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Ch.18 - Free Energy and Thermodynamics
All textbooksTro 4th EditionCh.18 - Free Energy and ThermodynamicsProblem 44
Chapter 18, Problem 44

Calculate the change in Gibbs free energy for each of the sets of ΔHrxn, ΔSrxn, and T given in Problem 42. Predict whether or not each reaction is spontaneous at the temperature indicated. (Assume that all reactants and products are in their standard states.)

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Identify the formula for Gibbs free energy change: \( \Delta G = \Delta H - T \Delta S \).
Substitute the given values for \( \Delta H \), \( \Delta S \), and \( T \) into the formula.
Ensure that the units are consistent, typically converting \( \Delta S \) from J/mol·K to kJ/mol·K by dividing by 1000.
Calculate \( \Delta G \) using the substituted values.
Determine spontaneity: if \( \Delta G < 0 \), the reaction is spontaneous; if \( \Delta G > 0 \), it is non-spontaneous.

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Key Concepts

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

Gibbs Free Energy (G)

Gibbs free energy is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is defined by the equation G = H - TS, where H is enthalpy, T is temperature, and S is entropy. A negative change in Gibbs free energy (ΔG < 0) indicates that a reaction is spontaneous, while a positive change (ΔG > 0) suggests non-spontaneity.
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Enthalpy (ΔH)

Enthalpy is a measure of the total heat content of a system and is used to quantify the energy changes during chemical reactions. The change in enthalpy (ΔH) can be either positive or negative, indicating whether a reaction absorbs heat (endothermic, ΔH > 0) or releases heat (exothermic, ΔH < 0). This value is crucial for determining the spontaneity of a reaction when combined with entropy changes.
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Enthalpy of Formation

Entropy (ΔS)

Entropy is a measure of the disorder or randomness in a system. The change in entropy (ΔS) during a reaction reflects how the distribution of energy changes, with positive ΔS indicating increased disorder and negative ΔS indicating decreased disorder. In the context of Gibbs free energy, a positive ΔS can favor spontaneity, especially at higher temperatures, as it contributes to a more negative ΔG.
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Related Practice
Textbook Question

Given the values of ΔH°rxn, ΔS°rxn, and T, determine ΔSuniv and predict whether or not each reaction is spontaneous. (Assume that all reactants and products are in their standard states.) a. ΔH°rxn = -95 kJ; ΔS°rxn = -157 J/K; T = 298 K

Textbook Question

Given the values of ΔH°rxn, ΔS°rxn, and T, determine ΔSuniv and predict whether or not each reaction is spontaneous. (Assume that all reactants and products are in their standard states.) c. ΔH°rxn = +95 kJ; ΔS°rxn = -157 J/K; T = 298 K

Textbook Question

Calculate the free energy change for this reaction at 25 °C. Is the reaction spontaneous? (Assume that all reactants and products are in their standard states.) C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(g) ΔH°rxn = -2217 kJ; ΔS°rxn = 101.1 J/K

Textbook Question

Calculate the free energy change for this reaction at 25 °C. Is the reaction spontaneous? (Assume that all reactants and products are in their standard states.) 2 Ca(s) + O2( g) → 2 CaO(s) ΔH°rxn = -1269.8 kJ; ΔS°rxn = -364.6 J/K

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Textbook Question

Fill in the blanks in the table. Both ΔH and ΔS refer to the system.