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Ch.19 - Free Energy & Thermodynamics
All textbooksTro 6th EditionCh.19 - Free Energy & ThermodynamicsProblem 44c
Chapter 19, Problem 44c

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

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 change in Gibbs free energy.
Determine the spontaneity of the reaction by checking the sign of \( \Delta G^\circ \). 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 a spontaneous reaction, while a positive ΔG suggests non-spontaneity.
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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 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 changes during a chemical reaction. A positive ΔH indicates that the reaction is endothermic, absorbing heat from the surroundings, while a negative ΔH indicates an exothermic reaction, releasing heat. The sign and magnitude of ΔH influence the overall Gibbs Free Energy and thus the spontaneity of the reaction.
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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 = +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.) 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

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

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.