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Ch.19 - Free Energy & Thermodynamics
All textbooksTro 5th EditionCh.19 - Free Energy & ThermodynamicsProblem 41a
Chapter 19, Problem 41a

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

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1. The first step is to convert the enthalpy change (ΔH°rxn) from kJ to J, because the entropy change (ΔS°rxn) is given in J/K. To do this, multiply the given ΔH°rxn by 1000. So, ΔH°rxn = +115 kJ * 1000 = +115000 J.
2. Next, calculate the change in entropy of the system (ΔSsys) using the formula ΔSsys = ΔH°rxn/T. Substitute the values of ΔH°rxn and T into the formula to get the value of ΔSsys.
3. The change in entropy of the universe (ΔSuniv) is given by the formula ΔSuniv = ΔSsys + ΔS°rxn. Substitute the values of ΔSsys and ΔS°rxn into the formula to get the value of ΔSuniv.
4. If ΔSuniv is greater than zero, the reaction is spontaneous. If ΔSuniv is less than zero, the reaction is non-spontaneous. If ΔSuniv equals zero, the reaction is at equilibrium.
5. Use the value of ΔSuniv obtained in step 3 to determine whether the reaction is spontaneous or not.

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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 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 required to break and form bonds 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 spontaneity of the reaction when combined with entropy changes.
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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.) 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.) a. ΔH°rxn = -95 kJ; ΔS°rxn = -157 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