Question

The enthalpy of combustion at \(25^{\circ} \mathrm{C}\) of \(\mathrm{H}_{2}(\mathrm{~g})\), cyclohexane(l) and cyclohexene(l) \(\begin{array}{lllll}\text { are }-241, & -3920 & \text { and } & -3800 & \mathrm{~kJ} / \mathrm{mol} \text { , }\end{array}\) respectively. \(\quad\) The enthalpy of hydrogenation of cyclohexene(1) is (a) \(-121 \mathrm{~kJ} / \mathrm{mol}\) (b) \(+121 \mathrm{~kJ} / \mathrm{mol}\) (c) \(-242 \mathrm{~kJ} / \mathrm{mol}\) (d) \(+242 \mathrm{~kJ} / \mathrm{mol}\)

Short answer

(b) +121 kJ/mol

Step-by-step solution

Understand the Definition of Enthalpy of Combustion

The enthalpy of combustion is the heat released when one mole of a substance is completely burned in oxygen under standard conditions. It is typically expressed in kJ/mol and is a negative value, indicating an exothermic reaction.

Understand the Definition of Enthalpy of Hydrogenation

The enthalpy of hydrogenation is the heat released when one mole of an alkene is hydrogenated to form an alkane. This reaction is also exothermic.

Write the Balanced Chemical Equations

For cyclohexene hydrogenation: \[\text{C}_{6}\text{H}_{10}(\mathrm{l}) + \text{H}_{2}(\mathrm{g}) \rightarrow \text{C}_{6}\text{H}_{12}(\mathrm{l})\]. The combustion of cyclohexane and cyclohexene can be represented as: \[\text{C}_{6}\text{H}_{12}(\mathrm{l}) + 9\text{O}_{2}(\mathrm{g}) \rightarrow 6\text{CO}_{2}(\mathrm{g}) + 6\text{H}_{2}\text{O}(\mathrm{l})\] and \[\text{C}_{6}\text{H}_{10}(\mathrm{l}) + 8.5\text{O}_{2}(\mathrm{g}) \rightarrow 6\text{CO}_{2}(\mathrm{g}) + 5\text{H}_{2}\text{O}(\mathrm{l})\], respectively.

Calculate the Enthalpy of Hydrogenation of Cyclohexene

Using Hess's Law, we can find the enthalpy change for the hydrogenation of cyclohexene by using the enthalpy changes of combustion for cyclohexane and cyclohexene. The enthalpy of hydrogenation will be the difference between the combustion enthalpies of cyclohexene and cyclohexane.\[\text{Enthalpy of hydrogenation} = \text{Enthalpy of combustion of cyclohexene} - \text{Enthalpy of combustion of cyclohexane}\] Substituting the given enthalpy values: \[-3800 \text{ kJ/mol} - (-3920 \text{ kJ/mol}) = +120 \text{ kJ/mol} \]

Determine the Correct Answer

Since the calculation yields a positive value of approximately +120 kJ/mol, the correct answer is the option (b) \(+121 \text{ kJ/mol}\).

Key concepts

Enthalpy of Combustion

The concept of enthalpy is pivotal in understanding the energetic change that accompanies a chemical reaction. The enthalpy of combustion specifically quantifies the heat energy released when a substance completely burns in the presence of oxygen. It's a crucial metric in the field of energy production and environmental science, as it aids in assessing the efficiency and impact of various fuels.

Typically, during the combustion, molecules break apart and recombine with oxygen to form carbon dioxide and water. This process releases energy, as chemical bonds formed in the products are stronger—and thus more stable—than those in the reactants. Since the release of energy is a hallmark of exothermic reactions, the enthalpy of combustion is assigned a negative value. This signifies that the system is relinquishing energy to its surroundings.

Understanding the enthalpy changes associated with different substances allows scientists and engineers to determine the most energy-efficient fuels, thus helping us to design greener combustion processes and better manage our energy resources.

Hess's Law

Hess's Law is like a puzzle master in the world of chemical thermodynamics, providing a method to deduce the enthalpy change of a reaction even when it cannot be measured directly. The law states that the total enthalpy change for a chemical reaction is the same, whether it occurs in one step or multiple steps. This principle stems from the fact that enthalpy is a state function—its value is determined only by the present conditions, not by the path the system took to reach those conditions.

In practice, Hess's Law allows us to combine known enthalpy changes of individual steps to find the unknown enthalpy change of a more complex reaction. This tool becomes indispensable when direct measurement is impractical or impossible, such as with highly explosive substances or reactions that are too slow or require extreme conditions. By using thermochemical equations like pieces in a game, scientists can construct or deconstruct chemical pathways to unveil the energetics of reactions, a method that is essential when dealing with complex organic transformations or industrial chemical processes.

Chemical Thermodynamics

At the core of predicting and controlling chemical reactions lies the field of chemical thermodynamics. It's the branch of science that deals with the relationships between heat, work, temperature, and energy in chemical processes. This domain is vast and encompasses laws that govern the conservation of energy, entropy changes, and the spontaneity of reactions.

The principles of thermodynamics inform us about the feasibility and extent of a reaction, guide the design of chemical process systems, and help in the development of energy-efficient technologies. A key concept within this field is the idea of a thermodynamic system and its interactions with its surroundings. Whether the focus is on tiny reactions that power cellular processes or the massive industrial procedures that synthesize materials and fuels, chemical thermodynamics provides the theoretical foundation for understanding and harnessing the power of chemical reactions.

Exothermic Reactions

An exothermic reaction is the term of choice when describing a chemical reaction that releases heat to its surroundings, resulting in an increase in temperature. Among exothermic reactions, combustion is one of the most commonly encountered examples, releasing large amounts of heat and light.

The science behind exothermic reactions is deeply rooted in the breaking and formation of chemical bonds. Bonds between atoms in the reactants must be broken before the new bonds in the products can form. If the energy required to break the initial bonds is less than the energy released when the new bonds are formed, the excess energy is expelled as heat.

These reactions are not just confined to laboratories or industrial processes; they are all around us: in the warmth of a campfire, the power that drives our vehicles, and even within our own bodies as cells metabolize food. Understanding and quantifying these reactions are essential for various applications, including chemical manufacturing, environmental engineering, and energy production.