Inorganic and Applied Chemistry

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Inorganic and Applied Chemistry

Example 6- G:

The use of the Nernst equation to calculate equilibrium constants

We have a galvanic cell consisting of the following two half cell reactions:

Ag+(aq) + e-  Ag(s)

Fe3+(aq) + e-  Fe2+(aq)

We wish to determine the equilibrium constant K for the overall cell reaction. At equilibrium the reaction

fraction for the cell reaction Y is equal to the equilibrium constant for the cell reaction which is why we

may be able to use the Nernst equation to determine the value for K. When there is equilibrium in a

galvanic cell no transfer of electrons takes place between the two half cell which is why^0 celle = 0.

From tables we have the following reduction potentials corresponding to the following reactions:

Ag+(aq) + e- Ag(s) ,^0 = 0.80 volt

Fe3+(aq)  Fe2+(aq) + e- ,^0 = 0.77 volt

As mentioned earlier it is necessary that the potential of the cell is positive (meaning that G is negative –

please refer to equation (6-2)). In order for the cell reaction to be able to proceed the reaction between

iron(II) and iron(III) ions has to run backwards. The overall cell reaction has to be (which was also shown

in example 6-E) with corresponding equilibrium expression:

Ag+(aq) + Fe2+(s)  Ag(s) + Fe3+(aq)

 

 



Fe Ag

K Fe

2

3

As mentioned it is the size of this equilibrium constant K, that we wish to determine in order to be able to

predict something about the equilibrium. The total standard potential of the cell is determined to be:

+^0 (cellen)    0. 80 V( 

0. 77 V)    0. 03 V

From the Nernst equation the equilibrium constant is found in the following manner (z = 1 as there is only

one electron transferred in the overall cell reaction):

K M

z V

K

K

z

Y vedligevægt

z

celle

celle celle celle

3. 2

0. 0592

10. 03

0. 0592

log

0. (^0592) log ( ) 0 0. (^0592) log
   0
   0 0
   (
    

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    • As the equilibrium constant is 3.2 M the equilibrium must be to the right under the given conditions.
      Electrochemistry