Free Energy & Equilibrium
- When ΔG° < 0 for a reaction at constant temperature and pressure, the reaction is thermodynamically favored
- This means that the products are favored when the reaction reaches equilibrium
- We can say that the equilibrium constant K, is above 1
- When ΔG° is above 0, the reaction is not thermodynamically favored
- The reaction will proceed in the reverse direction
- The equilibrium constant, K, is below 1
- When ΔG° is equal to zero the reaction is at equilibrium and no further reaction occurs
- The equilibrium constant will be close to 1
- The qualitative relationship between ΔG°, the equilibrium constant, and temperature can be represented as:
ΔG° = -RT In K
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- R is the ideal gas constant
- T represents the absolute temperature in Kelvin.
- ln is the natural logarithm.
- To find the equilibrium constant we use:
K = e-ΔG°/RT
Worked example
At 298 K, the value of the equilibrium constant is 45.
Calculate a value for ΔG° for the reaction at 298 K.
R = 8.314 J mol-1 K-1
Identify whether the reaction will move in the forward or reverse direction.
Answer:
- ΔG° = -RT In K
- ΔG° = -(8.314) (298) [In(45)]
- ΔG° = -9431 J mol-1
- ΔG° = -9.43 kJ mol-1
- ΔG° is negative so the reaction will proceed in the forward direction
Free energy diagrams
- Remember: ΔG is an indication of whether the forward or backward reaction is favoured
- For a thermodynamically favored reaction:
- Most of the reactants are converted into products as the minimum is closer to the product side
- The slope of the curved line is to the left-hand side of the equilibrium point so ΔG° is negative and the reaction moves towards the products (and the minimum
Free energy diagram for a thermodynamically favored reaction
The reaction favors the products
- For a not thermodynamically favored reaction:
- A small amount of reactant is converted into products at equilibrium (where the minimum is)
- The slope and ΔG° are positive so the reaction proceeds towards the reactants (and towards the minimum)
Free energy diagram for a not thermodynamically favored reaction
The reaction favors the reactants
Exam Tip
You are given the equation, ΔGꝋ = -RT In K, in your exam.