Multiple Choice
Calculate ∆G° for the following reaction: P4 (s) + 5 O2 (g) → P4O10 (s), ∆H° = −2940 kJ/mol, 25 °C.
Does the reaction favor reactants or products?
19. Chemical Thermodynamics
Gibbs Free Energy Calculations
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Calculate the standard free-energy change (ΔG°) at 25 °C for the reaction: Mg(s) + Fe²⁺(aq) → Mg²⁺(aq) + Fe(s). Given: E°(Mg²⁺/Mg) = -2.37 V and E°(Fe²⁺/Fe) = -0.44 V.
A
-100 kJ/mol
B
-199 kJ/mol
C
-150 kJ/mol
D
-250 kJ/mol
Verified step by step guidance1
Identify the half-reactions involved in the redox process. The oxidation half-reaction is Mg(s) → Mg²⁺(aq) + 2e⁻, and the reduction half-reaction is Fe²⁺(aq) + 2e⁻ → Fe(s).
Determine the standard electrode potentials for each half-reaction. The standard reduction potential for Mg²⁺/Mg is E° = -2.37 V, and for Fe²⁺/Fe, it is E° = -0.44 V.
Calculate the standard cell potential (E°cell) using the formula: E°cell = E°(cathode) - E°(anode). Here, the cathode is the Fe²⁺/Fe couple, and the anode is the Mg²⁺/Mg couple.
Use the Nernst equation to relate the standard cell potential to the standard free-energy change: ΔG° = -nFE°cell, where n is the number of moles of electrons transferred (n = 2 for this reaction), and F is the Faraday constant (approximately 96485 C/mol).
Substitute the values for n, F, and E°cell into the equation to calculate ΔG°. Ensure the units are consistent, converting the result to kJ/mol if necessary.
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