# 5.1.7 Gibbs Free Energy

### Gibbs Free Energy

#### Gibbs free energy

• As we have seen in the previous sections, 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 K1 mol1 by dividing by 1000)

Calculating ΔG

• There are two ways you can calculate the value of ΔG
• From ΔHand ΔSvalues
• From ΔGꝋ  values of all the substances present

#### Worked Example

ΔGfrom ΔHand ΔSvalues

Calculate the free energy change for the following reaction:

2NaHCO3 (s) → Na2CO3 (s) + H2O (l) + CO2 (g)

ΔH= +135 kJ mol-1        ΔS= +344 J K-1 mol-1

Step 1: Convert the entropy value in kilojoules

ΔS= +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

ΔGfrom other ΔGvalues

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

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

ΔG= ΣΔGproducts – ΣΔGreactants

ΔG= [(2 x CO2 ) + (3 x H2O )] – [(C2H5OH) + (3 x O2)]

ΔG= [(2 x -394 ) + (3 x -229 )] – [-175 + 0]

ΔG= -1300 kJ mol-1

#### 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!

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