Class 12- Electrochemistry / How to do numericals on Nernst equation / gibbs free energy/ Kc / Emf

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What is the Nernst Equation?
The Nernst equation calculates electrochemical cell potential at any known temperature, pressure, and concentration. The equation relates the reduction potential of the cell at a non-standard condition to that of the standard conditions (298K, 1 atm, and 1 M concentration).

ECell = cell potential
E0 = Cell potential under standard conditions
R = Universal gas constant (8.314 J/(mol*K))
T = Temperature
n = Number of electrons transferred in the reaction
F = Faraday constant (96485 C/mol)
Q = Reaction Quotient

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how to find emf by nernst equation
What is Nernst Equation?

The Nernst equation provides a relation between the cell potential of an electrochemical cell, the standard cell potential, temperature, and the reaction quotient. Even under non-standard conditions, the cell potentials of electrochemical cells can be determined with the help of the Nernst equation.

The Nernst equation is often used to calculate the cell potential of an electrochemical cell at any given temperature, pressure, and reactant concentration. The equation was introduced by a German chemist Walther Hermann Nernst.
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The Gibbs Free Energy and Cell Voltage
The maximum amount of work that can be produced by an electrochemical cell ( wmax ) is equal to the product of the cell potential ( E∘cell ) and the total charge transferred during the reaction ( nF ):

wmax=nFEcell
Work is expressed as a negative number because work is being done by a system (an electrochemical cell with a positive potential) on its surroundings.

The change in free energy ( ΔG ) is also a measure of the maximum amount of work that can be performed during a chemical process ( ΔG=wmax ). Consequently, there must be a relationship between the potential of an electrochemical cell and ΔG ; this relationship is as follows:

ΔG=−nFEcell
A spontaneous redox reaction is therefore characterized by a negative value of ΔG and a positive value of E∘cell , consistent with our earlier discussions. When both reactants and products are in their standard states, the relationship between ΔG° and E∘cell is as follows:

ΔG∘=−nFE∘cell
A spontaneous redox reaction is characterized by a negative value of ΔG°, which corresponds to a positive value of E°cell.

The Relationship between Cell Potential & the Equilibrium Constant
We can use the relationship between ΔG∘ and the equilibrium constant K , to obtain a relationship between E∘cell and K . Recall that for a general reaction of the type aA+bB→cC+dD , the standard free-energy change and the equilibrium constant are related by the following equation:

ΔG°=−RTlnK
Significance

The above equation helps us to predict the feasibility of the cell reaction. For a cell reaction to be spontaneous, ΔrG must be negative. This means that E must be positive for a spontaneous cell reaction.
Electrochemical Cell and Gibbs energy of the Reaction
In electrochemical cells, the chemical energy is converted into electrical energy. The cell potential is related to Gibbs energy change.

In an electrochemical cell, the system does work by transferring electrical energy through an electric circuit.

ΔrG = maximum work

For a reaction, occurring in an electrochemical cell whose electrodes differ in a potential by Ecell , the work done when amount of charge nF is pushed along by the potential of the cell is given by nFEcell so that

Maximum work = nFEcell

where F is the Faraday constant (the charge on one mole of electrons) and n is the number of moles of electrons transferred in them. When voltaic cell operates, work is done on the surroundings, as electrical energy flows through the external circuit. Such work by convention is taken as negative.

Thus,

ΔrGø = wmax = -nFEøcell

We use standard cell potential, Eøcell

Therefore

ΔrGø = -nFEøcell

where ΔrGø is the standard Gibbs energy for the reaction.

If the activity of all the reacting species is unity, then E=Eø and we have

ΔrGø = -nFEøcell

Thus, from the measurement of Eø we can calculate an important thermodynamic property. From the temperature dependence of Eø we can also calculate ΔrHø and ΔrSø

From the standard Gibbs energy, we can also calculate equilibrium constant by the equation: