5.4.3 Gibbs Free Energy

Gibbs free energy

• 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 

Calculating ΔG^Θ

• This can be done by using the Gibbs equation, using enthalpy change, ΔH^ꝋ, and entropy change, ΔS^ꝋ, values

Answer:

Step 1: Convert the entropy value in kilojoules

ΔS^ꝋ = +344 J K^-1 mol^-1  ÷ 1000 = +0.344 kJ K^-1 mol^-1 

Step 2: Substitute the terms into the Gibbs Equation

ΔG^ꝋ= ΔH_reaction^ꝋ– TΔS_system^ꝋ

= +135 – (298 x 0.344)

= +32.49 kJ mol^-1 

The temperature is 298 K since standard values are quoted in the question

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

ΔG^ꝋ = ΔH_reaction^ꝋ - TΔS_system^ꝋ

• Remember, for a reaction to be feasible ΔG^Θꝋmust be zero or negative

0 = ΔH^ꝋ - TΔS^ꝋ

ΔH^ꝋ = TΔS^ꝋ

T = ΔH^ꝋ ÷ ΔS^ꝋ

Answer:

• • If ΔG^ꝋ = 0 then T = ΔH^ꝋ ÷ ΔS^ꝋ
  • Covert ΔS^ꝋ to kJ K^-1 mol^-1 by dividing by 1000
  • T = 1336 ÷ (581/1000)
  • T = 2299 K

Temperature and Gibbs free energy 

• When ΔG^ꝋ is negative, the reaction is spontaneous / feasible and likely to occur
• When ΔG^ꝋ is positive, the reaction is not spontaneous / feasible and unlikely to occur
• We can also look at the the values for enthalpy change, ΔH, and entropy change, ΔS
  • Depending on the value for ΔH and ΔS we can determine whether the reaction is spontaneous at a given temperature (T)

Summary for temperature and Gibbs free energy