The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane (C₂H₆), is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen: 2 CH₄(g) → C₂H₆(g) + H₂(g) In practice, this reaction is carried out in the presence of oxygen: 2 CH₄(g) + 12 O₂(g) → C₂H₆(g) + H₂O(g) (b) Is the difference in ΔG° for the two reactions due primarily to the enthalpy term (ΔH) or the entropy term (-TΔS)?

Verified step by step guidance

1. Identify the reactions involved and write down their balanced chemical equations. For the first reaction: 2 CH₄(g) → C₂H₆(g) + H₂(g). For the second reaction: 2 CH₄(g) + 12 O₂(g) → C₂H₆(g) + H₂O(g).
2. Understand the Gibbs free energy change (ΔG°) for a reaction, which is given by the equation ΔG° = ΔH° - TΔS°, where ΔH° is the change in enthalpy, T is the temperature in Kelvin, and ΔS° is the change in entropy.
3. Analyze the enthalpy change (ΔH°) for both reactions. The addition of oxygen in the second reaction likely increases the exothermic nature of the reaction, thus decreasing ΔH° (making it more negative).
4. Consider the entropy change (ΔS°) for both reactions. The second reaction produces fewer gas molecules (1 mole of water vapor) compared to the first reaction (1 mole of hydrogen gas), which might decrease the entropy.
5. Compare the magnitude of changes in ΔH° and -TΔS° for both reactions to determine which term contributes more significantly to the difference in ΔG°. A larger change in ΔH° suggests that the enthalpy term is more influential, whereas a larger change in -TΔS° suggests that the entropy term is more influential.

Key Concepts

Gibbs Free Energy (ΔG)

Gibbs Free Energy (ΔG) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It combines the system's enthalpy (ΔH) and entropy (ΔS) to determine spontaneity; a negative ΔG indicates a spontaneous process. Understanding ΔG is crucial for analyzing chemical reactions, particularly in determining whether a reaction will proceed under given conditions.

Enthalpy (ΔH)

Enthalpy (ΔH) is a measure of the total heat content of a system, reflecting the energy required to create the system and the energy associated with the pressure and volume of the system. In chemical reactions, ΔH can indicate whether a reaction is exothermic (releases heat) or endothermic (absorbs heat). The change in enthalpy is a key factor in determining the overall energy change during a reaction, influencing the ΔG value.

Entropy (ΔS)

Entropy (ΔS) is a measure of the disorder or randomness in a system. It reflects the number of ways a system can be arranged, with higher entropy indicating greater disorder. In the context of chemical reactions, changes in entropy can significantly affect the spontaneity of a reaction, especially when combined with temperature (as seen in the term -TΔS in the Gibbs Free Energy equation). Understanding entropy is essential for evaluating the driving forces behind chemical processes.