15.2.4 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 be 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

• We can also look at the the values for enthalpy change, ΔH, and entropy change, ΔS
  • Depending on the value for ΔH and ΔS we can determine whether the reaction is spontaneous at a given temperature (T)

Factors affecting ΔG and the spontaneity / feasibility of a reaction 

Answers:

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^ꝋ to kJ K^-1 mol^-1

• • ΔS_system^ꝋ = -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 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

Exothermic reactions

• In exothermic reactions, ΔH_reaction^ꝋ is negative
• If the ΔS_system^ꝋ is positive:
  • Both the first and second term 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 at normal conditions

The diagram shows under which conditions exothermic reactions are feasible

 Summary of factors affecting Gibbs free energy