Final answer:
When ln K is negative, it means the equilibrium constant K is less than one, which results in a positive Gibbs free energy (ΔGrxn), indicating that the reaction is spontaneous in the reverse direction.
Step-by-step explanation:
If ln K is negative, this indicates that the equilibrium constant, K, is less than one. According to thermodynamic principles, this means that the Gibbs free energy (ΔGrxn) for the reaction under standard conditions is positive, and therefore, the reaction is spontaneous in the reverse direction.
This is because the natural logarithm of a number less than one yields a negative value, and since ΔG° is related to ln K by the negative product with the gas constant (R) and temperature (T), ΔG° becomes positive when ln K is negative. So, the correct statement is 'ΔGrxn is positive and the reaction is spontaneous in the reverse direction.' A negative ΔGrxn would indicate a reaction that is spontaneous in the forward direction. If ΔGrxn were zero, the system would be at equilibrium and K would equal one.