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Ch.18 - Free Energy and Thermodynamics
All textbooksTro 4th EditionCh.18 - Free Energy and ThermodynamicsProblem 38
Chapter 18, Problem 38

Without doing any calculations, determine the signs of ΔS_sys and ΔS_surr for each chemical reaction. In addition, predict under what temperatures (all temperatures, low temperatures, or high temperatures), if any, the reaction is spontaneous. a. 2 CO(g) + O2(g) → 2 CO2(g) ΔH_rxn° = -566.0 kJ b. 2 NO2(g) → 2 NO(g) + O2(g) ΔH_rxn° = +113.1 kJ c. 2 H2(g) + O2(g) → 2 H2O(g) ΔH_rxn° = -483.6 kJ d. CO2(g) → C(s) + O2(g) ΔH_rxn° = +393.5 kJ

Verified step by step guidance
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For each reaction, determine the sign of \( \Delta S_{sys} \) by considering the change in the number of moles of gas. If the number of moles of gas increases, \( \Delta S_{sys} \) is positive; if it decreases, \( \Delta S_{sys} \) is negative.
For each reaction, determine the sign of \( \Delta S_{surr} \) using the sign of \( \Delta H_{rxn}^\circ \). If \( \Delta H_{rxn}^\circ \) is negative (exothermic), \( \Delta S_{surr} \) is positive; if \( \Delta H_{rxn}^\circ \) is positive (endothermic), \( \Delta S_{surr} \) is negative.
Use the Gibbs free energy equation \( \Delta G = \Delta H - T \Delta S \) to predict spontaneity. A reaction is spontaneous when \( \Delta G < 0 \).
For exothermic reactions (negative \( \Delta H_{rxn}^\circ \)), if \( \Delta S_{sys} \) is negative, the reaction is spontaneous at low temperatures. If \( \Delta S_{sys} \) is positive, the reaction is spontaneous at all temperatures.
For endothermic reactions (positive \( \Delta H_{rxn}^\circ \)), if \( \Delta S_{sys} \) is positive, the reaction is spontaneous at high temperatures. If \( \Delta S_{sys} \) is negative, the reaction is non-spontaneous at all temperatures.

Key Concepts

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

Entropy (ΔS)

Entropy, denoted as ΔS, is a measure of the disorder or randomness in a system. In chemical reactions, an increase in the number of gas molecules typically leads to a positive ΔS, indicating greater disorder. Conversely, a decrease in gas molecules or a transition to a more ordered state results in a negative ΔS. Understanding the changes in entropy is crucial for predicting the spontaneity of reactions.
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Enthalpy (ΔH) and Spontaneity

Enthalpy, represented as ΔH, reflects the heat content of a system during a reaction. A negative ΔH indicates an exothermic reaction, which generally favors spontaneity, while a positive ΔH suggests an endothermic reaction that may not be spontaneous. The relationship between ΔH and temperature is essential for determining the conditions under which a reaction can occur spontaneously, as described by the Gibbs free energy equation.
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Gibbs Free Energy (ΔG)

Gibbs free energy, ΔG, combines the effects of enthalpy and entropy to determine the spontaneity of a reaction at constant temperature and pressure. A reaction is spontaneous if ΔG is negative, which can occur when the enthalpy change is favorable (negative ΔH) and/or the entropy change is favorable (positive ΔS). The temperature plays a critical role in this relationship, particularly for reactions with positive ΔH and ΔS, where spontaneity can be temperature-dependent.
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Related Practice
Textbook Question

Without doing any calculations, determine the signs of ΔSsys and ΔS surr for each chemical reaction. In addition, predict under what temperatures (all temperatures, low temperatures, or high temperatures), if any, the reaction is spontaneous. a. C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(g) ΔH°rxn = -2044 kJ

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Textbook Question

Without doing any calculations, determine the signs of ΔSsys and ΔSsurr for each chemical reaction. In addition, predict under what temperatures (all temperatures, low temperatures, or high temperatures), if any, the reaction is spontaneous. c. 2 N2(g) + O2(g) → 2 N2O(g) ΔH°rxn = +163.2 kJ

Textbook Question

Calculate ΔSsurr at the indicated temperature for each reaction. d. ΔH°rxn = +114 kJ; 77 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 = +115 kJ; ΔS°rxn = -263 J/K; T = 298 K