Problem 112 - Chemistry: The Central Science in SI Units, Global Edition

Question

The hydrocarbons cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}(l), \Delta H_{f}^{\circ}=-156\right.\) \(\mathrm{kJ} / \mathrm{mol}\) ) and 1-hexene \(\left(\mathrm{C}_{6} \mathrm{H}_{12}(l), \Delta H_{f}^{\circ}=-74 \mathrm{~kJ} / \mathrm{mol}\right)\) have the same empirical formula. (a) Calculate the standard enthalpy change for the transformation of cyclohexane to 1-hexene. (b) Which has greater enthalpy, cyclohexane or 1-hexene? (c) Without doing a further calculation and knowing the answer to (b), do you expect cyclohexane or 1-hexene to have the larger combustion enthalpy?

Step-by-Step Solution

Answer

(a) The standard enthalpy change for the transformation of cyclohexane to 1-hexene is 82 kJ/mol. (b) Cyclohexane has a greater enthalpy. (c) We can expect cyclohexane to have the larger combustion enthalpy compared to 1-hexene.

Step 1: Calculate the standard enthalpy change for the transformation

In order to calculate the standard enthalpy change for the transformation of cyclohexane to 1-hexene, use the standard enthalpy of formation values: \(\Delta H_{f}^{\circ}(\mathrm{C}_{6} \mathrm{H}_{12}(l))\) \[ \Delta H_{transformation} = \Delta H_f^{\circ} (1\text{-hexene}) - \Delta H_f^{\circ} (\text{cyclohexane}) \] Plug in the given values: \[ \Delta H_{transformation} = (-74 \,\mathrm{kJ/mol}) - (-156\, \mathrm{kJ/mol}) \]

Step 2: Solve for the enthalpy change

Add the values to get the enthalpy change of the transformation: \[ \Delta H_{transformation} = 82\, \mathrm{kJ/mol} \] (a) The standard enthalpy change for the transformation of cyclohexane to 1-hexene is 82 kJ/mol.

Step 3: Compare enthalpies

Compare the standard enthalpy of formation values provided in the exercise. We have: \[ \Delta H_f^{\circ} (\text{cyclohexane}) = -156\, \mathrm{kJ/mol} \] \[ \Delta H_f^{\circ} (1\text{-hexene}) = -74\, \mathrm{kJ/mol} \] A more negative enthalpy of formation indicates a more stable compound. (b) Since the enthalpy of formation of cyclohexane is more negative than that of 1-hexene, cyclohexane has a greater enthalpy.

Step 4: Predict combustion enthalpy

Knowing that cyclohexane has greater enthalpy (more stable) and without calculating the actual combustion enthalpies, we can expect a more stable compound to release more energy upon combustion. (c) Therefore, we can expect cyclohexane to have the larger combustion enthalpy compared to 1-hexene.

Key Concepts

Standard Enthalpy of Formation

The standard enthalpy of formation, denoted as \( \Delta H_f^{\circ} \), is a fundamental concept in thermochemistry. It represents the enthalpy change when one mole of a compound is formed from its elements in their standard states.
This value is crucial because it provides a reference point for calculating the enthalpy changes in chemical reactions. For example, the standard enthalpy of formation for cyclohexane is \(-156\, \text{kJ/mol}\), meaning that forming 1 mole of cyclohexane from carbon and hydrogen releases 156 kJ of energy.
Values of \( \Delta H_f^{\circ} \) are typically negative for stable compounds, indicating that energy is released when the compound forms. A more negative \( \Delta H_f^{\circ} \) implies greater stability of the compound compared to others with similar molecular makeup. Thus, when comparing compounds, such as cyclohexane and 1-hexene, the compound with the more negative \( \Delta H_f^{\circ} \) is usually more energy-efficient and stable.
In context, since cyclohexane has a \( \Delta H_f^{\circ} \) of \(-156\, \text{kJ/mol}\) and 1-hexene has \(-74\, \text{kJ/mol}\), cyclohexane is more stable.

Hydrocarbons

Hydrocarbons are organic compounds made up entirely of carbon and hydrogen atoms. They serve as a primary source of energy and are the fundamental building blocks for complex organic molecules.
Cyclohexane and 1-hexene are examples of hydrocarbons, both with the chemical formula \( \text{C}_6\text{H}_{12}\). However, despite having the same molecular formula, the two compounds have different structures and properties.
Cyclohexane is a saturated hydrocarbon, forming a ring structure that doesn't contain any double bonds. In contrast, 1-hexene is an unsaturated hydrocarbon, with a linear chain and a double bond which contributes to its different chemical behavior.
Such structural variations lead to differences in their standard enthalpy of formations and stability. Understanding these differences helps explain why different hydrocarbons release varying amounts of energy when burned, making it a critical aspect of fields like energy production and material science.

Combustion Enthalpy

Combustion enthalpy, or the heat of combustion, is the amount of energy released when one mole of a substance fully reacts with oxygen under standard conditions. This concept is central to the study of energy released from fuels.
The heat released during combustion can be better understood using the concepts of stability and enthalpy of formation. More stable compounds often have higher (more negative) \( \Delta H_f^{\circ} \) and tend to release more energy upon combustion. Thus, even without direct calculation, comparing enthalpies provides insight into combustion characteristics.
In the given exercise, cyclohexane, with a more negative enthalpy of formation than 1-hexene, can be expected to have a higher combustion enthalpy. This implies it potentially releases more energy when burned, which is a significant factor in industries where hydrocarbons are used as fuel sources.
Understanding how different hydrocarbons behave during combustion helps us discern which compounds offer more energetic outputs, guiding the selection of fuels for various applications.