Free Energy

The Gibbs free energy, also commonly known as the Gibbs function, Gibbs energy, or free enthalpy, is a thermodynamic potential that is used to measure the maximum amount of work done in any given thermodynamic system when the temperature and pressure of the system are kept constant. Gibbs free energy is denoted by the letter G. Its value is usually expressed in either Joules or Kilojoules as it is also a form of energy. Gibbs free energy is defined as the maximum amount of work done that can be extracted from a closed thermodynamic system.

Gibbs energy is a thermodynamic property and it was determined by American scientist Josiah Willard Gibbs in the year 1876 when he was conducting experiments to predict the behaviour of systems when combined together or whether a process could take place simultaneously and spontaneously at a given temperature. Gibbs free energy was also known as available energy. Gibbs free energy can be visualized as the total amount of useful energy present in a thermodynamic system that can be utilized to perform some work.

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Gibbs Energy

Gibbs energy is also known as Gibbs free energy, it is one of the four thermodynamic potentials. Gibbs free energy is equal to the difference in enthalpy of the system with the product of the temperature and entropy. The equation is given as:

G= H - TS

Where,

G = Gibbs free energy

H = enthalpy

T = temperature

S = entropy

Gibbs free energy is a state function thus it doesn’t depend on the path (i.e., its path independent entity). Thus, the change in Gibbs free energy will be equal to the difference in the change in enthalpy with the product of temperature and entropy change of the system.

ΔG= ΔH - Δ(TS)

If the reaction is carried out under constant temperature i.e., assuming that the reaction is isothermal in nature, (ΔT=0) then:

ΔG= ΔH - TΔS

This equation is called the Gibbs Helmholtz equation.

Now, depending on the value of the change in Gibbs free energy, we can define many new reactions:

• Suppose the change in Gibbs free energy is greater than zero (ΔG > 0), then the reaction is nonspontaneous and endergonic.

• Suppose the change in Gibbs free energy is less than zero (ΔG < 0), then the reaction is spontaneous and exergonic.

• Suppose the change in Gibbs free energy is equal to zero (ΔG = 0), then the reaction is at equilibrium condition.

There are some important key points to be remembered regarding Gibbs free energy such as:

1. According to the second law of thermodynamics, the entropy of the universe always increases for a spontaneous process and it can never be equal to zero.

2. The change in Gibbs free energy (ΔG) determines the direction and extent of chemical change.

3. The change in Gibbs free energy (ΔG) is useful only for reactions in which the temperature and pressure remain constant (i.e., it is in good agreement with the isothermal and isobaric process). The system is usually open to the atmosphere (constant pressure) and we initiate and terminate the process at room temperature (after any heat we have supplied or which is released by the reaction has dissipated).

4. Standard Gibbs free energy is often used as the single master variable that determines whether a given chemical change is thermodynamically possible. Thus, if the change in free energy of the reactants is more than that of the products, the entropy of the world will increase when the reaction takes place as written, and so the reaction will tend to take place spontaneously. 

       ΔS_universe =  ΔS_system + ΔS_surroundings

5. If the change in Gibbs free energy is negative, the process will occur spontaneously and is referred to as exergonic.

6. Therefore spontaneity of the reaction is dependent on the temperature of the system (Gibbs free energy spontaneous).

Even though the change in Gibbs free energy is temperature-dependent, we assume the change in enthalpy ΔH and the change in entropy ΔS independent of temperature when there is no phase change in the reaction. So if we know the change in enthalpy ΔH and the change in entropy ΔS, we can calculate the change in Gibbs free energy ΔG at any temperature.

Relationship Between Free Energy and Equilibrium Constant

The change in Gibbs free energy of the thermodynamic reaction in any state, ΔG (at equilibrium) is related to the standard free energy change of the reaction, ΔG° (that is equal to the difference in the free energies of creation of the products and reactants both in their standard states) 

According to the equation:

ΔG = ΔG⁰ + RT In Q

Where,

Q- The reaction quotient.

ΔG=0 and Q become adequate to the constant. Hence the equation becomes,

⇒ ΔG⁰=-RT ln K_eq

⇒ ΔG⁰= -2.303 RT log K_eq

Where,

R=gas constant = 8.31 J mol^-1 K^-1 or 0.008314 kJ mol^-1 K^-1 

T is the temperature on the Kelvin scale

In any reversible reaction, the free energy of the reaction mixture is less than the free energy of reactants also as products. Hence, Gibbs free energy decreases whether we start from reactants or products i.e, ΔG is -ve in both backward and the forward reactions.

Relationship Between Gibbs Free Energy and EMF of a Cell

In the case of galvanic cells, Gibbs energy change ΔG is said to be the trade done by the cell.

ΔG = - nFE_cell

Where,

n = no. of moles of electrons involved

F = the Faraday constant

E = emf of the cell

We know that 1 Faraday=96500 coulombs.

Did You Know?

• We know that both the enthalpy of the system and the Gibbs free energy are the thermodynamic potentials, and one of the unique facts is that even the unit of ΔG is the same as that of ΔH.

• The tesla free energy is modern free energy, though it is named free energy it is not free, it requires components. Usually found in a free electricity generator or free energy motor.

• A free energy generator magnet follows a mechanism that generates electrical energy using the neodymium magnet theory. There are various sizes of generators, and one kind of generator that produces electrical energy is the free energy generator.