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Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium
All textbooksMcMurry 8th EditionCh.18 - Thermodynamics: Entropy, Free Energy & EquilibriumProblem 8
Chapter 18, Problem 8

Calculate ∆Stotal, and determine whether the reaction is spon-taneous or nonspontaneous under standard-state conditions. (a) -429 J/K; nonspontaneous (b) -123 J/K; spontaneous (c) +3,530 J/K; nonspontaneous (d) +184 J/K; nonspontaneous

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1
Identify the given values for \( \Delta S_{\text{total}} \) in each option.
Recall that a reaction is spontaneous if \( \Delta S_{\text{total}} > 0 \) and nonspontaneous if \( \Delta S_{\text{total}} < 0 \).
Analyze each option: (a) \( \Delta S_{\text{total}} = -429 \text{ J/K} \), (b) \( \Delta S_{\text{total}} = -123 \text{ J/K} \), (c) \( \Delta S_{\text{total}} = +3,530 \text{ J/K} \), (d) \( \Delta S_{\text{total}} = +184 \text{ J/K} \).
Determine the spontaneity of each option based on the sign of \( \Delta S_{\text{total}} \).
Match the spontaneity conclusion with the given options to identify the correct answer.

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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. A reaction is spontaneous if the change in Gibbs Free Energy (∆G) is negative. The relationship between Gibbs Free Energy, enthalpy (H), and entropy (S) is given by the equation ∆G = ∆H - T∆S, where T is the temperature in Kelvin.
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Entropy (S)

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, an increase in entropy (∆S > 0) generally favors spontaneity, as systems tend to evolve towards states of higher disorder. The total entropy change (∆Stotal) for a reaction includes both the system and the surroundings, and a positive ∆Stotal indicates a spontaneous process.
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Standard-State Conditions

Standard-state conditions refer to a set of specific conditions used to measure and compare thermodynamic properties, typically defined as 1 bar of pressure and a specified temperature (usually 25°C). Under these conditions, the standard enthalpy and entropy values are used to calculate the Gibbs Free Energy change, allowing for the assessment of reaction spontaneity in a consistent manner.
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Related Practice
Textbook Question
What is the change in entropy (∆S) when 1.32 g of propane (C3H8) at 0.100 atm pressure is compressed by a factor of five at a constant temperature at 20°C? Assume that propane behaves as an ideal gas. (a) ∆S = +13 J/K(b) ∆S = -13 J/K (c) ∆S = - 0.40 J/K(d) ∆S = + 0.40 J/K
Textbook Question
Magnesium m#etal has ΔHfusion = 9.037 kJ>mol and ΔSfusion = 9.79 J>1K mol2. What is the melting point of magnesium in °C? (LO 11.4)(a) 0.923 °C (b) 923 °C(c) 650 °C (d) 1.08 * 103 °C
Textbook Question
Identify the true statement about a spontaneous process. (a) A reaction that is nonspontaneous in the forward direction is spontaneous in the reverse direction.(b) Adding a catalyst will cause a nonspontaneous reaction to become spontaneous.(c) In a spontaneous process, the entropy of the system always decreases.(d) An endothermic reaction is always spontaneous.
Textbook Question
Consider the following endothermic reaction of gaseous AB3 molecules with A2 molecules.

Identify the true statement about the spontaneity of the reaction. (a) The reaction is likely to be spontaneous at high temperatures. (b) The reaction is likely to be spontaneous at high temperatures. (c) The reaction is always spontaneous.(d) The reaction is always spontaneous.
Textbook Question
Nitrogen reacts with fluorine to form nitrogen trifluoride: Calculate ∆G°, and determine whether the equilibrium composition should favor reactions or products at 25 °C(a) ∆G° = -6.7 kJ; the equilibrium composition should favor products. (b) ∆G° = -332 kJ; the equilibrium composition should favor reactants (c) ∆G° = -166 kJ; the equilibrium composition should favor products (d) ∆G° = +82.6 kJ; the equilbirum composiiton should favor reactants.