Gibbs Free Energy and Equilibrium HL Only
Quick Notes:
- As a reaction moves toward equilibrium, ΔG increases, becoming less negative, until ΔG = 0 at equilibrium.
- Two key equations:
- ΔG = ΔG⦵ + RT lnQ
- ΔG⦵ = −RT lnK
- Where:
- ΔG = Gibbs energy at any point in the reaction
- ΔG⦵ = standard Gibbs energy change
- R = gas constant = 8.31 J mol⁻¹ K⁻¹
- T = temperature in Kelvin
- Q = reaction quotient
- K = equilibrium constant
- If ΔG⦵ < 0 then K > 1 and products favoured
- If ΔG⦵ > 0 then K < 1and reactants favoured
Full Notes:
How Is ΔG Related to Equilibrium?
Essential ideas:
- Gibbs free energy (ΔG) indicates how far a reaction is from equilibrium.
- At equilibrium, ΔG = 0 and all concentrations of reactants and products remain constant.
- As a reaction proceeds, ΔG becomes less negative or less positive, approaching zero.
Understanding the link:
Chemical reactions tend to move toward a more stable state – in thermodynamic terms, a state of lower Gibbs free energy.
- When a system is far from equilibrium, ΔG is large (positive or negative), and the reaction proceeds in the direction that reduces ΔG.
- Over time, ΔG decreases until it reaches zero, and the system reaches equilibrium.
At equilibrium:
- The forward and reverse reactions occur at the same rate.
- The system’s free energy is at its lowest possible value.
- ΔG = 0 (no net driving force in either direction).
The Equation: ΔG = ΔG⦵ + RT lnQ
Most reactions don't occur under standard conditions. The equation below allows us to calculate Gibbs free energy change (ΔG) at any stage of the reaction and not just under standard conditions:
- ΔG = Gibbs free energy at current conditions
- ΔG⦵ = Gibbs free energy change under standard conditions
- R = Gas constant (8.31 J mol⁻¹ K⁻¹)
- T = Temperature (K)
- Q = Reaction quotient
How Is Q Calculated?
Q is the reaction quotient reflects the ratio of products to reactants at a specific moment in time.
It is calculated just like K (the equilibrium constant - see here for more detail), but using the current concentrations or pressures:
Q = [products]ⁿ / [reactants]ᵐ
For example, for a general equation such as:
The expression for Q is:
Don’t get confused about K and Q!
Q is the ratio of product to reactant concentrations at any moment in time - the system doesn't have to be at equilibrium.
K is what the ratio of product to reactant concetrations is at equilibrium.
If Q = K then that means the reaction is at equilibrium, however if Q doesn't equal K, then that the means the system isn't at equilibrium and the reaction will continue to proceed in the direction that will make Q = K and reach equilibrium.
What Does Q Tell Us About Spontaneity?
- If Q < K then ΔG < 0 and this means the forward direction is favoured.
- If Q > K then ΔG > 0 and this means the reverse direction is favoured.
- If Q = K then ΔG = 0 and this means equilibrium reached.
At Equilibrium: ΔG⦵ = –RT lnK
At equilibrium, ΔG = 0, so the previous equation becomes:
This links thermodynamic data (ΔG⦵) to the equilibrium constant (K):
| ΔG⦵ | K value | Reaction position |
|---|---|---|
| ΔG⦵ < 0 | K > 1 | Products favoured |
| ΔG⦵ = 0 | K = 1 | Equal amounts of reactants/products |
| ΔG⦵ > 0 | K < 1 | Reactants favoured |
Summary
- ΔG decreases as a reaction approaches equilibrium, reaching 0 at equilibrium.
- ΔG = ΔG⦵ + RT lnQ can be used to calculate Gibbs free energy under non-standard conditions.
- ΔG⦵ = –RT lnK links Gibbs free energy to equilibrium constant.
- If ΔG⦵ < 0, products are favoured; if ΔG⦵ > 0, reactants are favoured.
Linked Course Question
What is the likely composition of an equilibrium mixture when ΔG⦵ is positive?
If ΔG⦵ is positive, the equilibrium position lies toward the reactants, meaning the equilibrium mixture is mostly reactants with only a small amount of products formed. The reaction is not spontaneous under standard conditions.