Open Question
Calculate the equilibrium constant at 25°C for a reaction for which ∆G° = -4.22 kcal/mol.
19. Chemical Thermodynamics
Gibbs Free Energy And Equilibrium
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A redox reaction has an equilibrium constant of K = 1.2 x 10^3. Which statement is true regarding ΔG°_rxn and E°_cell for this reaction?
A
E°_cell is negative and ΔG°_rxn is negative.
B
E°_cell is positive and ΔG°_rxn is positive.
C
E°_cell is negative and ΔG°_rxn is positive.
D
E°_cell is positive and ΔG°_rxn is negative.
Verified step by step guidance1
Understand the relationship between the equilibrium constant (K), the standard Gibbs free energy change (ΔG°_rxn), and the standard cell potential (E°_cell). The key equations are ΔG°_rxn = -RT ln(K) and ΔG°_rxn = -nFE°_cell, where R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, and F is Faraday's constant.
Since K = 1.2 x 10^3 is greater than 1, the reaction favors the formation of products at equilibrium. This implies that the reaction is spontaneous under standard conditions.
For a spontaneous reaction, ΔG°_rxn must be negative. This is because a negative ΔG°_rxn indicates that the reaction can occur without the input of external energy.
Using the equation ΔG°_rxn = -nFE°_cell, if ΔG°_rxn is negative, then E°_cell must be positive. This is because the product of a negative number (ΔG°_rxn) and a positive number (nF) results in a positive E°_cell.
Therefore, the correct statement is that E°_cell is positive and ΔG°_rxn is negative, which aligns with the characteristics of a spontaneous redox reaction with K > 1.
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