Gibbs Free Energy Relationships

ΔG° < 0 (Spontaneous reaction):

• K > 1: When ΔG° is negative, the reaction is spontaneous, and the equilibrium favors the products, meaning the equilibrium constant (K) will be greater than 1.

• lnK > 0: Since ΔG° = -RT lnK, a negative ΔG° means lnK must be positive.

• ΔH < 0 (Exothermic): In many cases, a negative ΔG° corresponds to a negative ΔH, indicating that the reaction is exothermic.

• ΔS > 0 (Increased disorder): A negative ΔG° is often associated with an increase in entropy (ΔS > 0), indicating a more disordered system at equilibrium.

• T > 0: The temperature in the equation ΔG° = ΔH° - TΔS° must be positive, as temperature is always positive in Kelvin.

ΔG° > 0 (Non-spontaneous reaction)

• K < 1: When ΔG° is positive, the reaction is non-spontaneous, and the equilibrium favors the reactants, so K will be less than 1.

• lnK < 0: A positive ΔG° means lnK will be negative, indicating a preference for reactants.

• ΔH > 0 (Endothermic): Many reactions with positive ΔG° are endothermic (ΔH > 0), requiring heat to proceed.

• ΔS < 0 (Decreased disorder): A positive ΔG° can be associated with a decrease in entropy (ΔS < 0), indicating that the system becomes more ordered.

• T < 0: A negative temperature is not physically meaningful in this context, but if you manipulate the equation, a negative temperature could "reverse" the behavior. However, in real conditions, T is positive.

ΔG° = 0 (Equilibrium)

• K = 1: If ΔG° equals zero, the system is at equilibrium, meaning the concentrations of products and reactants are equal, so K = 1.

• lnK = 0: With ΔG° = 0, lnK is also 0, meaning the system is at equilibrium.

• ΔH and ΔS: For this to occur, ΔH and ΔS must balance in such a way that ΔH = TΔS at the temperature of interest.

Relationship Between Gibbs Energy and Thermodynamic Parameters

• ΔG° < 0 ⇒ K > 1 ⇒ lnK > 0 ⇒ ΔH < 0 (usually) ⇒ ΔS > 0 (usually) ⇒ T > 0

• ΔG° > 0 ⇒ K < 1 ⇒ lnK < 0 ⇒ ΔH > 0 (usually) ⇒ ΔS < 0 (usually) ⇒ T > 0

• ΔG° = 0 ⇒ K = 1 ⇒ lnK = 0 ⇒ ΔH = TΔS