Nernst equation is the one which relates the cell potential and the concentration of the species involved in an electrochemical reaction.

__Nernst equation__

Nernst equation is the one which relates the cell potential and the
concentration of the species involved in an electrochemical reaction. Let us
consider an electrochemical cell for which the overall redox reaction is,

*x*A* *+* y*B â†” *l*C* *+* *mD

The reaction quotient Q for the above reaction is given below

We have already learnt that,

âˆ†G = âˆ†Gâ€™ + RT
lnQ .....(9.29)

The Gibbs free energy can be related to the cell emf as follows [ âˆ´ equation
(9.24) and (9.25) ]

âˆ†G = - nFE_{cell};
âˆ†G^{o}= - nFE_{cell}^{o}

Substitute these values and Q from (9.28) in the equation (9.29)

(9.29) â‡’ - nFE_{cell} = - nFE^{o}_{cell}^{
}+ RT ln { [C]* ^{l}*[D]

Divide the whole equation (9.30) by (-nF)

The above equation (9.31) is called the Nernst equation

At 25Âº C
(298K), the above equation (9.31) becomes,

Let us calculate the emf of the following cell at 25^{o}C using
Nernst equation.

Cu (s) | Cu^{2+} (0.25 aq, M) | | Fe^{3+} (0.005 aq M) |
Fe^{2+} (0.1 aq M) | Pt (s)

Given : ( EÂº )_{Fe3+|Fe2+}
= 0.77V and ( EÂº ) _{Cu2+
| Cu }= 0.34 V

Half reactions are

Cu (s) â†’ Cu^{2+} (aq) + 2e^{-} .....
(1)

2 Fe^{3+} â†’ (aq) + 2e-
â†’ 2Fe^{2+} (aq) ..... (2)

the overall reaction is

Cu (s) + 2 Fe^{3+} (aq) â†’ Cu^{2+} (aq) + 2 Fe^{2+}
(aq), and n = 2

Apply Nernst equation at . 25ÂºC .

Given standard reduction potential of Cu^{2+} | Cu is 0.34V

(E^{o}_{ox} )_{Cu|Cu2+} = - 0.34V

(E^{o}_{red}) _{Fe3+|Fe 2+} = 0.77V

EÂº_{cell} = - 0.34
+ 0.77

EÂº_{cell} = 0.43V

** **

The electrochemical cell reaction of the Daniel cell is

Zn (s) + Cu^{2+} (aq) â†’ Zn^{2+} (aq)+Cu (s)

What is the change in the cell voltage on increasing the
ion concentration in the anode compartment by a factor 10?

** **

Tags : Thermodynamics of cell reactions | Electro Chemistry , 12th Chemistry : UNIT 9 : Electro Chemistry

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12th Chemistry : UNIT 9 : Electro Chemistry : Nernst equation | Thermodynamics of cell reactions | Electro Chemistry

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