Problem 31 - Chemistry in 30 days

Question

The enthalpy of combustion of cyclohexane, cyclohexene and \(\mathrm{H}_{2}\) are respectively \(-3920,-3800\) and \(-241 \mathrm{~kJ} \mathrm{~mol}^{-1}\). The heat of hydrogenation of cyclohexene is (a) \(-121 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(+121 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-242 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(+242 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Step-by-Step Solution

Answer

The heat of hydrogenation of cyclohexene is \(-121 \text{ kJ mol}^{-1}\), option (a).

Step 1: Understanding the Problem

We need to find the heat of hydrogenation of cyclohexene. The heat of hydrogenation is defined as the enthalpy change when one mole of an unsaturated compound reacts with hydrogen to form a saturated compound. Thus, we need to determine the enthalpy change when cyclohexene is converted to cyclohexane with hydrogen gas.

Step 2: Writing the Reaction

The reaction for the hydrogenation of cyclohexene to cyclohexane can be written as: \[ \text{cyclohexene} + \text{H}_2 \rightarrow \text{cyclohexane} \]

Step 3: Applying Hess's Law

According to Hess's Law, the total enthalpy change for the reaction is the sum of the enthalpy changes for each step. We can express this as: \[ \Delta H_{hyd} = \Delta H_{comb} (\text{cyclohexane}) - \left( \Delta H_{comb} (\text{cyclohexene}) + \Delta H_{comb} (\text{H}_2) \right) \]Here, \( \Delta H_{comb} \) represents the enthalpy of combustion of each substance.

Step 4: Calculating the Heat of Hydrogenation

Substituting the given values into the Hess's Law equation:\[ \Delta H_{hyd} = (-3920) - \left( -3800 + (-241) \right) \]\[ \Delta H_{hyd} = -3920 + 3800 + 241 \]\[ \Delta H_{hyd} = -121 \text{ kJ mol}^{-1} \]

Step 5: Conclusion

The calculated heat of hydrogenation of cyclohexene is \(-121 \text{ kJ mol}^{-1}\). This corresponds to the option (a) given in the problem.

Key Concepts

Enthalpy of Combustion

The enthalpy of combustion is the energy released when one mole of a substance is burned in the presence of oxygen. It's a vital concept in thermochemistry because it quantifies the energy contained in chemical bonds. For instance, when cyclohexane combusts completely, it releases -3920 kJ/mol of energy. Similarly, the combustion of cyclohexene and hydrogen releases -3800 kJ/mol and -241 kJ/mol, respectively. Knowing the enthalpy of combustion of substances can tell us a lot about their stability and reactivity. Substances with high negative enthalpy values release more energy, indicating that they have strong bonds that store a lot of energy which is released during combustion.
To summarize, the enthalpy of combustion is a crucial parameter for understanding the energy profile and tendencies of chemical reactions.

Hess's Law

Hess's Law is a principle of chemistry that states the total enthalpy change during a chemical reaction is the same, no matter how many steps the reaction is carried out in. This concept is incredibly useful for calculating enthalpy changes that are difficult to measure directly. In our original exercise, we applied Hess’s Law to determine the heat of hydrogenation of cyclohexene.
The idea is straightforward: since the change in energy from reactants to products is independent of the pathway taken, you can add up the enthalpy changes of individual steps to find the overall change. In the problem, we used the enthalpies of combustion for cyclohexane, cyclohexene, and hydrogen gas to find the enthalpy change for converting cyclohexene to cyclohexane. This allows us to approach complex reactions in a manageable way by focusing on known values of simpler reactions.

Cyclohexane

Cyclohexane is a saturated hydrocarbon with the chemical formula C\(_6\)H\(_{12}\). It's a cycloalkane, meaning it has a ring structure made entirely of carbon atoms connected by single bonds. As a saturated compound, cyclohexane is very stable due to its single bonds, which release a significant amount of energy when they react, especially evident in its combustion process with an enthalpy change of -3920 kJ/mol.
In practical applications, cyclohexane is often used as a solvent and as a precursor in the production of other compounds, such as nylon. Understanding cyclohexane's chemical properties provides insight into its role in various chemical reactions, including its reaction with cyclohexene during hydrogenation.

Cyclohexene

Cyclohexene is an unsaturated hydrocarbon with the chemical formula C\(_6\)H\(_{10}\). As a member of the alkene family, it contains a double bond within its carbon ring. This double bond makes cyclohexene more reactive than its saturated cousin, cyclohexane. The reactivity is a result of the presence of the double bond, which can readily participate in chemical reactions, such as hydrogenation.
The heat of hydrogenation for cyclohexene is -121 kJ/mol, which is an energy release associated with converting cyclohexene to cyclohexane through the addition of hydrogen. Cyclohexene's unsaturation points to its lesser stability compared to saturated hydrocarbons, as demonstrated by its higher enthalpy of combustion at -3800 kJ/mol. This makes it an interesting compound for studying reactions that involve the conversion of unsaturated to saturated compounds.

Thermochemistry

Thermochemistry is the study of energy changes, specifically heat, involved in chemical reactions. This field helps us understand how energy is absorbed or released during reactions. It's crucial for predicting reaction behavior and determining energy efficiencies, especially for industrial processes.
In thermochemistry, we often deal with enthalpy changes, like the enthalpy of combustion or the heat of hydrogenation. By analyzing these parameters, we gain insight into the energy profile of a molecule—knowing how much energy a reaction releases or consumes can guide synthetic chemistry projects, energy production, and environmental management.
Understanding thermochemistry allows chemists to harness chemical reactions for practical applications, ensuring processes are energetically favorable and sustainable.