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Ch.18 - Free Energy and Thermodynamics
All textbooksTro 4th EditionCh.18 - Free Energy and ThermodynamicsProblem 42a
Chapter 18, Problem 42a

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 = -95 kJ; ΔS°rxn = -157 J/K; T = 298 K

Verified step by step guidance
1
Calculate the change in Gibbs free energy (ΔG°rxn) using the formula ΔG°rxn = ΔH°rxn - TΔS°rxn. Convert ΔH°rxn from kJ to J by multiplying by 1000 to ensure consistent units.
Substitute the given values into the equation: ΔH°rxn = -95000 J, ΔS°rxn = -157 J/K, and T = 298 K.
Calculate ΔG°rxn by performing the arithmetic operation: ΔG°rxn = -95000 J - (298 K × -157 J/K).
Determine the sign of ΔG°rxn. If ΔG°rxn is negative, the reaction is spontaneous; if positive, it is non-spontaneous.
Calculate ΔSuniv using the formula ΔSuniv = -ΔG°rxn / T. Substitute the calculated ΔG°rxn and given T into the formula to find ΔSuniv.

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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 changes during a chemical reaction. A negative ΔH indicates that the reaction is exothermic, releasing heat, which often contributes to spontaneity. Conversely, a positive ΔH indicates an endothermic reaction, absorbing heat, which may require other factors, such as an increase in entropy, to be spontaneous.
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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 = +115 kJ; ΔS°rxn = -263 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 = -115 kJ; ΔS°rxn = -263 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 = +95 kJ; ΔS°rxn = -157 J/K; T = 298 K

Textbook Question

Calculate the change in Gibbs free energy for each of the sets of ΔHrxn, ΔSrxn, and T given in Problem 42. Predict whether or not each reaction is spontaneous at the temperature indicated. (Assume that all reactants and products are in their standard states.)