) is \(-121 \, \text{kJ/mol}\).