Relation Between Gibbs Energy Change and EMF of a Cell

While you might be trying to perceive the connection between EMF of the cell and Gibbs free energy, it is essential to explore the fundamental and surprisingly the most complicated components involved in this relationship.

What is the so-called Gibbs Free Energy and EMF?

Gibbs energy is also known as the standard Gibbs free energy formula. It can be described as the maximum amount of non-expansion work that can be extracted from a closed system. It also provides a measure to determine the feasibility of a reaction.

Emf or electromotive force is the work done per unit charge to take it around a circuit.

potential.

Gibbs Free Energy Formula

ΔG = ΔH – TΔS

Where ΔG addresses Gibbs free energy

ΔH = The change in enthalpy

T = The temperature,

and

ΔS is the adjustment of entropy

If ΔG < 0, then the Energy reaction is spontaneous

Energy reactions will, in general, be non-spontaneous if ΔG > 0. What’s more;

If ΔG = 0, Then the reaction shows equilibrium . However these conditions are true only at constant temperature and pressure.

Relation between Gibbs Free Energy and EMF of cell

Gibbs free energy and cell EMF relationship is G = -nFE_cell. G represents the Gibbs free energy and is expressed in terms of  n, number of electrons absorbed or released, F represents Faraday, and E cell represents standard electrode potential. Or it can also be represented as follows;

W = nFE (cell)

Here,

W = The work done,

nF = charge passed TOTALLY and;

E_cell = The emf of cell

When the charge reversibly passes via the galvanic cell, you’ll notice that the galvanic cell completes the most amount of the work. Furthermore, the work amount of the reversible work results in reducing Gibbs energy in a given reaction.

Δr G = −W

Δr G = −nFE_cell

You can use the above-given reaction for calculating the potential of a standard cell.

When every target reacting species have the same concentration, the equation becomes:

E_cell = E_{o cell}

⇒ Δ_o G_o = −nFE_{o cell}

A certain reaction’s Gibbs energy value is known as the extensive thermodynamic characteristic, which indicates its main value relies on n. Therefore, on the other hand, when two different cell reactions have specific values of n, it is further observed the variation in different Gibbs free energy’s values.

As per thermodynamics, a reaction’s Gibbs energy can be related to the Q_r or reaction quotient. Further, the moment reaction reaches equilibrium may relate to the present equilibrium constant. Furthermore, a reaction’s Gibbs energy is subject to the emf of the cell, and the cell reaction’s equilibrium constant could relate to the potential of a standard cell.

When at a state of equilibrium,

Δ_r G_o = −nFE_{o cell}

Δ_r G_o = − R.T. ln K

−nFE_{o cell} = − RT ln K

E_{o cell} = (RT/nF) ln K

K is also called the equilibrium constant

R is also called universal gas constant

Due to the given-equation, it can be stated that:

• When the K > 1, E_{o cell}> 0, the entire reaction would be carried out spontaneously; on the other hand, it would favour product formation.
• When K < 1,  E_{o cell}<0, the reaction seems non-spontaneous. It will support the reactants’ formation.

The above explanation is perfect for clarifying the relationship between Gibbs free energy and the emf of a cell.

Conclusion

In this article, we studied the relation between Gibbs energy change and EMF of cells. Gibbs free energy is a measure of a reaction’s spontaneity. Gibbs free energy drops as the cell approaches a more equilibrium point in a spontaneous galvanic cell. The reaction is energised in an electrolytic cell.

Since gibbs free energy and emf of a cell are related the spontaneity of an electrolytic reaction can be determined from its emf.