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Ch.19 - Free Energy & Thermodynamics
All textbooksTro 6th EditionCh.19 - Free Energy & ThermodynamicsProblem 43c
Chapter 19, Problem 43c

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

Verified step by step guidance
1
Convert \( \Delta H^\circ_{rxn} \) from kJ to J by multiplying by 1000, since \( \Delta S^\circ_{rxn} \) is given in J/K.
Use the formula \( \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \) to calculate the Gibbs free energy change, \( \Delta G^\circ \).
Determine the spontaneity of the reaction: if \( \Delta G^\circ < 0 \), the reaction is spontaneous; if \( \Delta G^\circ > 0 \), it is non-spontaneous.
Calculate \( \Delta S_{univ} \) using the formula \( \Delta S_{univ} = \Delta S^\circ_{rxn} + \frac{-\Delta H^\circ_{rxn}}{T} \).
Interpret \( \Delta S_{univ} \): if \( \Delta S_{univ} > 0 \), the reaction is spontaneous; if \( \Delta S_{univ} < 0 \), 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

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a reaction at constant temperature and pressure. It is calculated using the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates that a reaction is spontaneous, while a positive ΔG suggests it is non-spontaneous.
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Entropy (ΔS)

Entropy (ΔS) is a measure of the disorder or randomness in a system. In the context of a chemical reaction, it quantifies the change in disorder between reactants and products. A positive ΔS indicates an increase in disorder, which generally favors spontaneity, while a negative ΔS suggests a decrease in disorder, which can hinder spontaneity.
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Enthalpy (ΔH)

Enthalpy (ΔH) is a measure of the total heat content of a system and reflects the energy change during a chemical reaction. A negative ΔH (exothermic reaction) indicates that the reaction releases heat, which can favor spontaneity. Conversely, a positive ΔH (endothermic reaction) absorbs heat, which may require a favorable entropy change to be spontaneous.
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Related Practice
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. C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(g) ΔH°rxn = -2044 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 = +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 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.)