Question

About 5 billion kilograms of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\), is made each year. Benzene is used as a starting material for many other compounds and as a solvent (although it is also a carcinogen, and its use is restricted). One compound that can be made from benzene is cyclohexane, \(\mathrm{C}_{6} \mathrm{H}_{12}.\) $$\begin{aligned} \mathrm{C}_{6} \mathrm{H}_{6}(\ell)+3 \mathrm{H}_{2}(\mathrm{g}) \rightarrow & \mathrm{C}_{6} \mathrm{H}_{12}(\ell) \\ \Delta_{\mathrm{r}} H^{\circ}=-206.7 \mathrm{kJ} ; \Delta_{\mathrm{r}} S^{\circ} &=-361.5 \mathrm{J} / \mathrm{K} \end{aligned}$$ Is this reaction predicted to be product-favored at equilibrium at \(25^{\circ} \mathrm{C} ?\) Is the reaction enthalpy- or entropy-driven?

Short answer

The reaction is product-favored at equilibrium and is enthalpy-driven.

Step-by-step solution

Determine Reaction Gibbs Free Energy

To predict whether the reaction is product-favored, we need to calculate the Gibbs Free Energy change (ΔG) using the formula:\[ \Delta G^{\circ} = \Delta H^{\circ} - T \Delta S^{\circ} \]where:- \( \Delta H^{\circ} = -206.7 \text{ kJ} \)- \( \Delta S^{\circ} = -361.5 \text{ J/K} = -0.3615 \text{ kJ/K} \)- \( T = 25^{\circ} \text{C} = 298 \text{ K} \).Now substitute these values into the formula:\[ \Delta G^{\circ} = -206.7 - (298 \times (-0.3615)) \]

Calculate Gibbs Free Energy

Carry out the multiplication and subtraction:\[ \Delta G^{\circ} = -206.7 + 107.667 = -99.033 \text{ kJ} \]The result is \( \Delta G^{\circ} = -99.033 \text{ kJ} \). A negative \( \Delta G^{\circ} \) indicates the reaction is product-favored at equilibrium.

Identify Reaction Driving Force

The reaction is enthalpy-driven because the reaction enthalpy \( \Delta H^{\circ} \) is negative and larger in magnitude compared to the product of temperature and entropy change \(-T \Delta S^{\circ}\), which is smaller in magnitude and positive. This results in a net negative overall \( \Delta G^{\circ} \).

Key concepts

Enthalpy-Driven Reactions

In the world of chemistry, reactions can be categorized as either enthalpy-driven or entropy-driven. This classification helps us understand the primary force propelling a reaction toward product formation. An enthalpy-driven reaction is characterized by a significant change in enthalpy (heat energy) during the reaction process.

In the given problem, the conversion of benzene (\(\text{C}_6\text{H}_6\)) to cyclohexane (\(\text{C}_6\text{H}_{12}\)) is an example of an enthalpy-driven reaction. This is because the reaction's enthalpy change, \(\Delta H^{\circ} = -206.7 \text{ kJ}\), indicates that a substantial amount of energy is released as heat.

Since the enthalpy change is negative and large, it signifies that the reaction is exothermic, releasing heat to the surroundings. As a result, even though the entropy change is also negative, the reaction remains product-favored. The strong enthalpy change overrides the unfavorable entropy change, driving the reaction toward completion.

Entropy Change

Entropy is a measure of disorder or randomness in a system. During a chemical reaction, changes in entropy can indicate alterations in the arrangement of molecules and energy. In some reactions, entropy can act as the main driving force, especially when reactions result in an increase in disorder.

For the conversion of benzene to cyclohexane, the entropy change \(\Delta S^{\circ} = -361.5 \text{ J/K}\) is negative. This tells us that the system loses entropy, moving towards a more ordered state during the reaction. Contrary to intuition, this means that molecules are more structured in cyclohexane than in benzene.

A negative entropy change typically makes reactions less favorable because systems naturally progress towards higher entropy. However, in this scenario, other factors come into play, such as the negative enthalpy change, which dictates the overall spontaneity and favorability of the reaction.

Chemistry

Chemistry is the branch of science that studies substances, their properties, reactions, and the changes they undergo. It is foundational to understanding not only how substances form and interact at a molecular level but also the energy dynamics involved in these changes.

Fundamental concepts like Gibbs Free Energy are important in chemistry. They help predict whether a chemical reaction will occur spontaneously. By analyzing both enthalpy and entropy in reactions, chemists can gain insight into the nature of the reaction under study.

Furthermore, chemistry provides tools to understand industrial processes, such as the production of benzene, where the strategic management of reaction conditions can lead to desired outcomes. This scientific discipline connects theory to practical applications, illustrating why reactions are relevant and beneficial in real-world scenarios.

Chemical Equilibrium

Chemical equilibrium is a state in which both the reactants and products of a chemical reaction are present in concentrations that remain constant over time. This occurs because the forward and reverse reactions proceed at the same rate.

In the context of the benzene to cyclohexane reaction, the equilibrium position is crucial to determining whether the reaction is product-favored. The negative value of Gibbs Free Energy change indicates that, at equilibrium, products are favored over reactants, meaning more cyclohexane is present relative to benzene.

At equilibrium, even if the reaction heavily favors products, it doesn't transition to completion. The presence of an equilibrium lets chemists understand and control reactive processes, allowing for optimization in various chemical syntheses and industrial applications. Equilibrium helps in predicting reaction yields and developing efficient pathways to maximize the production of target compounds.