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Ch.19 - Free Energy & Thermodynamics
Tro - Chemistry: A Molecular Approach 6th Edition
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Not the one you use?Change textbook
All textbooksTro 6th EditionCh.19 - Free Energy & ThermodynamicsProblem 50d
Chapter 19, Problem 50d

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)

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Identify the sign of the enthalpy change (\(\Delta H\)) for the reaction. Since the reaction is described as endothermic, \(\Delta H\) is positive.
Consider the entropy change (\(\Delta S\)) of the reaction. Since the reaction involves the decomposition of two moles of NO2 into three moles of gas (2 NO and 1 O2), the entropy increases, making \(\Delta S\) positive.
Use the Gibbs free energy equation, \(\Delta G = \Delta H - T\Delta S\), to analyze the spontaneity of the reaction. Here, \(T\) represents the temperature in Kelvin.
Since both \(\Delta H\) and \(\Delta S\) are positive, the sign of \(\Delta G\) depends on the relative magnitudes of \(\Delta H\) and \(T\Delta S\). As temperature increases, \(T\Delta S\) becomes more significant.
Conclude that the reaction is spontaneous at high temperatures where \(T\Delta S\) outweighs \(\Delta H\), making \(\Delta G\) negative.

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Key Concepts

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

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a reaction at constant temperature and pressure. A reaction is spontaneous if the change in Gibbs Free Energy (ΔG) is negative. The relationship between enthalpy (ΔH), entropy (ΔS), and temperature (T) is given by the equation ΔG = ΔH - TΔS, where a negative ΔG indicates a spontaneous process.
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Endothermic Reactions

Endothermic reactions absorb heat from their surroundings, resulting in a positive change in enthalpy (ΔH > 0). For such reactions to be spontaneous, the increase in entropy (ΔS) must be sufficiently large to overcome the positive ΔH when multiplied by the temperature (T). This means that at higher temperatures, the entropy term becomes more significant, potentially making the reaction spontaneous.
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Entropy and Temperature

Entropy (S) is a measure of the disorder or randomness in a system. In the context of chemical reactions, an increase in entropy (ΔS > 0) favors spontaneity. For endothermic reactions, higher temperatures can enhance the impact of entropy on Gibbs Free Energy, making it more likely for the reaction to be spontaneous as temperature increases, thus favoring the formation of products.
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Related Practice
Textbook Question

How does the molar entropy of a substance change with increasing temperature?

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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

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Textbook Question

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.)

Textbook Question

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