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Ch.7 Chemical Reactions: Energy, Rate and Equilibrium
McMurry - Fundamentals of General, Organic, and Biological Chemistry 8th Edition
McMurry8th EditionFundamentals of General, Organic, and Biological ChemistryISBN: 9780134015187Not the one you use?Change textbook
All textbooksMcMurry 8th EditionCh.7 Chemical Reactions: Energy, Rate and EquilibriumProblem 22b
Chapter 7, Problem 22b

The following diagram portrays a reaction of the type A(s) → B(g) + C(g), where the different-colored spheres represent different molecular structures. Assume that the reaction has ∆H = +9.1 kcal/mol (+38.1 kJ/mol).

b. Is the reaction likely to be spontaneous at all temperatures, nonspontaneous at all temperatures, or spontaneous at some but nonspontaneous at others?

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1
Step 1: Analyze the reaction type and the diagram. The reaction A(s) → B(g) + C(g) involves a solid reactant (A) breaking down into two gaseous products (B and C). The diagram shows the solid spheres (A) on the left transforming into dispersed spheres (B and C) on the right, indicating an increase in disorder or entropy (ΔS > 0).
Step 2: Recall the thermodynamic equation for spontaneity: ΔG = ΔH - TΔS. Here, ΔH is given as +9.1 kcal/mol (+38.1 kJ/mol), which is positive, indicating the reaction is endothermic. ΔS is positive due to the increase in entropy as the solid reactant forms gaseous products.
Step 3: Consider the temperature dependence of spontaneity. For an endothermic reaction (ΔH > 0) with a positive ΔS, the term -TΔS becomes more negative as temperature (T) increases. At high temperatures, the negative contribution of -TΔS can outweigh the positive ΔH, making ΔG negative and the reaction spontaneous.
Step 4: Evaluate the spontaneity at low temperatures. At low temperatures, the positive ΔH dominates because the -TΔS term is small, resulting in a positive ΔG. Therefore, the reaction is nonspontaneous at low temperatures.
Step 5: Conclude the temperature dependence. The reaction is spontaneous at high temperatures due to the favorable entropy change and nonspontaneous at low temperatures due to the endothermic nature of the reaction. Thus, the reaction is spontaneous at some temperatures but nonspontaneous at others.

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Key Concepts

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

Enthalpy (∆H)

Enthalpy is a thermodynamic property that reflects the total heat content of a system. In the context of a chemical reaction, the change in enthalpy (∆H) indicates whether the reaction absorbs or releases heat. A positive ∆H, such as +9.1 kcal/mol, signifies that the reaction is endothermic, meaning it requires heat input to proceed, which can affect its spontaneity.
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Spontaneity of Reactions

The spontaneity of a reaction refers to its ability to occur without external intervention. It is determined by the Gibbs free energy change (∆G), which combines enthalpy and entropy changes. A reaction is spontaneous if ∆G is negative, which can occur at certain temperatures depending on the balance between enthalpy and entropy, especially in endothermic reactions.
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Entropy (S)

Entropy is a measure of the disorder or randomness in a system. In chemical reactions, an increase in entropy (positive ∆S) generally favors spontaneity, as systems tend to evolve towards greater disorder. In the given reaction, the transition from solid A to gaseous products B and C suggests an increase in entropy, which can contribute to the reaction's spontaneity at higher temperatures despite its positive enthalpy.
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Related Practice
Textbook Question

Is the total enthalpy (H) of the reactants for an endothermic reaction greater than or less than the total enthalpy of the products?

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Textbook Question

The vaporization of Br2 from the liquid to the gas state requires 7.4 kcal/mol (31.0 kJ/mol).

c. How many kilojoules are needed to evaporate 82 g of Br2?

Textbook Question

What effect do the listed changes have on the position of the equilibrium in the reaction of carbon with hydrogen?

C(s) + 2 H2(g) ⇌ CH4(g) ∆H = -18 kcal/mol (-75kJ/mol)

c. Allowing CH4 to escape continuously from the reaction vessel

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Textbook Question

The vaporization of Br2 from the liquid to the gas state requires 7.4 kcal/mol (31.0 kJ/mol).

a. What is the sign of ∆H for this process? Write a reaction showing heat as a product or reactant.

Textbook Question

Two curves are shown in the following energy diagram:

b. Which curve represents the spontaneous reaction, and which the nonspontaneous?

Textbook Question

The following diagram portrays a reaction of the type A(s) → B(g) + C(g), where the different-colored spheres represent different molecular structures. Assume that the reaction has ∆H = +9.1 kcal/mol (+38.1 kJ/mol).

a. What is the sign of ∆S for the reaction?