Gibbs Energy and Equilibrium
ΔG = ΔH − TΔS and its relation to the equilibrium constant. (Chemistry › Thermodynamics, NEET UG syllabus.)
What is Gibbs Energy and Equilibrium?
A thermodynamic potential that measures the 'useful' or process-initiating work obtainable from an isothermal, isobaric thermodynamic system. Its change (ΔG) determines spontaneity.
Key formula / rule: Gibbs-Helmholtz Equation
Key points
- Define Gibbs free energy and its significance in chemical thermodynamics.
- Apply the Gibbs-Helmholtz equation (ΔG = ΔH - TΔS) to calculate ΔG.
- Predict the spontaneity of a reaction based on the sign of ΔG.
- Understand the conditions under which a reaction becomes spontaneous or non-spontaneous.
Common exam trap
Forgetting to convert temperature from Celsius to Kelvin.
Definitions
- Term
Gibbs Free Energy (G)
- Meaning
A thermodynamic potential that measures the 'useful' or process-initiating work obtainable from an isothermal, isobaric thermodynamic system. Its change (ΔG) determines spontaneity.
- Term
Spontaneity
- Meaning
The natural tendency of a process to occur without continuous external intervention. A process is spontaneous if ΔG < 0.
- Term
Equilibrium Constant (K)
- Meaning
A value that expresses the ratio of product concentrations to reactant concentrations at equilibrium, with each concentration raised to the power of its stoichiometric coefficient. It indicates the extent of a reaction at equilibrium.
- Term
Standard Gibbs Free Energy Change (ΔG°)
- Meaning
The change in Gibbs free energy for a reaction when all reactants and products are in their standard states (1 atm partial pressure for gases, 1 M concentration for solutions, pure solids/liquids).
Learning objectives
Define Gibbs free energy and its significance in chemical thermodynamics.
Apply the Gibbs-Helmholtz equation (ΔG = ΔH - TΔS) to calculate ΔG.
Predict the spontaneity of a reaction based on the sign of ΔG.
Understand the conditions under which a reaction becomes spontaneous or non-spontaneous.
Relate standard Gibbs free energy change (ΔG°) to the equilibrium constant (K).
Calculate K from ΔG° and vice versa, using ΔG° = -RT ln K.
Explain the relationship between ΔG, ΔG°, and the reaction quotient Q.
Formulae
- Name
Gibbs-Helmholtz Equation
- Note
Relates Gibbs free energy change to enthalpy change, entropy change, and absolute temperature. Predicts spontaneity.
- Expression
ΔG = ΔH - TΔS
- Name
Gibbs Free Energy Change (Non-Standard Conditions)
- Note
Relates Gibbs free energy change under any conditions to standard Gibbs free energy change and reaction quotient Q.
- Expression
ΔG = ΔG° + RT ln Q
- Name
Standard Gibbs Free Energy Change and Equilibrium Constant
- Note
Fundamental equation linking thermodynamics (ΔG°) to chemical equilibrium (K). Derived from ΔG = ΔG° + RT ln Q at equilibrium (ΔG=0, Q=K).
- Expression
ΔG° = -RT ln K
- Name
Equilibrium Constant from Standard Gibbs Free Energy Change
- Note
Rearrangement of ΔG° = -RT ln K, useful for calculating K.
- Expression
K = e^(-ΔG° / RT)
Prerequisites
Basic concepts of thermodynamics (system, surroundings, state functions).
First Law of Thermodynamics (conservation of energy).
Enthalpy (ΔH) and its relation to heat changes.
Entropy (ΔS) and its relation to disorder/randomness (Second Law of Thermodynamics).
Chemical equilibrium and the equilibrium constant (K).
Reaction quotient (Q).
Common mistakes
Forgetting to convert temperature from Celsius to Kelvin.
Confusing ΔG (non-standard conditions) with ΔG° (standard conditions).
Incorrectly interpreting the sign of ΔG for spontaneity.
Using incorrect units for R (e.g., using L atm mol⁻¹ K⁻¹ instead of J mol⁻¹ K⁻¹ for energy calculations).
Assuming ΔG = 0 for all spontaneous reactions; it's only 0 at equilibrium.
Misinterpreting the relationship between ΔG° and K (e.g., thinking a positive ΔG° means K is positive, instead of K < 1).
Keywords
Gibbs Free Energy
Spontaneity
Equilibrium
Enthalpy
Entropy
Gibbs-Helmholtz Equation
Equilibrium Constant
Standard State
Reaction Quotient
Practice preview
For a spontaneous process under constant temperature and pressure, the change in Gibbs free energy (ΔG) must be:…
easy
For a reaction, ΔH = -50 kJ mol⁻¹ and ΔS = -100 J K⁻¹ mol⁻¹. At what temperature will the reaction be at equilibrium?…
medium
For a certain reaction, ΔH = +30 kJ mol⁻¹ and ΔS = +75 J K⁻¹ mol⁻¹. Above what temperature will the reaction become spontaneous?…
hard