Calculating the Change in Gibbs Free Energy

The American scientist Josiah Willard Gibbs gave Gibbs free energy. The benefits of thermodynamics laws and Gibbs’s free energy equations will reduce experimental cost and time. Gibbs free energy is based on thermodynamic second law, which means “In an isolated system entropy of a system is always increased if there is no additional force”. Calculating the change in Gibbs free energy is the energy change between products and reactants.

Gibbs free energy equation 

Gibbs free energy is defined as the enthalpy of the system minus products of temperature and entropy of the system. Here, the SI unit for Gibbs free energy is Joules. Gibbs’s free energy can balance the potential driving forces of chemical reactions.

ΔG =ΔH – TΔS 

Where,

 ΔG – change in Gibbs Free Energy

 ΔH – change in Enthalpy

 T – Temperature

 ΔS – change in Entropy

Entropy (S)

Entropy is defined as a thermal energy per unit temperature unavailable in the system to do valuable work. SI unit for entropy is Joule / Kelvin.

Enthalpy (H)

Enthalpy is defined as a sum of internal energy and pressure time’s volume. SI unit for enthalpy is Joule.

H = U + PV

Here, U – Internal energy, SI unit for internal energy is Joule

P – Pressure, SI unit for Pressure is Pa

V – Volume, SI unit for Volume is m3

Change in Gibbs free energy

Change in Gibbs free energy is the change in energy between reactants and products. 

ΔGrxn = ΔG(products) – ΔG(reactants)

• If the product is more stable, ΔGrxn is negative. It means the reaction is exergonic.
• If the reactant is more stable, ΔGrxn is positive. It means the reaction is endergonic.

A relationship between change in standard free energy and equilibrium constant is derived as,

ΔGrxn = -2.303 RT logKeq (R=8.314 kj/ Kelvin/mol)

Spontaneous Process

If the reaction occurs without any additional force, it is known as a spontaneous process, which may be slower or faster. The spontaneity of the system does not depend upon kinetic or reaction.

Example: Carbon diamond turning into graphite

Non-Spontaneous Process 

If the reaction occurs with any additional force is known as the Non-spontaneous process.

Example: Melting of ice into water.

Exergonic Process

The exergonic reaction is a reaction where energy is released without any additional force. Here, the change in free energy will be negative.

ΔG < 0 “G” is Negative

Endergonic Process 

An endergonic reaction is a reaction where energy is released with any additional force. Here, the change in free energy will be positive. The endergonic process will act in the reverse direction to obtain more starting material.

ΔG > 0 “G” is Positive

Calculating the change in Gibbs free energy

• For CO + H₂O → CO₂ + H₂ (∆S = -135 J/K, ∆H = -41.2), find

1. i) ∆G =? ii) ∆G at 305 K. Explain which reaction is spontaneous?

Answer:

 i)∆G = ∆H – T∆S

 = -41.2 – (298 x(-135 x 10⁻3))

 = – 97 KJ

 ∆G is less than 0, therefore spontaneous.

1. ii) ∆G = ∆H – T∆S

 = -41.2 – (305 (-135 x 10-3))

 =0

When ∆G is less than 0 = reaction is spontaneous

When ∆G is greater than 0, the reverse reaction is spontaneous.

•  Calculate equilibrium constant, K at 298 K (∆G= 33.4)

Answer:

∆G= -RT In K

33.4 = – (8.314 x 10-3) 298 In K

In K = -13.5

K= 1.4 x 10-6

• Calculate equilibrium constant K at 298 K

For

2N2O +3O2 4NO2           ∆H = -31.6 kJ, ∆S = -98 J/K

Answer:

∆G = T – ∆S

 = -31.6 – (298 x -98 x 10-3)

 =- 2.40 KJ 

Therefore,

K,

 ∆G= – RT InK

 -2.40 = -( (8.314 x 10-3 ) x 298 ) In K

 K = 2.64

•  When ATP is converted to ADP at 293 K. calculate the change in energy? (∆H = 19.07 Kcal, ∆S = 90 cal/K)

Answer : 

∆G = ∆H – T∆S

 = 19.07 – ( 293 (90 x 10-3))

 = – 7.3 Kcal

•  Calculate ΔG of a reaction at 298.15 K

 (ΔH= -128.3 kJ, ΔS =- 159.5 J K-1)

 Answer: ΔG = ΔH – TΔS

 = -128- ( 298.15 x -159.5)

 = -80.75 kJ

Conclusion

Gibbs’s free energy formula will help to find the result of experiments before doing work, which will allow finding other parameters like Enthalpy (Δ H), Entropy (Δ S) and Process direction (Spontaneous or nonspontaneous). The change in Gibbs free energy is the change in energy between products and reactants. If the product is stable, the difference in energy will be negative- Exergonic. If not, the change in Gibbs free energy will be positive- Endergonic.