Gibbs Free Energy: Equation and Numericals

Gibbs free energy in thermodynamics, is defined as the maximum work that can be performed by a thermodynamically closed system. 

• This is work other than the pressure-volume work and is done at constant temperature and pressure. 
• The symbol of Gibbs free Energy is G and the formula is ΔG° = ΔH° – TΔS°. 
• Here, H is the enthalpy, S is the entropy and T is the temperature.

Key Terms: Gibbs free energy, thermodynamics, closed system, pressure-volume work, entropy

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What is Gibbs free energy? 

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The potential at which a closed system attains a chemical equilibrium, at a constant pressure and temperature. 

• The symbol G is used to represent Gibbs free energy and the concept was given by Josiah Willard Gibbs in the 1870s. 
• The three main state functions that are considered during Gibbs free energy are enthalpy, temperature, and Entropy. 
• Enthalpy: Enthalpy is the sum of the internal energy (U) and the product of volume and pressure(pV). It is denoted by the symbol H and the formula for enthalpy is given by:

H = U + pV

• Entropy: Entropy is an extensive property, It measures the randomness in the system. The more disorder in the system, the more will be its entropy. The symbol for entropy is S, and the SI unit is JK^-1. An irreversible system will increase the entropy of the universe. The change in the entropy (ΔS) can be calculated by:

ΔS = \(\frac{Q}{T}\)

Where Q is the heat that transfers energy and T is the absolute temperature 

Read more: Difference between Enthalpy and Entropy 

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Equation for Gibbs free energy

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Gibbs function is an extensive property and also a state function. The change in the Gibbs Free Energy is given by: 

ΔG° = ΔH° – TΔS° (this is change at a constant temperature)

Thus, Gibbs energy change = change in enthalpy - temperature* entropy change. This is called as Gibbs Equation. At equilibrium, the Gibbs free energy is zero. The spontaneity of the reaction can be given ΔG:

• If ΔG is positive, it means the process is nonspontaneous. 
• If ΔG is negative, it means the process is spontaneous. 

The signs and magnitude of free energy can help to understand the chemical reaction in two ways: 

• Prediction of the spontaneity
• Prediction of the useful work that can be extracted. 

At equilibrium:

A + B ⇄ C + D, ΔG = 0

0= ΔrG + RT lnK 

ΔrG= - RT lnK

ΔrG= - 2.303 RT log K,

Where, K is the equilibrium constant 

Therefore, we can say that ΔG° = ΔH° – TΔS° = - RT ln K

Read more: Gibbs Free Energy Formula

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Things to Remember 

• The maximum amount of work that is done by the closed system is called Gibbs free energy. 
• ΔG° = ΔH°– TΔS° gives the formula for the Gibbs Free Energy, where S is the entropy and H is the heat. 
• Entropy is defined as the randomness of an object. 
• If ΔG is positive, it means the process is nonspontaneous. 
• If ΔG is negative, it means the process is spontaneous. 
• At equilibrium, the reaction is A+B ⇄ C+D, here ΔG is 0, and the formula is given by ΔrG= - 2.303 RT log K
• If ΔH, ΔS and ΔG are - ,+ and - respectively then the reaction will be spontaneous at all temperatures.

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