Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook

McMurry 8th Edition

Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

Problem 133

Chapter 18, Problem 133

The following reaction, sometimes used in the laboratory to generate small quantities of oxygen gas, has ∆G° = -224.4 kJ/mol at 25°C:
Use the following additional data at 25 °C to calculate the standard molar entropy S° of O2 at 25°C: ∆H°f(KClO3) = -397.7 kJ/mol, ∆H°f(KCl) = -436.5 kJ/mol, S°(KClO3) = 143.1 J/(Kmol), and S°(KCl) = 82.6 J/(Kmol).

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Write the balanced chemical equation for the decomposition of KClO3: 2 KClO3(s) → 2 KCl(s) + 3 O2(g).

Use the given standard enthalpies of formation (ΔH°f) to calculate the ΔH° for the reaction: ΔH° = [2ΔH°f(KCl) + 3ΔH°f(O2)] - [2ΔH°f(KClO3)].

Since ΔH°f(O2) = 0 (standard state), substitute the given values: ΔH° = [2(-436.5 kJ/mol) + 3(0)] - [2(-397.7 kJ/mol)].

Use the given standard molar entropies (S°) to calculate the ΔS° for the reaction: ΔS° = [2S°(KCl) + 3S°(O2)] - [2S°(KClO3)].

Rearrange the Gibbs free energy equation ΔG° = ΔH° - TΔS° to solve for S°(O2): S°(O2) = [ΔH° - ΔG°] / T.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gibbs Free Energy (∆G°)

Gibbs Free Energy 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 (∆G°) indicates the spontaneity of a reaction; a negative value (like -224.4 kJ/mol) suggests that the reaction is spontaneous under standard conditions.

Standard Molar Entropy (S°)

Standard molar entropy is a measure of the disorder or randomness of a system at standard conditions (1 bar, 25°C). It is expressed in units of J/(K·mol). The entropy values of reactants and products are crucial for calculating the overall entropy change in a reaction, which can help determine the feasibility of the reaction.

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same, regardless of the number of steps taken to complete the reaction. This principle allows for the calculation of enthalpy changes using known enthalpy values of formation and can be applied to derive the standard molar entropy of a substance by combining the enthalpy and entropy data of the involved species.

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Hess's Law

Related Practice

Textbook Question

Trouton's rule says that the ratio of the molar heat of vaporization of a liquid to its normal boiling point (in kelvin) is approximately the same for all liquids: ∆H_vap/T_bp ≈ 88 J/(K*mol) (b) Explain why liquids tend to have the same value of ∆Hvap/Tbp.

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Textbook Question

The normal boiling point of bromine is 58.8 °C, and the standard entropies of the liquid and vapor are S°[Br2(l) = 152.2 J/(K*mol); S°[Br2(g) = 245.4 J/(K*mol). At what temperature does bromine have a vapor pressure of 227 mmHg?

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Textbook Question

Tell whether reactions with the following values of ΔH and ΔS are spontaneous or nonspontaneous and whether they are exothermic or endothermic. (a) ΔH = - 48 kJ; ΔS = + 135 J>K at 400 K (b) ΔH = - 48 kJ; ΔS = - 135 J>K at 400 K (c) ΔH = + 48 kJ; ΔS = + 135 J>K at 400 K (d) ΔH = + 48 kJ; ΔS = - 135 J>K at 400 K

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Textbook Question

Suppose that a reaction has ΔH = - 33 kJ and ΔS = - 58 J>K. At what temperature will it change from spontaneous to nonspontaneous?

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Textbook Question

A mixture of 14.0 g of N2 and 3.024 g of H2 in a 5.00 L container is heated to 400 °C. Use the data in Appendix B to calculate the molar concentrations of N2, H2, and NH3 at equilibrium. Assume that ∆H° and ∆S° are independent of temperature, and remember that the standard state of a gas is defined in terms of pressure.

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Textbook Question

The lead storage battery uses the reaction: (b) Calculate ∆G for this reaction on a cold winter's day (10 °F) in a battery that has run down to the point where the sulfuric acid concentration is only 0.100 M.

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