Using standard free energies of formation, calculate ΔG° at 25 °C for each reaction in Problem 62. How do the values of ΔG° calculated this way compare to those calculated from ΔH° and ΔS°? Which of the two methods can determine how ΔG° changes with temperature?

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Identify the chemical reactions from Problem 62 for which you need to calculate \( \Delta G^\circ \).

Use the standard free energies of formation \( \Delta G_f^\circ \) for each reactant and product to calculate \( \Delta G^\circ \) for the reaction using the formula: \( \Delta G^\circ = \sum \Delta G_f^\circ (\text{products}) - \sum \Delta G_f^\circ (\text{reactants}) \).

Compare the \( \Delta G^\circ \) values obtained from the standard free energies of formation with those calculated using the equation \( \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ \), where \( \Delta H^\circ \) is the standard enthalpy change and \( \Delta S^\circ \) is the standard entropy change.

Discuss how the two methods compare in terms of accuracy and applicability, especially considering that the \( \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ \) method can be used to determine how \( \Delta G^\circ \) changes with temperature.

Conclude which method is more suitable for predicting the temperature dependence of \( \Delta G^\circ \) and why.

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 calculated using the standard free energies of formation of reactants and products. A negative ΔG° indicates a spontaneous reaction, while a positive value suggests non-spontaneity.

Standard Free Energies of Formation

Standard free energies of formation are the change in Gibbs free energy when one mole of a compound is formed from its elements in their standard states. These values are tabulated and can be used to calculate the ΔG° for a reaction by subtracting the sum of the free energies of the reactants from that of the products, providing insight into the reaction's spontaneity.

Temperature Dependence of ΔG°

The temperature dependence of Gibbs Free Energy can be analyzed using the relationship ΔG° = ΔH° - TΔS°, where ΔH° is the change in enthalpy and ΔS° is the change in entropy. This equation shows that ΔG° changes with temperature due to the TΔS° term, allowing for the determination of how ΔG° varies as temperature changes, unlike calculations based solely on standard free energies of formation.

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Related Practice

Textbook Question

For each reaction, calculate ΔH°_rxn, ΔS°_rxn, and ΔG°_rxnat 25 °C and state whether or not the reaction is spontaneous. If the reaction is not spontaneous, would a change in temperature make it spontaneous? If so, should the temperature be raised or lowered from 25 °C? c. N₂(g) + O₂(g) → 2 NO(g)

Textbook Question

For each reaction, calculate ΔH°_rxn, ΔS°_rxn, and ΔG°_rxn at 25 °C and state whether or not the reaction is spontaneous. If the reaction is not spontaneous, would a change in temperature make it spontaneous? If so, should the temperature be raised or lowered from 25 °C? d. 2 KClO₃(s) → 2 KCl(s) + 3 O₂(g)

Textbook Question

Use standard free energies of formation to calculate ΔG° at 25 °C for each reaction in Problem 61. How do the values of ΔG° calculated this way compare to those calculated from ΔH° and ΔS°? Which of the two methods could be used to determine how ΔG° changes with temperature?

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Textbook Question

Consider the reaction: 2 NO(g) + O₂(g) → 2 NO₂(g) Estimate ΔG° for this reaction at each temperature and predict whether or not the reaction is spontaneous. (Assume that ΔH° and ΔS° do not change too much within the given temperature range.) b. 715 K