AQA A Level Chemistry复习笔记5.1.8 Reaction Feasibility

• The Gibbs equation can be used to calculate whether a reaction is feasible or not

ΔGꝋ = ΔHreactionꝋ - TΔSsystemꝋ

• When ΔGꝋ is negative, the reaction is feasible and likely to occur
• When ΔGꝋis positive, the reaction is not feasible and unlikely to occur
• Feasible and spontaneous are fairly similar terms to describe reactions
  • Feasible tends to be used to describe reactions which are energetically favourable, so reactions that should go
  • Spontaneous tends to be used to describe reactions that go of their own accord

  Summary for temperature and Gibbs free energy

  

Answer

Step 1: Calculate ΔSsystemꝋ

ΔSsystemꝋ = ΣΔSproductsꝋ - ΣΔSreactantsꝋ

ΔSsystemꝋ = (2 x ΔSꝋ [CaO(s)]) -  (2 x ΔSꝋ [Ca(s)] + ΔSꝋ [O2(g)])

= (2 x 40.00) - (2 x 41.00 + 205.0)

= -207.0 J K-1 mol-1

Step 2: Convert ΔSꝋ to kJ K-1 mol-1

= -207.0 J K-1 mol-1÷ 1000 = -0.207 kJ mol-1

Step 3: Calculate ΔGꝋ

ΔGꝋ = ΔHreactionꝋ - TΔSsystemꝋ

= -635.5 - (298 x -0.207)

= -573.8 kJ mol-1

Step 4: Determine whether the reaction is feasible

Since the ΔGꝋ is negative the reaction is feasible

• The feasibility of a reaction can be affected by the temperature
• The Gibbs equation will be used to explain what will affect the feasibility of a reaction for exothermic and endothermic reactions

Exothermic reactions

• In exothermic reactions, ΔHreactionꝋ is negative
• If the ΔSsystemꝋ is positive:
  • Both the first and second term will be negative
  • Resulting in a negative ΔGꝋ so the reaction is feasible
  • Therefore, regardless of the temperature, an exothermic reaction with a positive ΔSsystemꝋ will always be feasible

   

• If the ΔSsystemꝋ is negative:
  • The first term is negative and the second term is positive
  • At very high temperatures, the -TΔSsystemꝋ will be very large and positive and will overcome ΔHreactionꝋ
  • Therefore, at high temperatures ΔGꝋ 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, ΔHreactionꝋ is positive
• If the ΔSsystemꝋ is negative:
  • Both the first and second term will be positive
  • Resulting in a positive ΔGꝋ so the reaction is not feasible
  • Therefore, regardless of the temperature, endothermic with a negative ΔSsystemꝋ will never be feasible

   

• If the ΔSsystemꝋ is positive:
  • The first term is positive and the second term is negative
  • At low temperatures, the -TΔSsystemꝋ will be small and negative and will not overcome the larger ΔHreactionꝋ
  • Therefore, at low temperatures ΔGꝋ 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 ΔHreactionꝋ resulting in a negative ΔGꝋ

   

• 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

A summary table of free energy conditions

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

ΔGꝋ = ΔHreactionꝋ - TΔSsystemꝋ

• For a reaction to be feasible ΔGꝋ must be zero or negative

0 = ΔHꝋ - TΔSꝋ

ΔHꝋ = TΔSꝋ

T= ΔHꝋ / ΔSꝋ

Answer:

If ΔG = 0 then ,   T= ΔHꝋ / ΔSꝋ

T= 1336 ÷ (581/1000)

T= 2299 K

Graphing the Gibbs Equation

• The Gibbs equation can be expressed as the equation for a straight line

ΔGꝋ = ΔHꝋ - TΔSꝋ

ΔGꝋ = - ΔSꝋT+ ΔHꝋ

y = mx + c

• A graph of free energy versus temperature (in K) will give a straight line, with slope -ΔSꝋ and y-intercept, ΔHꝋ.
• The variation of ΔGꝋ against T for the synthesis of ammonia has been plotted below:

N2 (g) + 3H2 (g)⇌ 2NH3 (g)

Graph of free energy versus temperature for the synthesis of ammonia

• From this graph you should be able to see some key features:
  • The x-intercept shows you where the reaction ceases to be spontaneous, in this case at 460 K (187 oC)
  • Above this temperature ΔGꝋ is positive so the reaction is not feasible
    • However, you may recall that the operating conditions of the Haber process are higher than this temperature, but this graph takes no account of the use of a catalyst which affects the energetics of the system, nor does it take into account anything about the rate of reaction or the fact that it is an equilibrium and removal of the ammonia as soon as it is formed also tips the balance in favour of the product

     

  • The y-intercept shows you reaction is exothermic which you can see from the enthalpy of formation; the value is approximately -46 kJ mol -1
  • An exothermic equilibrium reaction would be favoured by lower temperatures - this is seen by the value of ΔGꝋ  becoming increasingly negative as the temperature falls