Consider the relationships between standard cell potential, standard free energy change, and the equilibrium constant. What is true when standard cell potential is a large negative number?

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BlackTom AI · Accepted Answer

When evaluating the relationship among E°cell, ΔG°°, and K, it's helpful to recall key formulas and what they imply about signs. Option A: ΔG° = + and K > 1. If ΔG° were positive, that would correspond to a non-spontaneous reaction under standard conditions. However, K > 1 indicates a spontaneous tendency toward products at standard conditions, which would yield a negative ΔG° (since ΔG° = -RT ln K). Therefore this combination is internally inconsistent. Option B: ΔG° = – and K < 1. Here a negative ΔG° suggests spontaneity and a tendency toward product formation, but K < 1 implies the reaction favors reactants at equilibrium. This mismatch means the pair cannot simultaneously be true for a single reaction under standard conditions (because ΔG° = -RT ln K would give a positive ΔG° when K < 1). Option C: ΔG° = + and K < 1. This pairing also conflicts with the thermodynamic relationships. A positive ΔG° indicates non-spontaneity and corresponds to K < 1, but the standard equation ΔG° = -RT ln K shows that K < 1 yields ΔG° > 0, so while the sign of ΔG° would align with K < 1, the overall interpretation for a large negative E°cell is not consistent; moreover the phrase "large negative E°" would drive ΔG° negative via ΔG° = -nFE° (with F positive and n > 0) rather than positive, so this combination misaligns with that expectation. Option D: ΔG° = – and K > 1. A large negative E° corresponds to a negative ΔG° through ΔG° = -nFE°. A negative ΔG° means the reaction is spontaneous under standard conditions, and a spontaneous reaction has K > 1 (since ΔG° = -RT ln K). Thus this pairing is consistent with the standard relationships among E°, ΔG°, and K, aligning signs across all three quantities. In summary, the signs must be such that a large negative E° (which drives ΔG° negative via ΔG° = -nFE°) corresponds to a K value greater than 1 (since ΔG° = -RT ln K and a negative ΔG° yields ln K positive). This consistency check helps discriminate among the options and rules out those with mismatched signs or implications.

Consider the relationships between standard cell potential, standard free energy change, and the equilibrium constant. What is true when standard cell potential is a large negative number?单项选择题

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