Using data from Appendix C, calculate the change in Gibbs free energy for each of the following reactions. In each case, indicate whether the reaction is spontaneous at 298 K under standard conditions.
(a) 2 Ag(s) + Cl2(g) → 2 AgCl(s)
(b) P₄O₁₀(s) + 16 H₂(g) → 4 PH₃(g) + 10 H₂O(g)
(c) CH₄(g) + 4 F₂(g) → CF₄(g) + 4 HF(g)
(d) 2 H₂O₂(l) → 2 H₂O(l) + O₂(g)

Verified step by step guidance

Identify the standard Gibbs free energy of formation (ΔG_f^°) for each reactant and product from Appendix C for each reaction.

For each reaction, use the formula ΔG_rxn^° = Σ(ΔG_f^° products) - Σ(ΔG_f^° reactants) to calculate the standard Gibbs free energy change.

For reaction (a), calculate ΔG_rxn^° using the values for Ag(s), Cl2(g), and AgCl(s).

For reaction (b), calculate ΔG_rxn^° using the values for P4O10(s), H2(g), PH3(g), and H2O(g).

Determine the spontaneity of each reaction at 298 K by checking if ΔG_rxn^° is negative (spontaneous) or positive (non-spontaneous).

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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 measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is calculated using the formula ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates that a reaction is spontaneous under the given conditions.

Standard Conditions

Standard conditions refer to a set of specific conditions used as a reference point in thermodynamics, typically defined as 1 bar of pressure and a specified temperature, usually 298 K (25°C). Under these conditions, the standard Gibbs free energy change (ΔG°) can be determined for reactions, allowing for the assessment of spontaneity and equilibrium. It is crucial to ensure that calculations are performed under these standardized conditions for consistency.

Spontaneity of Reactions

The spontaneity of a reaction indicates whether it can occur without external intervention. A reaction is considered spontaneous if it has a negative Gibbs free energy change (ΔG < 0) at the specified conditions. Factors influencing spontaneity include enthalpy changes (ΔH), entropy changes (ΔS), and temperature. Understanding these factors helps predict the direction of chemical reactions and their feasibility.

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Related Practice

Textbook Question

Use data in Appendix C to calculate ΔH°, ΔS°, and ΔG° at 25 °C for each of the following reactions.

a. 4 Cr(s) + 3 O₂(g) → 2 Cr₂O₃(s)

b. BaCO₃(s) → BaO(s) + CO₂(g)

c. 2 P(s) + 10 HF(g) → 2 PF₅(g) + 5 H₂(g)

d. K(s) + O₂(g) → KO₂(s)

Textbook Question

Using data from Appendix C, calculate ΔG° for the following reactions. Indicate whether each reaction is spontaneous at 298 K under standard conditions.

(a) 2 SO₂(g) + O₂(g) → 2 SO₃(g)

(b) NO₂(g) + N₂O(g) → 3 NO(g)

(d) SO₂(g) + 2 H₂(g) → S(s) + 2 H₂O(g)

Textbook Question

Sulfur dioxide reacts with strontium oxide as follows: SO₂(g) + SrO(g) → SrSO₃(s) (a) Without using thermochemical data, predict whether ΔG° for this reaction is more negative or less negative than ΔH°.

Textbook Question

Classify each of the following reactions as one of the four possible types summarized in Table 19.3: (i) spontanous at all temperatures; (ii) not spontaneous at any temperature; (iii) spontaneous at low T but not spontaneous at high T; (iv) spontaneous at high T but not spontaneous at low T.

(a) N₂(g) + 3 F₂(g) → 2 NF₃₍g) ΔH° = -249 kJ; ΔS° = -278 J/K

(b) N₂(g) + 3 Cl₂(g) → 2 NCl₃(g) ΔH° = 460 kJ; ΔS° = -275 J/K