15.2.3 Gibbs Free Energy

Gibbs Free Energy Change

Gibbs free energy

• The feasibility of a reaction is determined by two factors, the enthalpy change and the entropy change
• The two factors come together in a fundamental thermodynamic concept called the Gibbs free energy (G)
• The Gibbs equation is:

ΔG = ΔHreaction – TΔSsystem

• The units of ΔG are in kJ mol1
• The units of ΔHreaction are in kJ mol1
• The units of T are in K
• The units of ΔSsystem are in J K-1 mol1(and must therefore be converted to kJ Kmol1 by dividing by 1000)

Calculating ΔGꝋ

• There are two ways you can calculate the value of ΔG
• From the Gibbs equation using enthalpy change, ΔH, and entropy change, ΔS, values
• From ΔG values of all the substances present

Worked Example

ΔGꝋ from ΔHꝋ and ΔSꝋ values

Calculate the free energy change for the following reaction:

2NaHCO(s) → Na2CO3 (s) + H2O (l) + CO2 (g)

ΔHꝋ = +135 kJ mol-1

ΔSꝋ = +344 J K-1 mol-1

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

• ΔG = ΔHreaction – TΔSsystem
• = +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

ΔGꝋ from other ΔGꝋ values

What is the standard free energy change, ΔG, for the following reaction?

C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O(g)

• This can be calculated in the same way as you complete enthalpy calculations
• ΔGꝋ = ΣΔGproducts – ΣΔGreactants
• ΔGꝋ = [(2 x CO) + (3 x H2O )] – [(C2H5OH) + (3 x O2)]
• ΔGꝋ = [(2 x -394 ) + (3 x -229 )] – [-175 + 0]
• ΔGꝋ -1300 kJ mol-1
• This can also be done by drawing a Hess cycle – find the way that is best for you

Exam Tip

The idea of free energy is what’s ‘leftover’ 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 our the reaction, so free energy is what is you are left with!

Calculating G from the Gibbs Equation

Calculating G from the Gibbs Equation

Calculating G from Formation

Calculating G from Formation

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