[NewtoAtoms]

Q:  Give the cell diagram notation of the electrochemical cell that could be used to determine experimentally the dissociation constant (Kw) of water.

The standard reduction potential for:

O₂ + 2H₂0 + 4e- ---------> 4 OH-                                     0.40 V

Q2:  Use the value from the above question to calculate the dissociation constant at 298 K.

A:  I have added a SHE to the standard reduction potential, to keep things easy:

Reduction Reaction (cathode)       O₂ + 2H₂0 + 4e- ---------> 4 OH-                                     0.40 V
Oxidation Reaction (anode)          2H₂   ----------> 4H+ + 4e-                                              0.00 V

 E^ocell = E^ocathode - E^oanode
 E^ocell = 0.40 V = 0.00
 E^ocell = 0.40 V

Now to relate this to calculating the Dissociation constant of water or (K) I related it back to the equation

E= E^ocell - 0.0257V/n (1n K)
1n K = nE^o / 0.0257 V

1n K = (4)(0.40) / 0.0257
1n K = 62.26
K = 1.09 x 10²⁷

Now my real issue with this question is that I know that the dissociation constant for water is

Kw = {H+}{OH-}

and I also know that 25^oC or 298 K the dissociation constant is 1.2 x 10^-14... obviously this is very different than the answer that I got from my calculations above.

That means that in accordance to the equation that I used above is my K correct?
Or have I once again so horribly fallen off the chemistry wagon.. oh brother!

Thank you for your assistance