The enthalpy of combustion of cyclohexane, cyclohexene and $H_{2}$ are respectively -3920, -3800 and -241 $kJmol^{-1}$. The heat of hydrogenation of cyclohexene is :

Question

Accepted Answer

To determine the heat of hydrogenation of cyclohexene, we need to consider the enthalpy changes involved in the combustion reactions provided and apply Hess's Law. Hess's Law states that the total enthalpy change for a reaction is the same, regardless of the pathway taken, as long as the initial and final conditions are the same.

Given:
- Enthalpy of combustion of cyclohexane ($C_6H_{12}$): $-3920 \, \text{kJ/mol}$
- Enthalpy of combustion of cyclohexene ($C_6H_{10}$): $-3800 \, \text{kJ/mol}$
- Enthalpy of combustion of hydrogen ($H_2$): $-241 \, \text{kJ/mol}$

The reaction for the hydrogenation of cyclohexene to cyclohexane is:
$$ C_6H_{10} + H_2 \rightarrow C_6H_{12} $$

To find the heat of hydrogenation, we can use the enthalpy changes of the combustion reactions:

1. Combustion of cyclohexene:
   $$ C_6H_{10} + \frac{17}{2} O_2 \rightarrow 6 CO_2 + 5 H_2O \quad \Delta H = -3800 \, \text{kJ/mol} $$

2. Combustion of hydrogen:
   $$ H_2 + \frac{1}{2} O_2 \rightarrow H_2O \quad \Delta H = -241 \, \text{kJ/mol} $$

3. Combustion of cyclohexane:
   $$ C_6H_{12} + 9 O_2 \rightarrow 6 CO_2 + 6 H_2O \quad \Delta H = -3920 \, \text{kJ/mol} $$

Using Hess's Law, the enthalpy change for the hydrogenation reaction can be calculated as follows:

$$
\Delta H_{\text{hydrogenation}} = \Delta H_{\text{combustion of cyclohexane}} - (\Delta H_{\text{combustion of cyclohexene}} + \Delta H_{\text{combustion of hydrogen}})
$$

Substituting the given values:

$$
\Delta H_{\text{hydrogenation}} = (-3920) - [(-3800) + (-241)]
$$

$$
\Delta H_{\text{hydrogenation}} = -3920 + 3800 + 241
$$

$$
\Delta H_{\text{hydrogenation}} = 121 \, \text{kJ/mol}
$$

Since the heat of hydrogenation is the energy released when cyclohexene is converted to cyclohexane, it is an exothermic process, and the value should be negative. Therefore, the correct answer is:

Option 1: $-121 \, \text{kJ/mol}$

Explanation for other options:
- Option 2: $121 \, \text{kJ/mol}$ is incorrect because it suggests an endothermic process, which is not the case for hydrogenation.
- Option 3: $-242 \, \text{kJ/mol}$ is incorrect because it does not match the calculated value.
- Option 4: $242 \, \text{kJ/mol}$ is incorrect because it suggests an endothermic process, which is not applicable here.

Thus, Option 1 is the correct answer, as it accurately represents the exothermic nature of the hydrogenation of cyclohexene.