An important reaction for the conversion of natural gas to other useful hydrocarbons is the conversion of methane to ethane. 2 CH₄(g) → C₂H₆(g) + H₂(g) In practice, this reaction is carried out in the presence of oxygen, which converts the hydrogen produced into water. 2 CH₄(g) + 12 O₂(g) → C₂H₆(g) + H₂O(g) Use Table 8.3 to estimate H for these two reactions. Why is the conversion of methane to ethane more favorable when oxygen is used? Why is the conversion of methane to ethane more favorable when oxygen is used?

Verified step by step guidance

1. Identify the two chemical reactions given in the problem. The first reaction is the conversion of methane to ethane and hydrogen: 2 CH_4(g) \rightarrow C_2H_6(g) + H_2(g). The second reaction includes oxygen and produces water instead of hydrogen: 2 CH_4(g) + 3 O_2(g) \rightarrow C_2H_6(g) + 2 H_2O(g).
2. Refer to Table 8.3 to find the standard enthalpy of formation (\Delta H_f^\circ) values for each reactant and product in both reactions. The values you need are for CH_4(g), C_2H_6(g), H_2(g), O_2(g), and H_2O(g).
3. Calculate the total enthalpy change (\Delta H) for each reaction using the formula: \Delta H = \sum (\Delta H_f^\circ \text{ of products}) - \sum (\Delta H_f^\circ \text{ of reactants}). Make sure to account for the stoichiometric coefficients in the reactions.
4. Compare the \Delta H values of the two reactions. A more negative \Delta H indicates a more exothermic reaction, which is generally more favorable in terms of energy efficiency.
5. Explain why the presence of oxygen makes the conversion of methane to ethane more favorable. Consider the enthalpy changes and the fact that converting hydrogen to water in the presence of oxygen releases additional energy, making the overall reaction more exothermic.

Key Concepts

Thermodynamics and Enthalpy Change (ΔH)

Thermodynamics is the study of energy transformations, and enthalpy change (ΔH) is a key concept that quantifies the heat absorbed or released during a chemical reaction. In the context of the given reactions, calculating ΔH helps determine the favorability of the conversion of methane to ethane. A negative ΔH indicates an exothermic reaction, which is generally more favorable as it releases energy, making the process more spontaneous.

Reaction Mechanism and Catalysis

The reaction mechanism describes the step-by-step process by which reactants are converted into products. In the presence of oxygen, the reaction may proceed through a more efficient pathway, potentially involving catalytic effects that lower the activation energy. This can enhance the rate of conversion of methane to ethane, making the reaction more favorable under practical conditions.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust to counteract the change and restore a new equilibrium. In the context of the methane to ethane conversion, the introduction of oxygen and the production of water can shift the equilibrium position, favoring the formation of ethane. This principle helps explain why the presence of oxygen makes the conversion more favorable.