Equilibrium Constant & Entropy
- The equation for calculating the total entropy change is:
ΔSꝋtotal = ΔS ꝋsys + ΔSꝋsurr
(sys = system and surr = surroundings)
- Remember that ΔSꝋtotal is positive for all spontaneous changes
- There is very little change in ΔSꝋsys with a change in temperature unless there is a change in the state of one of the reactants or products
- There will be a significant change in ΔSꝋsurr however
- The entropy change of the surroundings during a chemical reaction is
- Where ΔH is the enthalpy change and T is the absolute temperature (measured in kelvin)
- We can use this information to determine whether a reaction is spontaneous at a given temperature
Worked example
Is the decomposition of calcium carbonate into calcium oxide and carbon dioxide spontaneous at the given temperatures?
CaCO3(s) → CaO(s) + CO2(g) ΔH = +177.9 kJ mol-1 ΔSsys = +160.4 J K-1 mol-1
- 293K (20 °C)
- 1173K (900 °C)
Answer 1: at 293 K (20°C)
- ΔSsurroundings = = -607.2 J K-1 mol-1
- ΔStotal(293K) = (+160.4 - 607.2) = -446.8 J K-1 mol-1
- The decomposition of calcium carbonate is not spontaneous at 293K
Answer 2: at 1173K (900°C)
- ΔSsurroundings = = -151.7 J K-1 mol-1
- ΔStotal(1173) = (+160.4 - 151.7) = +8.7 J K-1 mol-1
- The decomposition of calcium carbonate is spontaneous when heated to 1173K
Relationship between entropy change and equilibrium constant
- For a reversible reaction that can reach equilibrium, the equilibrium position can be reached from either side of the reaction
- This means that both the forward and backward reactions are spontaneous
- ΔS must be positive in both directions
- For example, consider the following reaction:
N2O4 (g) ⇌ 2NO2 (g)
A graph of entropy against the percentage of NO2 in a mixture of N2O4 and NO2
- The entropy of N2O4 is less than the entropy of the equilibrium mixture
- The change in entropy from pure N2O4 to the equilibrium mixture is positive
- The change is spontaneous
- The entropy change for NO2 to the equilibrium mixture is also positive
- This change is also spontaneous
- The entropy change for a mixture of the gases in any proportions moving towards the equilibrium position is also positive
- Neither the forward nor backward reaction can go to completion as the entropy change from the equilibrium mixture to either the reactants or products is negative
- At equilibrium, the total entropy change is zero
ΔStotal [forward reaction] = ΔStotal [backward reaction]
- The relationship between the total entropy of the reaction and the equilibrium constant (Kc or Kp) is
ΔStotal = R lnK
Using total entropy change to calculate an equilibrium constant
- Rearranging the equation mentioned above we get:
lnK =
- Hence:
K =
Relationship between equilibrium constant and equilibrium position
- There is no hard rule for the relationship between equilibrium constant and the position of equilibrium
- As a general rule, we can say a very large value of K suggests the equilibrium position is pushed towards the products (right-hand side)
- Similarly, a very small value of K suggests the equilibrium position is pushed towards the reactants (left-hand side)