Spontaneous Reactions (HL) (DP IB Chemistry)

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 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^ꝋ will be very large and positive and 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

• These reactions are therefore usually spontaneous under normal conditions

Flow chart to determine the feasibility of exothermic reactions

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^ꝋ will be small and negative and will not overcome the larger ΔH_reaction^ꝋ

  • Therefore, at low temperatures ΔG^ꝋ is 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

The diagram shows under which conditions endothermic reactions are feasible

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 =