Equilibrium Constant and Gibbs Energy HL Only
Quick Notes
- Gibbs free energy change (ΔG°) is related to the position of equilibrium via the equation:
- R = 8.31 J mol⁻¹ K⁻¹
- T = temperature in Kelvin
- K = equilibrium constant
- If ΔG° < 0 then K > 1 → products favoured
- If ΔG° > 0 then K < 1 → reactants favoured
- If ΔG° = 0 then K = 1 → significant amounts of both
Full Notes
The Equation
There’s a direct relationship between Gibbs free energy and equilibrium position:
Where:
- ΔG° is the standard Gibbs free energy change (J mol⁻¹)
- R is the gas constant: 8.31 J mol⁻¹ K⁻¹
- T is temperature in kelvin (K)
- ln K is the natural logarithm of the equilibrium constant
Note: This equation is given in the IB data booklet.
What Does the Equation Tell Us?
This equation bridges thermodynamics and equilibrium.
If ΔG° is very negative: K must be large and equilibrium lies far to the right (mostly products).
If ΔG° is positive : K is small and equilibrium lies to the left (mostly reactants).
If ΔG° = 0 : K = 1 and equilibrium is balanced between products and reactants.
Equally:
- A reaction with a large K value (many products) will have a strongly negative ΔG°.
- A reaction with a small K value (mostly reactants) will have a positive ΔG°.
Worked Example
Question:
At 298 K, the standard Gibbs free energy change for a reaction is ΔG° = −12.0 kJ mol⁻¹. Calculate the equilibrium constant (K) for the reaction at this temperature.
- Step 1: Convert units
ΔG° = −12.0 kJ mol⁻¹ = −12000 J mol⁻¹ - Step 2: Use the equation
ΔG° = −RT lnK
−12000 = −(8.31)(298) lnK - Step 3: Rearrange to solve for lnK
lnK = 12000 / (8.31 × 298) ≈ 4.84 - Step 4: Calculate K
K = e^4.84 ≈ 126
Conclusion:
Since K > 1, the equilibrium lies to the right — the reaction favours the formation of products.
Rearranging the Equation
The equation can be rearranged if needed to find K and ΔG:
- To find K: K = e^(−ΔG° / RT)
- To find ΔG°: ΔG° = −RT lnK
- Use Kelvin for temperature and ensure consistent units (ΔG° must be in J mol⁻¹ if using R = 8.31).
Linked Course Question
How can Gibbs energy be used to explain which of the forward or backward reaction is favoured before reaching equilibrium?
Before equilibrium is reached, the value of ΔG indicates the direction the reaction will proceed:
- If ΔG < 0 → forward reaction is favoured (spontaneous forward).
- If ΔG > 0 → backward reaction is favoured (spontaneous reverse).
- At equilibrium, ΔG = 0 → neither direction is favoured, and the system is at its most stable state.
This helps predict the spontaneous direction of a reaction under non-equilibrium conditions.
Summary
- ΔG° is linked to K by the equation ΔG° = −RT lnK.
- Negative ΔG° means K > 1 and products are favoured.
- Positive ΔG° means K < 1 and reactants are favoured.
- At ΔG° = 0, K = 1 and both are present in significant amounts.
- The relationship connects thermodynamics with equilibrium position.