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Ch.19 - Free Energy & Thermodynamics
All textbooksTro 6th EditionCh.19 - Free Energy & ThermodynamicsProblem 46
Chapter 19, Problem 46

Calculate the change in Gibbs free energy for each of the sets of ΔH°rxn, ΔS°rxn, and T given in Problem 44. 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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1
Identify the formula for Gibbs free energy change: \( \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \).
Substitute the given values for \( \Delta H^\circ_{rxn} \), \( \Delta S^\circ_{rxn} \), and \( T \) into the formula.
Ensure that the units are consistent, typically converting \( \Delta S^\circ_{rxn} \) from J/mol·K to kJ/mol·K by dividing by 1000, if necessary.
Calculate \( \Delta G^\circ \) using the substituted values.
Determine spontaneity: if \( \Delta G^\circ < 0 \), the reaction is spontaneous; if \( \Delta G^\circ > 0 \), 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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Gibbs Free Energy of Reactions

Enthalpy (ΔH°<sub>rxn</sub>)

Enthalpy change (ΔH°<sub>rxn</sub>) is the heat content change associated with a chemical reaction at standard conditions. It can be either exothermic (releasing heat, ΔH < 0) or endothermic (absorbing heat, ΔH > 0). The sign and magnitude of ΔH°<sub>rxn</sub> significantly influence the spontaneity of a reaction, as it contributes to the overall Gibbs free energy change.
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Entropy (ΔS°<sub>rxn</sub>)

Entropy (ΔS°<sub>rxn</sub>) is a measure of the disorder or randomness in a system. In the context of a chemical reaction, an increase in entropy (ΔS > 0) generally favors spontaneity, as systems tend to evolve towards greater disorder. The relationship between entropy, enthalpy, and temperature is crucial for determining the spontaneity of reactions through the Gibbs free energy equation.
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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.) c. ΔH°rxn = -135 kJ; ΔS°rxn = -282 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.) a. ΔH°rxn = -75 kJ; ΔS°rxn = -127 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 = +75 kJ; ΔS°rxn = -127 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.) 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.

Textbook Question

Predict the conditions (high temperature, low temperature, all temperatures, or no temperatures) under which each reaction is spontaneous. a. H2O(g) → H2O(l) b. CO2(s) → CO2(g) c. H2(g) → 2 H(g) d. 2 NO2(g) → 2 NO(g) + O2(g) (endothermic)