Methanol (CH₃OH) is made industrially in two steps from CO and H₂. It is so cheap to make that it is being considered for use as a precursor to hydrocarbon fuels, such as methane (CH₄):
Step 1. CO(g) + 2 H₂(g) S CH₃OH(l) ΔS° = - 332 J/K
Step 2. CH₃OH₁l₂ → CH₄(g) + 1/2 O₂(g) ΔS° = 162 J/K
(k) Calculate an overall ΔG°, ΔH°, and ΔS° for the formation of CH₄ from CO and H₂.

검증된 단계별 안내

Identify the given reactions and their respective \( \Delta S^\circ \) values: Step 1: \( \text{CO(g) + 2 H}_2\text{(g) } \rightarrow \text{ CH}_3\text{OH(l) } \Delta S^\circ = -332 \text{ J/K} \), Step 2: \( \text{CH}_3\text{OH(l) } \rightarrow \text{ CH}_4\text{(g) + } \frac{1}{2} \text{O}_2\text{(g) } \Delta S^\circ = 162 \text{ J/K} \).

To find the overall \( \Delta S^\circ \), add the \( \Delta S^\circ \) values of the two steps: \( \Delta S^\circ_{\text{overall}} = \Delta S^\circ_{\text{Step 1}} + \Delta S^\circ_{\text{Step 2}} \).

Use Hess's Law to determine \( \Delta H^\circ \) and \( \Delta G^\circ \) for each step if not given, or assume standard enthalpy and Gibbs free energy changes if provided.

Calculate the overall \( \Delta H^\circ \) and \( \Delta G^\circ \) by summing the values from each step: \( \Delta H^\circ_{\text{overall}} = \Delta H^\circ_{\text{Step 1}} + \Delta H^\circ_{\text{Step 2}} \) and \( \Delta G^\circ_{\text{overall}} = \Delta G^\circ_{\text{Step 1}} + \Delta G^\circ_{\text{Step 2}} \).

Ensure all units are consistent and check if any additional data or assumptions are needed to complete the calculations, such as standard enthalpies or Gibbs free energies of formation.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 is calculated using the equation ΔG° = ΔH° - TΔS°, where ΔH° is the change in enthalpy and ΔS° is the change in entropy. A negative ΔG° indicates that a reaction is spontaneous under standard conditions.

Enthalpy (ΔH°)

Enthalpy (ΔH°) is a measure of the total heat content of a system and reflects the energy required to break and form bonds during a chemical reaction. It is an important factor in determining the heat absorbed or released in a reaction. The overall ΔH° for a reaction can be calculated by summing the ΔH° values of individual steps, following Hess's law.

Entropy (ΔS°)

Entropy (ΔS°) is a measure of the disorder or randomness in a system. In chemical reactions, it reflects the distribution of energy among the particles and the number of ways the system can be arranged. A positive ΔS° indicates an increase in disorder, which often favors spontaneity, while a negative ΔS° suggests a decrease in disorder, which can hinder spontaneity.