Answer

Thermodynamic Parameters Determinable from Equilibrium Constants

By measuring the equilibrium constant (K) at two different temperatures, the following thermodynamic parameters can be determined using the van’t Hoff equation:

ln(K₂/K₁) = - (ΔrH° / R) × (1/T₂ - 1/T₁)
  

✅ Parameters That Can Be Determined

• Standard reaction enthalpy (Δ_rH°)
  Can be calculated from the slope of the van’t Hoff plot (ln K vs. 1/T).
• Standard reaction entropy (Δ_rS°)
  Can be obtained from intercept of van’t Hoff plot or from ΔG° = ΔH° − TΔS° at a known temperature.
• Standard free energy at T₁ (Δ_rG°_T₁)
  From the equation ΔG° = −RT ln K at T₁ using measured K.
• Standard free energy at T₂ (Δ_rG°_T₂)
  Likewise, calculated from ΔG° = −RT ln K at T₂.

❌ Parameters That CANNOT Be Determined

• Activation energy (E_a)
  Requires kinetic data, not equilibrium data.
• Collision factor (A_c)
  This is part of the Arrhenius equation and relates to reaction kinetics, not thermodynamics.
• Activation enthalpy (Δ_rH^‡)
  Depends on transition state energy, not accessible from equilibrium constants.
• Activation entropy (Δ_rS^‡)
  Requires rate data and transition state theory analysis.
• Activation free energy (Δ_rG^‡)
  Cannot be inferred without kinetic data.
• Reaction rate constant (k)
  Direct measurement of k is needed, not derivable from K alone.

Conclusion

From equilibrium constants at two temperatures, you can estimate or calculate:

• Δ_rH° (Standard Enthalpy)
• Δ_rS° (Standard Entropy)
• Δ_rG° at both temperatures (from ln K)