Spontaneous Reactions (HL) (DP IB Chemistry): Revision Note

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^ꝋ is 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

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

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 and a feasible reaction

  • 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^ꝋ term:

    • Will be very large and positive 

    • Will overcome ΔH_reaction^ꝋ

  • Therefore, at high temperatures ΔG^ꝋ is 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

  • ΔH is often hundreds of kJ, whereas TΔS is typically smaller

  • This means that it is rare for entropy to “overcome” enthalpy unless temperatures are very high

• These reactions are therefore usually spontaneous under normal conditions

Flow chart to determine the feasibility of exothermic reactions

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^ꝋ term:

    • Will be small and negative 

    • Will not overcome the larger ΔH_reaction^ꝋ

  • At low temperatures, ΔG^ꝋ is positive and the reaction is not feasible

  • The reaction is more feasible at high temperatures 

    • This is because the as the –TΔS_system^ꝋ term will become negative enough to overcome the ΔH_reaction^ꝋ 

    • This results in a negative ΔG^ꝋ

• So, certain reactions that are not feasible at room temperature can become feasible at higher temperatures

  • An example of this is found in metal extractions

  • Iron extraction in the blast furnace is 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

Summary of factors affecting Gibbs free energy 

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 =