Electrochemistry | Nernst Equation#
Nernst Equation#
- Nernst Equation is used to calculate EMF of a cell.
Nernst Equation derivation
At temperature T, change in Gibbs Free Energy is given by:
\[ ΔG = ΔG^0 + RTlnQ \]
where, Q = Reaction quotient, R = Universal Gas Constant
We know that:
\[ΔG^0 = -nFE^0_{cell}\]
\[ΔG = -nFE_{cell}\]
Putting these two values in above equation:
\[ -nFE_{cell} = -nFE^0_{cell} + RTlnQ \]
\[ E_{cell} = E^0_{cell} - {RT \over {nF}}lnQ \]
\[ E_{cell} = E^0_{cell} - {2.303RT \over {nF}}logQ \]
This equation is known as Nernst Equation.
If T = 298 K and putting the values of F and R in the given equation:
\[ E_{cell} = E^0_{cell} - {0.0591 \over n}logQ \]
Here, n = Number of electrons exchanged during cell reaction
How to apply Nernst Equation?#
- Calculate E0cell = E0cathode - E0anode
- Write oxidation half and reduction half reactions.
- Add oxidation half and reduction half reactions to obtain net cell reaction.
- Find number of electrons exchanged, n.
- Calculate reaction quotient of the net cell reaction.
- Use Nernst Equation to find Ecell:
\[ E_{cell} = E^0_{cell} - {0.0591 \over n}logQ \]
Nernst Equation during Equilibrium#
- At equilibrium, we know that change in Gibbs Free Energy is zero.
\[ΔG = 0\]
\[-nFE_{cell} = 0\]
\[E_{cell} = 0\]
-
Also, at equilibrium: \(Q = K_c\)
-
Therefore, at equilibrium, Nernst equation can be written as:
\[ E_{cell} = E^0_{cell} - {0.0591 \over n}logQ \]
\[ 0 = E^0_{cell} - {0.0591 \over n}logK_c \]
\[ E^0_{cell} = {0.0591 \over n}logK_c \]
Nernst Equation For Half Cell Reactions#
-
Nernst Equation is applicable for half cell as well as complete cell.
-
For oxidation half cell, we can write:
\[ E_{ox} = E^0_{ox} - {0.0591 \over n}logQ_1 \]
- For reduction half cell, we can write:
\[ E_{red} = E^0_{red} - {0.0591 \over n}logQ_2 \]
- Adding oxidation and reduction half cell reaction, we get net cell reaction and Nernst equation of cell can be written as:
\[ E_{ox} + E_{red} = E^0_{ox} + E^0_{red} - {0.0591 \over n}log(Q_1Q_2) \]
We know that: \(E_{ox} + E_{red} = E_{cell}\)
\[E_{cell} = E^0_{cell} - {0.0591 \over n}log(Q)\]
Electrochemical cell and Gibbs Energy of a Reaction#
- Change in Gibbs Free Energy is given by:
\[ΔG = -nFE_{cell}\]
- Standard Change in Gibbs Free Energy is given by:
\[ΔG^0 = -nFE^0_{cell}\]
Also,
\[ΔG^0 = -RTlnK_c\]