4.2.4 Reaction Feasibility

Summary 

• For ΔS_total to be positive and therefore the reaction feasible: 
  • Both ΔS_system and ΔS_surroundings are positive 
  • ΔS_surroundings is positive and ΔS_system is negative, but ΔS_surroundings > ΔS_system
  • ΔS_surroundings is negative and ΔS_system is positive, but ΔS_surroundings < ΔS_system 

Feasibility

• Generally, entropy will increase in the order:
• • solid < liquid < gas
• Therefore we can determine the change in entropy and the feasibility by considering the change in state of reactants to products 

• Example 1: the reaction between magnesium and oxygen at 293 K is feasible

Mg (s) + O₂ (g) → MgO (s) 

• This reaction produces a solid from a solid and a gas. Therefore entropy of the system is negative (ΔS_system < ΔS_surroundings)
• But since the entropy of the surroundings is very large as this reaction is very exothermic 
• This outweighs the entropy of the system, so the total entropy is positive therefore the reaction is spontaneous

• Example 2: the reaction between ethanoic acid and ammonium carbonate 

2CH₃COOH (aq) + (NH₄)₂CO₃ (s) → 2CH₃COONH₄ (aq) + H₂O (l) + CO₂ (g) 

• This reaction is endothermic, therefore ΔS_surroundings is negative 
• However, a gas is produced from a solid and liquid, so ΔS_system is positive
• ΔS_system > ΔS_surroundings and the reaction is spontaneous 

Gibbs free energy

• We can also use Gibbs free energy to work out if a reaction is feasible or not (this is not required as a part of the course) 
• The feasibility of a reaction is determined by two factors
  • The enthalpy and entropy change
• The two factors come together in a fundamental thermodynamic concept called the Gibbs free energy (G)
• The Gibbs equation is:

ΔG^ꝋ = ΔH_reaction^ꝋ – TΔS_system^ꝋ

• • The units of ΔG^ꝋ are in kJ mol^–1
  • The units of ΔH_reaction^ꝋare in kJ mol^–1
  • The units of T are in K
  • The units of ΔS_system^ꝋ are in J K^-1 mol^–1(and must therefore be converted to kJ K^–1 mol^–1by dividing by 1000)

• For a reaction to be feasible, ΔG^ꝋ must be equal or less than zero 

Temperature & feasibility

• We can 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 can 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

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)

The diagram shows under which conditions endothermic reactions are feasible

 Summary of factors affecting Gibbs free energy 

Answer

• As both ΔH and ΔS are positive, ΔG will become negative if TΔS > ΔH.
  
• The temperature at which this reaction becomes spontaneous can be calculated. This will be when ΔG = 0.
• If ΔG = 0, then T = ΔH / ΔS*
• T =
• T = 2299 K

*Don't forget to convert this into kJ

Key Terms

• Thermodynamically stable
  • Depends upon whether or not a reaction is spontaneous
  • The reaction is feasible if the total entropy is positive so there is a reduction in overall entropy
• Kinetic stability
  • Depends in the rate of reaction and activation energy (E_a)
  • Reactions which have a high E_a will not take place at room temperature 
• For example, methane will not form carbon dioxide and water unless it is ignited

• Another example is the decomposition of hydrogen peroxide at 298 K

H₂O₂ (l) → H₂O (l) + ½O₂ (g)

• This reaction has a very large E_a so must be catalysed using manganese dioxide, MnO₂
• If the reaction was left for long enough, the hydrogen peroxide would eventually decompose, however the addition of the MnO₂ allows the reaction to take place via an alternative route with a lower E_a