Spontaneous Reactions (HL) | HL IB Chemistry Revision Notes 2025

Spontaneous Reactions

Gibbs free energy provides an effective way of focusing on a reaction system at constant temperature and pressure to determine its spontaneity
For a reaction to be spontaneous, Gibbs free energy must have a negative value (ΔG^ꝋ ≤ 0)
We can use the Gibbs equation to calculate whether a reaction is spontaneous / feasible or not

ΔG^ꝋ = ΔH_reaction^ꝋ – TΔS_system^ꝋ

- When ΔG^ꝋ is negative, the reaction is spontaneous / feasible and likely to occur
- When ΔG^ꝋis positive, the reaction is not spontaneous / feasible and unlikely to occur
Depending on the value for ΔH and ΔS we can determine whether the reaction is spontaneous at a given temperature (T)
We can also look at the values for enthalpy change, ΔH, and entropy change, ΔS

Worked example

Determining if a reaction is feasible / spontaneous

Calculate the Gibbs free energy change for the following reaction at 298 K
Determine whether the reaction is feasible.

2Ca (s) + O₂(g) → 2CaO (s) ΔH = -635.5 kJ mol^-1

S^ꝋ[Ca(s)] = 41.00 J K^-1 mol^-1
S^ꝋ[O₂(g)] = 205.0 J K^-1 mol^-1
S^ꝋ[CaO(s)] = 40.00 J K^-1 mol^-1

Answer 1:

Step1: Calculate ΔS_system^ꝋ

- ΔS_system^ꝋ= ΣΔS_products^ꝋ – ΣΔS_reactants^ꝋ

- ΔS_system^ꝋ= (2 x ΔS^ꝋ [CaO(s)]) – (2 x ΔS^ꝋ [Ca(s)] + ΔS^ꝋ[O₂(g)])
  - = (2 x 40.00) – (2 x 41.00 + 205.0)
  - = -207.0 J K^-1 mol^-1

Step 2: Convert ΔS^ꝋto kJ K^-1 mol^-1

- ΔS_system^ꝋ= $\frac{- 207.0 J K^{- 1} {mol}^{- 1}}{1000}$ -0.207 kJ mol^-1

Step 3: Calculate ΔG^ꝋ

- ΔG^ꝋ = ΔH_reaction^ꝋ – TΔS_system^ꝋ

ΔG^ꝋ = -635.5 – (298 x -0.207)

= –573.8 kJ mol^-1

Answer 2:

- Since ΔG^ꝋ is negative, the reaction is feasible

Factors affecting ΔG and the spontaneity / feasibility of a reaction

We can also look at the values for ΔH and ΔS to determine whether the reaction is spontaneous / feasible at a given temperature (T)
The Gibbs equation will be used to explain what will affect the spontaneity / feasibility of a reaction for exothermic and endothermic reactions

Gibbs free energy equation

Gibbs Free Energy Equation

Exothermic reactions

In exothermic reactions, ΔH_reaction^ꝋ is negative
If the ΔS_system^ꝋ is positive:
- Both the first and second terms will be negative
- Resulting in a negative ΔG^ꝋ so the reaction is feasible
- Therefore, regardless of the temperature, an exothermic reaction with a positive ΔS_system^ꝋ will always be feasible
If the ΔS_system^ꝋ is negative:
- The first term is negative and the second term is positive
- At very high temperatures, the –TΔS_system^ꝋwill be very large and positive and will overcome ΔH_reaction^ꝋ
- Therefore, at high temperatures ΔG^ꝋis positive and the reaction is not feasible
Since the relative size of an entropy change is much smaller than an enthalpy change, it is unlikely that TΔS > ΔH as temperature increases
These reactions are therefore usually spontaneous under normal conditions

Flow chart to determine the feasibility of exothermic reactions

Feasibility summary of an exothermic reaction

The diagram shows under which conditions exothermic reactions are feasible

Endothermic reactions

In endothermic reactions, ΔH_reaction^ꝋ is positive
If the ΔS_system^ꝋ is negative:
- Both the first and second term will be positive
- Resulting in a positive ΔG^ꝋ so the reaction is not feasible
- Therefore, regardless of the temperature, endothermic with a negative ΔS_system^ꝋ will never be feasible
If the ΔS_system^ꝋ is positive:
- The first term is positive and the second term is negative
- At low temperatures, the –TΔS_system^ꝋwill be small and negative and will not overcome the larger ΔH_reaction^ꝋ
- Therefore, at low temperatures ΔG^ꝋis positive and the reaction is not feasible
- The reaction is more feasible at high temperatures as the second term will become negative enough to overcome the ΔH_reaction^ꝋ resulting in a negative ΔG^ꝋ
This tells us that for certain reactions which are not feasible at room temperature, they can become feasible at higher temperatures
- An example of this is found in metal extractions, such as the extraction if iron in the blast furnace, which will be unsuccessful at low temperatures but can occur at higher temperatures (~1500 ^oC in the case of iron)

Flow chart to determine the feasibility of endothermic reactions

Feasibility summary of an endothermic reaction

The diagram shows under which conditions endothermic reactions are feasible

Summary of factors affecting Gibbs free energy

If ΔH ....

And if ΔS ....

Then ΔG is

Spontaneous?

Because

is negative

< 0

exothermic

is positive

> 0

more disorder

always negative

< 0

Always

Forward reaction spontaneous at any T

is positive

> 0

endothermic

is negative

< 0

more order

always positive

> 0

Never

Reverse reaction spontaneous at any T

is negative

< 0

exothermic

is negative

< 0

more order

negative at low T

positive high T

Dependent on T

Spontaneous only at low T

TΔS < H

is positive

> 0

endothermic

is positive

> 0

more disorder

negative at high T

positive low T

Dependent on T

Spontaneous only at high T

TΔS > H

Temperature & Spontaneity

Rearranging the Gibbs equation allows you to determine the temperature at which a non-spontaneous reaction become feasible

ΔG^ꝋ = ΔH_reaction^ꝋ - TΔS_system^ꝋ

Remember, for a reaction to be feasible ΔG^Θꝋmust be zero or negative
- 0 = ΔH^ꝋ - TΔS^ꝋ
- ΔH^ꝋ = TΔS^ꝋ
- T= $\frac{∆ H^{θ}}{∆ S^{θ}}$

Worked example

At what temperature will the reduction of aluminium oxide with carbon become spontaneous?

Al₂O₃ (s) + 3C (s)→ 2Al (s) + 3CO (g)

ΔH^ꝋ = +1336 kJ mol^-1

ΔS^ꝋ = +581 J K^-1mol^-1

Answer:

If ΔG^ꝋ = 0 then T= $\frac{∆ H^{θ}}{∆ S^{θ}}$
Covert ΔS^ꝋto kJ K^-1mol^-1by dividing by 1000
T= $\frac{1336}{(\frac{581}{1000})}$ = 2299 K

Spontaneous Reactions (HL) (HL IB Chemistry)

Revision Note