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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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.

CHEM 1220 SP2025 (18215) CHEM 1220 Practice Exam #4 v1 (17.4 - 17.6, 19, 20.1 - 20.5)- Requires Respondus LockDown Browser

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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