The enthalpy of combustion at `25^(@)C` of `H_(2)(g)`, cyclohexane and cyclohexene are -241, 3920 and `-3717 kJ "mole"^(-1)` respectively. The heat of hydrogenation of cyclohexene is ( Kcal/mole) approximate integer:

Explanation

To find the heat of hydrogenation of cyclohexene, we will use the given enthalpy of combustion values and apply Hess's law. Here’s a step-by-step solution:

### Step 1: Write down the given enthalpy values
- Enthalpy of combustion of \( H_2(g) \): \( \Delta H = -241 \, \text{kJ/mol} \)
- Enthalpy of combustion of cyclohexane \( (C_6H_{12}) \): \( \Delta H = -3920 \, \text{kJ/mol} \)
- Enthalpy of combustion of cyclohexene \( (C_6H_{10}) \): \( \Delta H = -3717 \, \text{kJ/mol} \)

### Step 2: Write the combustion reactions
1. For hydrogen:
\[ H_2(g) + \frac{1}{2} O_2(g) \rightarrow H_2O(l) \quad \Delta H = -241 \, \text{kJ/mol} \]

2. For cyclohexene:
\[ C_6H_{10} + 7.5 O_2(g) \rightarrow 6 CO_2(g) + 5 H_2O(l) \quad \Delta H = -3717 \, \text{kJ/mol} \]

3. For cyclohexane:
\[ C_6H_{12} + 6 O_2(g) \rightarrow 6 CO_2(g) + 6 H_2O(l) \quad \Delta H = -3920 \, \text{kJ/mol} \]

### Step 3: Set up the desired reaction
The desired reaction for the hydrogenation of cyclohexene is:
\[ C_6H_{10} + H_2(g) \rightarrow C_6H_{12} \]

### Step 4: Manipulate the equations
To find the heat of hydrogenation, we can use Hess's law:
- We will add the combustion of hydrogen and cyclohexene and subtract the combustion of cyclohexane:
\[ \Delta H_{\text{hydrogenation}} = \Delta H_{\text{combustion of } H_2} + \Delta H_{\text{combustion of } C_6H_{10}} - \Delta H_{\text{combustion of } C_6H_{12}} \]

### Step 5: Substitute the values
Substituting the values we have:
\[ \Delta H_{\text{hydrogenation}} = (-241) + (-3717) - (-3920) \]

### Step 6: Calculate the result
Calculating the above expression:
\[ \Delta H_{\text{hydrogenation}} = -241 - 3717 + 3920 \]
\[ \Delta H_{\text{hydrogenation}} = -38 \, \text{kJ/mol} \]

### Step 7: Convert kJ to kcal
To convert kJ to kcal, we use the conversion factor \( 1 \, \text{kJ} = 0.239 \, \text{kcal} \):
\[ \Delta H_{\text{hydrogenation}} = -38 \, \text{kJ/mol} \times 0.239 \, \text{kcal/kJ} \approx -9.06 \, \text{kcal/mol} \]

### Step 8: Round to the nearest integer
Rounding -9.06 gives us approximately:
\[ \Delta H_{\text{hydrogenation}} \approx -9 \, \text{kcal/mol} \]

### Final Answer
The heat of hydrogenation of cyclohexene is approximately **-9 kcal/mol**.