Methanol (CH3OH) can be made by the controlled oxidation of methane: CH4(g) + 1/2 O2(g) → CH3OH(g) (c) Calculate ΔG° at 298 K. Under standard conditions, is the reaction spontaneous at this temperature? (d) Is there a temperature at which the reaction would be at equilibrium under standard conditions and that is low enough so that the compounds involved are likely to be stable?

Verified step by step guidance

To calculate ΔG° at 298 K, use the equation ΔG° = ΔH° - TΔS°. You will need the standard enthalpy change (ΔH°) and the standard entropy change (ΔS°) for the reaction.

Look up the standard enthalpy of formation (ΔH°f) and standard entropy (S°) values for each compound involved in the reaction: CH4(g), O2(g), and CH3OH(g).

Calculate ΔH° for the reaction using the formula: ΔH° = Σ(ΔH°f of products) - Σ(ΔH°f of reactants).

Calculate ΔS° for the reaction using the formula: ΔS° = Σ(S° of products) - Σ(S° of reactants).

Determine if the reaction is spontaneous at 298 K by evaluating the sign of ΔG°. If ΔG° is negative, the reaction is spontaneous under standard conditions. For part (d), consider the temperature at which ΔG° = 0, which indicates equilibrium, and assess the stability of the compounds at that temperature.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 used to predict the spontaneity of a reaction: if ΔG is negative, the reaction is spontaneous; if positive, it is non-spontaneous. At equilibrium, ΔG equals zero, indicating no net change in the concentrations of reactants and products.

Standard Conditions

Standard conditions refer to a set of specific conditions used to measure and compare thermodynamic properties, typically defined as 1 bar of pressure and a specified temperature, usually 298 K (25°C). Under these conditions, the standard Gibbs free energy change (ΔG°) can be calculated, allowing for the assessment of reaction spontaneity and equilibrium. It is crucial to ensure that all reactants and products are in their standard states.

Equilibrium and Temperature

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. The temperature can influence the position of equilibrium, as described by Le Chatelier's principle. For a reaction to be at equilibrium under standard conditions, the temperature must be adjusted to a point where ΔG° equals zero, which can be determined using the van 't Hoff equation, considering the stability of the compounds involved.

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Textbook Question

The accompanying diagram shows how entropy varies with temperature for a substance that is a gas at the highest temperature shown. (c) If this substance is a perfect crystal at T = 0 K, what is the value of S at this temperature?

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Textbook Question

Isomers are molecules that have the same chemical formula but different arrangements of atoms, as shown here for two isomers of pentane, C₅H₁₂.

(a) Do you expect a significant difference in the enthalpy of combustion of the two isomers? Explain.

Textbook Question

Isomers are molecules that have the same chemical formula but different arrangements of atoms, as shown here for two isomers of pentane, C₅H₁₂.

(b) Which isomer do you expect to have the higher standard molar entropy? Explain.

Textbook Question

The accompanying diagram shows how ΔH (red line) and TΔS (blue line) change with temperature for a hypothetical reaction.

(b) In what temperature range is this reaction spontaneous?

Textbook Question

Consider a reaction A₂(𝑔) + B₂(𝑔) ⇌ 2 AB(𝑔), atoms of A shown in red in the diagram and atoms of B shown in blue. (a) If 𝐾_𝑐 = 1, which box represents the system at equilibrium?

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