# Nernst Equation and Calculation of Emf

Chemistry

## definition

### Calculate EMF or Cell Potential

The potential difference between the two electrodes in a galvanic cell is called a 'Cell Potential' or 'EMF' of the cell. It is measured in volts.
Standard EMF of the cell = Standard Reduction Potential of the half cell on the right hand side (Cathode) - Standard Reduction Potential of the half cell on the left hand side (Anode)
For example, EMF of Daniell cell,

If we were taking Oxidation Potentials into account,
Standard EMF of the cell = Standard Oxidation Potential of the half cell on the left hand side (Anode)-Standard Oxidation Potential of the half cell on the right hand side (Cathode). For example, EMF of Daniell cell,

## definition

### Nernst Equation for Electrode Potential

Electrode potential varies rapidly with temperature and concentrations of the species involved. Hence, to define one particular reference for electrode potentials, standard set of conditions have been defined. If potential is measured under these conditions, it is known as 'Standard Potential'.
The Nernst Equation enables the determination of cell potential under non-standard conditions. It relates the measured cell potential to the reaction quotient and allows the accurate determination of equilibrium constants (including solubility constants).
Nernst equation is given as:

i.e. at
The equation above indicates that the electrical potential of a electrode depends upon the reaction quotient of the reaction.
So if we are trying to determine reduction potential of electrode, we will have to consider
We can then Nernst Equation as:
at
This way we can determine the for Copper electrode at any temperature and concentration, if we know the standard reduction potential of Copper electrode i.e.

## definition

### Nernst Equation for EMF of a cell

The Nernst Equation enables the determination of cell potential under non-standard conditions. It relates the measured cell potential to the reaction quotient and allows the accurate determination of equilibrium constants (including solubility constants).
Nernst equation is given as:

i.e. at
The equation above indicates that the electrical potential of a cell depends upon the reaction quotient of the reaction.
For a cell:

We have a net chemical reaction of
If the concentrations of the ions are not 1.0 M, and the pressure is not 1.0 atm, then the cell potential may be calculated using the Nernst equation:

## example

### Numerical on Nernst Equation

Q. Find the cell potential of a galvanic cell based on the following reduction half-reactions at C.

where,

Solution:
The first step is to determine the cell reaction and total cell potential.
In order for the cell to be galvanic, reactions need to be spontaneous i.e. .
Since Cadmium is having lesser reduction potential amongst the two, Cadmium must undergo oxidation. Hence reactions involved will be:

Hence, overall reaction will be:

Now, from Nernst Equation we have,
at
Here,  we can write Nernst Equation as,

i.e.