Question

Cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)\) is a liquid hydrocarbon at room temperature. (a) Write a balanced equation for the combustion of \(\mathrm{C}_{6} \mathrm{H}_{12}(l)\) to form \(\mathrm{CO}_{2}(\mathrm{~g})\) and \(\mathrm{H}_{2} \mathrm{O}(l)\). (b) Without using thermochemical data, predict whether \(\Delta G^{\circ}\) for this reaction is more negative or less negative than \(\Delta H^{\circ}\).

Short answer

The balanced equation for the combustion of cyclohexane (C6H12) to form CO2(g) and H2O(l) is: \[C_6H_{12}(l) + 9 O_2(g) \rightarrow 6 CO_2(g) + 6 H_2O(l)\] As for part (b), the standard Gibbs free energy change (ΔG°) for this reaction is expected to be less negative than the standard enthalpy change (ΔH°) because combustion reactions are exothermic (negative ΔH°) and the entropy change (ΔS°) is expected to be positive.

Step-by-step solution

Determine the Reactants and Products

In the combustion of cyclohexane (C6H12), the reactants are cyclohexane and oxygen (O2), and the products are carbon dioxide (CO2) and water (H2O). Unbalanced equation: \[C_6H_{12}(l) + O_2(g) \rightarrow CO_2(g) + H_2O(l)\]

Balance the Equation

To balance the equation, we must ensure that the number of atoms of each element is equal on both sides. 1. There are 6 carbon atoms in cyclohexane, so we need 6 CO2 molecules: \(C_6H_{12}(l) + O_2(g) \rightarrow 6 CO_2(g) + H_2O(l)\) 2. There are 12 hydrogen atoms in cyclohexane, so we need 6 H2O molecules: \(C_6H_{12}(l) + O_2(g) \rightarrow 6 CO_2(g) + 6 H_2O(l)\) 3. Finally, we balance the oxygen atoms. We have 12 oxygen atoms in the 6 CO2 molecules and 6 oxygen atoms in the 6 H2O molecules, so we need a total of 18 oxygen atoms as reactants: \(C_6H_{12}(l) + 9 O_2(g) \rightarrow 6 CO_2(g) + 6 H_2O(l)\) The balanced equation is: \[C_6H_{12}(l) + 9 O_2(g) \rightarrow 6 CO_2(g) + 6 H_2O(l)\] #Part b: Predicting ΔG°#

Combustion of Cyclohexane

Combustion reactions are exothermic, which means heat is released and the standard enthalpy change ΔH° is negative.

Entropy Change

In this reaction, gases react to produce both gases and liquids. While there are fewer gaseous products, the increase in the number and amount of molecular species in the products contributes to an increase in entropy (ΔS°) since more possible microstates exist for the products. As a result, ΔS° is expected to be positive.

Relationship between ΔG°, ΔH°, and ΔS°

The standard Gibbs free energy change (ΔG°) is related to the standard enthalpy change (ΔH°) and the standard entropy change (ΔS°) by the following equation at a constant temperature T: \[ΔG° = ΔH° - TΔS°\]

Predicting the Sign of ΔG°

Since ΔH° is negative (exothermic) and ΔS° is positive (entropy increases), the term \(-TΔS°\) is also negative. So, ΔG° = ΔH° - (-TΔS°), which means ΔG° is less negative than ΔH°. Therefore, the standard Gibbs free energy change (ΔG°) is less negative than the standard enthalpy change (ΔH°).

Key concepts

Chemical Reactions

Chemical reactions involve the transformation of one set of chemical substances, known as reactants, into another set, named products. These transformations occur through the breaking and forming of bonds, resulting in different structural rearrangements of atoms. The combustion of cyclohexane \( C_6H_{12}(l) \) is a prime example of a chemical reaction where cyclohexane reacts with oxygen \( O_2(g) \) to produce carbon dioxide \( CO_2(g) \) and water \( H_2O(l) \).

In education, it's essential to grasp the concept of a balanced chemical equation. Each element's atoms must be conserved from reactants to products, respecting the law of conservation of mass. This balance helps predict the amounts of products generated and the reactants required, which is fundamental knowledge for laboratory work and industrial process design.

Combustion reactions, such as the one involving cyclohexane, are characterized by their exothermic nature—they release energy, usually in the form of heat, making them an invaluable source of energy in various applications.

Enthalpy Change

Enthalpy change \( \Delta H^{\circ} \) is a thermodynamic property that denotes the heat exchange under constant pressure during a chemical reaction. When a substance burns, such as cyclohexane in its combustion reaction, the process is typically exothermic—heat is released. This is indicated by a negative enthalpy change, saying the reaction liberates energy to the surroundings.

Understanding the concept of enthalpy is crucial for students as it dictates whether a reaction is endothermic (absorbing heat) or exothermic (releasing heat), which, in turn, influences reaction rates and conditions required to make the reaction feasible. The enthalpy change also has practical implications for designing energy systems, such as engines and heaters, where energy efficiency and output need to be meticulously calculated.

Gibbs Free Energy

Gibbs free energy change \( \Delta G^{\circ} \) is the measure of the spontaneity of a chemical reaction and potential work that can be extracted from the process at constant temperature and pressure. It combines enthalpy, entropy (a measure of disorder \( \Delta S^{\circ} \) ), and temperature to predict whether a reaction can occur without additional energy input.

In the context of the combustion of cyclohexane, Gibbs free energy helps students understand not just whether the reaction releases heat, but also whether the reaction will proceed on its own. The equation \( \Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ} \) integrates these factors and provides a method to predict the spontaneity of reactions. A negative Gibbs free energy implies a spontaneous reaction, which is a key consideration for chemical engineers and anyone operating with chemical reactions.

Chemical Equation Balancing

Balancing chemical equations is a fundamental practice in chemistry, ensuring that the same number of each element's atoms is represented on both the reactants and the products sides. This ensures compliance with the law of conservation of mass. The balanced equation for the combustion of cyclohexane is \[ C_6H_{12}(l) + 9 O_2(g) \rightarrow 6 CO_2(g) + 6 H_2O(l) \].

Correctly balancing equations is essential for calculating reactant and product quantities, both in small-scale laboratory experiments and large-scale industrial productions. For students, developing the skill to balance equations is foundational for progress in chemical education. It's not just about making numbers match—it's about understanding the stoichiometry, which is the quantitative relationship between reactants and products in a chemical reaction. This skill set is beneficial across various scientific disciplines and industries where precise chemical reactions are crucial.