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Ch.19 - Chemical Thermodynamics
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.19 - Chemical ThermodynamicsProblem 7b
Chapter 19, Problem 7b

The accompanying diagram shows how ΔH (red line) and TΔS (blue line) change with temperature for a hypothetical reaction.
(b) In what temperature range is this reaction spontaneous?

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1
Understand the concept of spontaneity: A reaction is spontaneous when the change in Gibbs free energy (\( \Delta G \)) is negative. The equation for Gibbs free energy is \( \Delta G = \Delta H - T\Delta S \).
Identify the given variables: \( \Delta H \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy.
Determine the relationship between \( \Delta H \) and \( T\Delta S \): For the reaction to be spontaneous, \( \Delta H < T\Delta S \).
Analyze the diagram: Look for the temperature range where the blue line (\( T\Delta S \)) is above the red line (\( \Delta H \)).
Conclude the temperature range: The reaction is spontaneous in the temperature range where the blue line is above the red line, indicating \( \Delta G < 0 \).

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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. A reaction is spontaneous when the change in Gibbs Free Energy (ΔG) is negative. The relationship is given by 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.
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Enthalpy (ΔH)

Enthalpy (ΔH) is a measure of the total heat content of a system. In the context of a reaction, it indicates whether the reaction absorbs heat (endothermic, ΔH > 0) or releases heat (exothermic, ΔH < 0). The sign and magnitude of ΔH influence the spontaneity of the reaction, particularly at different temperatures.

Entropy (ΔS)

Entropy (ΔS) is a measure of the disorder or randomness in a system. A positive change in entropy (ΔS > 0) indicates an increase in disorder, which favors spontaneity. The temperature (T) plays a crucial role in the Gibbs Free Energy equation, as higher temperatures can make a reaction spontaneous even if ΔH is positive, provided ΔS is also positive.
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Related Practice
Textbook Question

Consider a reaction A2(𝑔) + B2(𝑔) ⇌ 2 AB(𝑔), atoms of A shown in red in the diagram and atoms of B shown in blue. (a) If 𝐾𝑐 = 1, which box represents the system at equilibrium?

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Textbook Question

The accompanying diagram shows how entropy varies with temperature for a substance that is a gas at the highest temperature shown. (c) If this substance is a perfect crystal at T = 0 K, what is the value of S at this temperature?

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Textbook Question

Which of the following processes are spontaneous and which are nonspontaneous: (d) lightning

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Textbook Question

Predict the signs of ΔH and ΔS for this reaction. Explain your choice.

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