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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Identify the chemical reactions from Problem 61 for which you need to calculate the standard Gibbs free energy change (ΔG°).

Use the formula ΔG° = Σ(ΔG°f products) - Σ(ΔG°f reactants), where ΔG°f is the standard free energy of formation for each substance, to calculate ΔG° for each reaction.

Compare the calculated ΔG° values with those obtained using the formula ΔG° = ΔH° - TΔS°, where ΔH° is the standard enthalpy change, T is the temperature in Kelvin, and ΔS° is the standard entropy change.

Discuss how the two methods differ in terms of their application: the ΔG° = ΔH° - TΔS° method can be used to determine how ΔG° changes with temperature, as it explicitly includes temperature as a variable.

Reflect on the advantages and limitations of each method, considering factors such as the availability of data and the temperature dependence of ΔG°.

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Key Concepts

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

Standard Free Energy of Formation (ΔG°f)

The standard free energy of formation (ΔG°f) is the change in free energy when one mole of a compound is formed from its elements in their standard states. It is a crucial value used in thermodynamics to predict the spontaneity of reactions. A negative ΔG°f indicates that the formation of the compound is energetically favorable under standard conditions.

Gibbs Free Energy Equation

The Gibbs free energy equation, ΔG = ΔH - TΔS, relates the change in free energy (ΔG) to the change in enthalpy (ΔH) and the change in entropy (ΔS) at a given temperature (T). This equation helps determine the spontaneity of a reaction; if ΔG is negative, the reaction is spontaneous. Understanding this relationship is essential for comparing ΔG° values calculated from different methods.

Temperature Dependence of ΔG°

The temperature dependence of ΔG° can be analyzed using the Gibbs free energy equation, particularly through the term -TΔS. As temperature changes, the impact of entropy (ΔS) on free energy becomes significant, allowing for the determination of how ΔG° varies with temperature. This understanding is vital for predicting reaction behavior under different thermal conditions.

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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? a. 2 CH₄(g) → C₂H₆(g) + H₂(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

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