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Ch.18 - Free Energy and Thermodynamics
All textbooksTro 4th EditionCh.18 - Free Energy and ThermodynamicsProblem 45
Chapter 18, Problem 45

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.) C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(g) ΔH°rxn = -2217 kJ; ΔS°rxn = 101.1 J/K

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Identify the given values: \( \Delta H^\circ_{\text{rxn}} = -2217 \text{ kJ} \) and \( \Delta S^\circ_{\text{rxn}} = 101.1 \text{ J/K} \).
Convert \( \Delta S^\circ_{\text{rxn}} \) from \( \text{J/K} \) to \( \text{kJ/K} \) by dividing by 1000: \( \Delta S^\circ_{\text{rxn}} = 0.1011 \text{ kJ/K} \).
Use the Gibbs free energy equation: \( \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \).
Substitute the values into the equation: \( \Delta G^\circ = -2217 \text{ kJ} - (298 \text{ K} \times 0.1011 \text{ kJ/K}) \).
Determine if the reaction is spontaneous by checking the sign of \( \Delta G^\circ \): if \( \Delta G^\circ < 0 \), the reaction is 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 measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. The change in Gibbs Free Energy (ΔG) for a reaction can be 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 under the given conditions.
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Standard State Conditions

Standard state conditions refer to a set of specific conditions used to measure the properties of substances, typically defined as 1 bar of pressure and a specified temperature, usually 25 °C (298 K). Under these conditions, the standard enthalpy (ΔH°) and standard entropy (ΔS°) values are determined for reactants and products. These values are essential for calculating the Gibbs Free Energy change for reactions, as they provide a reference point for the thermodynamic properties.
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Spontaneity of Reactions

The spontaneity of a chemical reaction is determined by the sign of the Gibbs Free Energy change (ΔG). If ΔG is negative, the reaction is spontaneous, meaning it can occur without external energy input. Conversely, if ΔG is positive, the reaction is non-spontaneous and requires energy to proceed. Understanding the relationship between ΔG, ΔH, and ΔS helps predict whether a reaction will occur under specific conditions.
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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.) 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.)

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.

Textbook Question

Predict the conditions (high temperature, low temperature, all temperatures, or no temperatures) under which each reaction is spontaneous. a. H2O(g) → H2O(l) b. CO2(s) → CO2(g) c. H2(g) → 2 H(g) d. 2 NO2(g) → 2 NO(g) + O2(g) (endothermic)