Gibbs Free Energy (AQA A Level Chemistry): Revision Note
Exam code: 7405
Gibbs Free Energy
The thermodynamic feasibility of a reaction depends on two factors: the enthalpy change (ΔH) and the entropy change (ΔS)
These factors are combined in the Gibbs free energy change, ΔG, which determines whether a reaction is thermodynamically feasible under standard conditions
The Gibbs equation is:
ΔGꝋ = ΔHreactionꝋ - TΔSsystemꝋ
Where:
ΔGꝋ is the standard Gibbs free energy change (kJ mol⁻¹)
ΔHreactionꝋ is the standard enthalpy change (kJ mol⁻¹)
T is the temperature in kelvin (K)
ΔSsystemꝋ is the standard entropy change (J K⁻¹ mol⁻¹)
Because ΔH° is given in kJ mol⁻¹ and ΔS° is usually given in J K⁻¹ mol⁻¹, the entropy value must be converted to kJ K⁻¹ mol⁻¹ (by dividing by 1000) before substituting into the equation
Calculating ΔGꝋ
There are two ways you can calculate the value of ΔGꝋ
From ΔHꝋ and ΔSꝋ values
From the ΔGꝋ values of all the substances present
Worked Example
Calculate the free energy change for the following reaction:
2NaHCO3 (s) → Na2CO3 (s) + H2O (l) + CO2 (g)
ΔHꝋ = +135 kJ mol-1 ΔSꝋ = +344 J K-1 mol-1
Answer
Step 1: Convert the entropy value in kilojoules
ΔSꝋ = +344 J K-1 mol-1 ÷ 1000 = +0.344 kJ K-1 mol-1
Step 2: Substitute the terms into the Gibbs Equation
ΔGꝋ = ΔHreactionꝋ - TΔSsystemꝋ
= +135 - (298 x 0.344)
= +32.49 kJ mol-1
The temperature is 298 K since standard values are quoted in the question
Worked Example
What is the standard free energy change, ΔGꝋ, for the following reaction?
C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O(g)
Substance | ΔGꝋ in kJ mol⁻¹ |
|---|---|
C2H5OH (l) | -175 |
O2 (g) | 0 |
CO2 (g) | -394 |
H2O (g) | -229 |
Answer
ΔGꝋ = ΣΔGproductsꝋ - ΣΔGreactantsꝋ
ΔGꝋ = [(2 x CO2 ) + (3 x H2O )] - [(C2H5OH) + (3 x O2)]
ΔGꝋ = [(2 x -394 ) + (3 x -229 )] - [-175 + 0]
ΔGꝋ = -1300 kJ mol-1
Examiner Tips and Tricks
The idea of free energy is what's left over to do useful work when you've carried out the reaction. The enthalpy change is the difference between the energy you put in to break the chemical bonds and the energy out when making new bonds; the entropy change is the 'cost' of carrying out the reaction, so free energy is what you are left with!
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