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 125

Chapter 18, Problem 125

Is it possible for a reaction to be nonspontaneous yet exo-thermic? Explain.

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Understand the terms: A reaction is exothermic if it releases heat, meaning the enthalpy change (ΔH) is negative. A reaction is nonspontaneous if it does not occur on its own without external input, which is determined by the Gibbs free energy change (ΔG).

Recall the Gibbs free energy equation: ΔG = ΔH - TΔS, where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.

Consider the conditions for spontaneity: A reaction is spontaneous if ΔG is negative. If ΔG is positive, the reaction is nonspontaneous.

Analyze the scenario: For a reaction to be exothermic (ΔH < 0) and nonspontaneous (ΔG > 0), the term TΔS must be positive and larger in magnitude than ΔH, meaning the entropy change (ΔS) is positive and significant enough to make ΔG positive.

Conclude: Yes, it is possible for a reaction to be nonspontaneous yet exothermic if the increase in entropy (ΔS) is large enough to make the TΔS term outweigh the negative ΔH, resulting in a positive ΔG.

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Key Concepts

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

Spontaneity of Reactions

Spontaneity refers to whether a reaction occurs naturally under given conditions without external influence. A spontaneous reaction has a negative Gibbs free energy change (ΔG < 0). However, spontaneity is not solely determined by enthalpy (heat content) but also by entropy (disorder), which can lead to nonspontaneous reactions even if they release heat.

Exothermic Reactions

Exothermic reactions are those that release heat to the surroundings, resulting in a negative change in enthalpy (ΔH < 0). While these reactions often favor spontaneity, they can still be nonspontaneous if the increase in entropy is insufficient to overcome the energy barrier, particularly at lower temperatures or under specific conditions.

Gibbs Free Energy

Gibbs free energy (G) combines enthalpy and entropy to determine the spontaneity of a reaction. The equation ΔG = ΔH - TΔS shows that a reaction can be exothermic (ΔH < 0) but still have a positive ΔG if the entropy change (ΔS) is negative or not large enough to offset the enthalpy term, resulting in a nonspontaneous process.

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Related Practice

Textbook Question

Consider the Haber synthesis of gaseous NH₃ (∆H°_f = -46.1 kJ/mol; ∆G°_f = -16.5 kJ/mol: (d) What are the equilibrium constants K_p and K_c for the reaction at 350 K? Assume that ∆H° and ∆S° are independent of temperature.

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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

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

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/(K*mol), and S°(KCl) = 82.6 J/(K*mol).

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Textbook Question