The standard reduction potential of the reaction, `2H_(2)O+2e rarr H_(2)+2OH^(-)` is `-0.8277V` at `25^(@)C`. Find the value of the equilibrium constant of the reaction `2H_(2)Orarr H_(3)O^(+)+OH^(-)` at the same temperature.

Explanation

`H_(2)O(l)+erarr(1)/(2)H_(2)(g)+OH^(-)(aq)`,
`DeltaG_(1)^(@)=+(Fxx0.8277)J`
`(1)/(2)H_(2)(g)rarrH^(+)(aq)+e, DeltaG_(2)^(@)=0J`
`therefore H_(2)O(l)rarrH^(+) (aq)+OH^(-)(aq)`
or, `DeltaG^(@)=DeltaG_(1)^(@)+DeltaG_(2)^(@)=+(Fxx0.8227)J`
or, `-RTln K=+(Fxx0.8277) therefore K=10^(-14)`