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) → CH₃OH(l) ΔS° = –332 J/K
Step 2. CH₃OH(l) → CH₄(g) + 1/2 O₂(g) ΔS° = 162 J/K
(a) Calculate ΔH° in kilojoules for step 1.

Verified step by step guidance

1. Identify the given values and the required calculation. For step 1, you are given the standard entropy change (ΔS°) and need to calculate the standard enthalpy change (ΔH°).
2. Recall the Gibbs free energy equation: ΔG° = ΔH° - TΔS°. You will need to rearrange this equation to solve for ΔH°.
3. Since the problem does not provide the temperature (T) or the Gibbs free energy change (ΔG°), you need to assume standard conditions. Standard temperature is typically 298 K.
4. Rearrange the Gibbs free energy equation to solve for ΔH°: ΔH° = ΔG° + TΔS°.
5. To find ΔG°, use the standard relation at equilibrium where ΔG° = 0. Substitute this value and the given ΔS° into the rearranged equation to calculate ΔH°.

Key Concepts

Enthalpy Change (ΔH°)

Enthalpy change (ΔH°) is a measure of the heat content of a system at constant pressure. It indicates whether a reaction is exothermic (releases heat, ΔH° < 0) or endothermic (absorbs heat, ΔH° > 0). To calculate ΔH°, one typically uses the standard enthalpies of formation of the reactants and products involved in the reaction.

Gibbs Free Energy and Entropy (ΔS°)

Gibbs free energy (G) combines enthalpy and entropy to predict the spontaneity of a reaction. The change in entropy (ΔS°) reflects the disorder of a system; a negative ΔS° indicates a decrease in disorder, while a positive ΔS° indicates an increase. Understanding the relationship between ΔH°, ΔS°, and temperature is crucial for determining the feasibility of a reaction.

Stoichiometry in Chemical Reactions

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. It allows chemists to predict the amounts of substances consumed and produced. In the context of the given question, stoichiometry is essential for determining the moles of CO and H2 required to produce methanol, which directly influences the calculation of ΔH° for the reaction.