Question

The standard enthalpy of combustion at \(25^{\circ} \mathrm{C}\) of \(\mathrm{H}_{2}\), \(\mathrm{C}_{6} \mathrm{H}_{10}\) and cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)\) are \(-241,-3800\) and \(-3920 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. Calculate heat of hydrogenation of cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{10}\right)\). (a) \(-161 \mathrm{kJmol}^{-1}\) (b) \(-131 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-121 \mathrm{kJmol}^{-1}\) (d) none

Short answer

The heat of hydrogenation is \(-121 \mathrm{kJmol}^{-1}\), which corresponds to option (c).

Step-by-step solution

Understanding the Problem

We need to find the heat of hydrogenation for the conversion of cyclohexene (\(\mathrm{C}_{6} \mathrm{H}_{10}\)) to cyclohexane (\(\mathrm{C}_{6} \mathrm{H}_{12}\)). We are provided enthalpies of combustion for hydrogen, cyclohexene, and cyclohexane at standard conditions.

Write Chemical Equations

The combustion equations in standard form are:1. \(\mathrm{H}_{2}(g) + \frac{1}{2}\mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2}\mathrm{O}(l)\)2. \(\mathrm{C}_{6} \mathrm{H}_{10}(l) + \frac{17}{2}\mathrm{O}_{2}(g) \rightarrow 6\mathrm{CO}_{2}(g) + 5\mathrm{H}_{2}\mathrm{O}(l)\)3. \(\mathrm{C}_{6} \mathrm{H}_{12}(l) + 9 \mathrm{O}_{2}(g) \rightarrow 6\mathrm{CO}_{2}(g) + 6\mathrm{H}_{2}\mathrm{O}(l)\)

Express Combustion Enthalpies

Using Hess's law, rewrite the given enthalpies:1. \(\Delta H_{comb}^{\mathrm{H}_{2}} = -241\, \mathrm{kJ} \mathrm{~mol}^{-1}\)2. \(\Delta H_{comb}^{\mathrm{C}_{6} \mathrm{H}_{10}} = -3800\, \mathrm{kJ} \mathrm{~mol}^{-1}\)3. \(\Delta H_{comb}^{\mathrm{C}_{6} \mathrm{H}_{12}} = -3920\, \mathrm{kJ} \mathrm{~mol}^{-1}\)

Write Transformation Reaction

The hydrogenation reaction should be:\(\mathrm{C}_{6}\mathrm{H}_{10} + \mathrm{H}_{2} \rightarrow \mathrm{C}_{6} \mathrm{H}_{12}\)

Apply Hess’s Law

Using Hess's law:\[\Delta\text{H}_{hydrogenation} = \Delta\text{H}_{comb,\mathrm{C}_{6} \mathrm{H}_{12}} - (\Delta\text{H}_{comb,\mathrm{C}_{6} \mathrm{H}_{10}} + \Delta\text{H}_{comb,\mathrm{H}_{2}})\]Substitute the given values:\[\Delta\text{H}_{hydrogenation} = (-3920) - ((-3800) + (-241))\]

Calculate Heat of Hydrogenation

Calculate the hydrogenation enthalpy:\[\Delta\text{H}_{hydrogenation} = -3920 + 3800 + 241\]\[\Delta\text{H}_{hydrogenation} = 121\, \mathrm{kJ} \mathrm{~mol}^{-1}\]

Identify the Option

The calculated heat of hydrogenation is \(-121 \mathrm{kJmol}^{-1}\). The option that matches this result is option (c).

Key concepts

Hess's Law

In chemical reactions, energy changes play a crucial role and one such principle is Hess's Law. This law enables us to determine the enthalpy change of a reaction without being concerned about the reaction path. It states that if a process can be written as the sum of several steps, then the enthalpy change of the overall process is the sum of the enthalpy changes of those steps. This impresses upon the fact that enthalpy is a state function, which means it depends only on the initial and final states, not on the path taken.
To illustrate, consider the exercise where enthalpies of combustion are given. Using Hess’s Law, we were able to construct an indirect pathway to determine the heat of hydrogenation for cyclohexene by utilizing its enthalpy of combustion, along with those for hydrogen and cyclohexane.
This demonstrated that through strategic rearrangement and combination of enthalpy values of known reactions, we can find the unknown enthalpy change for any reaction that might be cumbersome to measure directly.

Heat of Hydrogenation

The heat of hydrogenation pertains to the enthalpy change observed when a molecule undergoes hydrogenation. Hydrogenation is an addition reaction where hydrogen is added to another compound, typically an alkene or alkyne, converting them into saturated compounds such as alkanes or cycloalkanes.
In the exercise, cyclohexene () reacts with hydrogen to form cyclohexane (). This conversion involves an energy release measured as the heat of hydrogenation. Such reactions are exothermic, meaning they release heat, as indicated by the negative sign in the calculated heat of hydrogenation. The larger this value, the more stable the alkene became after hydrogenation. Understanding this concept helps comprehend the stability and energy dynamics of different molecules, as well as provides insight into how double bonds affect molecular structures.

Chemical Thermodynamics

Chemical thermodynamics deals with the study of energy transformations in chemical reactions. It applies laws of thermodynamics to chemical reactions to predict reaction spontaneity, equilibrium position, and energy requirements.
The role of chemical thermodynamics in this exercise arises in the calculation of enthalpies—particularly in how energy is conserved and transformed during the combustion and hydrogenation reactions. Through this methodical approach, we explored how the standard enthalpy of combustion data integrates into determining heats of reaction and hydrogenation using Hess’s Law.
This foundational understanding is pivotal, as it allows chemists to predict how reactions proceed, how energy-efficient these processes are, and their feasibility in industrial or laboratory settings. Within the broader scope of studying chemical reactions, thermodynamics offers invaluable insights into the energetic profile and potential applications of chemical substances.