Calculate ΔS° values for the following reactions by using tabulated S° values from Appendix C. In each case, explain the sign of ΔS°. (a) HNO3(g) + NH3(g) → NH4NO3(s) (b) 2 Fe2O3(s) → 4 Fe(s) + 3 O2(g) (c) CaCO3(s, calcite) + 2 HCl(g) → CaCl2(s) + CO2(g) + H2O(l) (d) 3 C2H6(g) → C6H6(l) + 6 H2(g)

Verified step by step guidance

Step 1: Identify the standard molar entropy (S°) values for each reactant and product in the given reactions from Appendix C.

Step 2: For each reaction, calculate the total entropy of the products by summing the S° values of all products, each multiplied by their respective stoichiometric coefficients.

Step 3: Calculate the total entropy of the reactants by summing the S° values of all reactants, each multiplied by their respective stoichiometric coefficients.

Step 4: Determine the change in standard entropy (ΔS°) for each reaction using the formula: ΔS° = ΣS°(products) - ΣS°(reactants).

Step 5: Analyze the sign of ΔS° for each reaction. A positive ΔS° indicates an increase in disorder, while a negative ΔS° indicates a decrease in disorder. Consider the physical states and the number of moles of gases involved to explain the sign of ΔS°.

Key Concepts

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

Entropy (S)

Entropy is a measure of the disorder or randomness in a system. It quantifies the number of ways a system can be arranged, with higher entropy indicating greater disorder. In chemical reactions, changes in entropy (ΔS) can be assessed by comparing the states and number of molecules of reactants and products, influencing the spontaneity of the reaction.

Standard Entropy (S°)

Standard entropy (S°) refers to the absolute entropy of a substance at standard conditions (1 bar, 25°C). It is tabulated for various substances and is essential for calculating the change in entropy (ΔS°) for reactions. By using these values, one can determine the overall change in disorder when reactants are converted to products.

Sign of ΔS°

The sign of ΔS° indicates whether the entropy of the system increases or decreases during a reaction. A positive ΔS° suggests an increase in disorder, often occurring when gases are produced or when solid reactants form gaseous products. Conversely, a negative ΔS° indicates a decrease in disorder, typically seen when gaseous reactants yield solid products.

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Related Practice

Textbook Question

The standard entropies at 298 K for certain group 4A elements are: C(s, diamond) = 2.43 J>mol@K, Si1s2 = 18.81 J>mol@K, Ge1s2 = 31.09 J>mol@K, and Sn1s2 = 51.818 J>mol@K. All but Sn have the same (diamond) structure. How do you account for the trend in the S° values?

Textbook Question

Three of the forms of elemental carbon are graphite, diamond,and buckminsterfullerene. The entropies at 298 Kfor graphite and diamond are listed in Appendix C.(b) What would you expect for the S° value of buckminsterfullerene(Figure 12.49, p. 509) relative to the valuesfor graphite and diamond? Explain.

Textbook Question

Using S° values from Appendix C, calculate ΔS° values for the following reactions. In each case, account for the sign of ΔS°.

(a) C₂H₄(g) + H₂(g) → C₂H₆(g)

(b) N₂O₄(g) → 2 NO₂(g)

(d) 2 CH₃OH(g) + 3 O₂(g) ⟶ 2 CO₂(g) + 4 H₂O(g)

Textbook Question

(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system?

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Textbook Question

(b) For a certain process that occurs at constant T and P, the value of ΔG is positive. Is the process spontaneous?