Accidentally chewing on a stray fragmet of aluminium foil can causes a sharp tooth path if the aluminium comes in contact with an amalgam filing. The filing, an alloy of silver, tin and mercury, acts as the cathode of a tiny galvanic cell, the aluminium behaves as the anode, and salivas serves as the electrolyte. when the aluminium and the filling come in contact, and electric current passage from the aluminium to the filling which is sensed by a nerve in the tooth. Aluminium is oxidized at the anode, and `O_(2)` gas is reduced to water at the cathode.
`E_(AI^(3+)//AI)^(@) =- 1.66 E_(O_(2)H^(+)//H_(2)O)6^(@) = 1.23 V`
The standard reduction potential of the reaction,
`H_(2)O +e^(-) rarr (1)/(2)H_(2)+OH^(-)` at `298K` is:

Options

A. `E^(@) =(RT)/(2F)In K_(w)`
B. `E^(@) =(RT)/(F)In ]P_(H_(2))]^(1//2) [OH^(-)]`
C. `E^(@) =(RT)/(F)In ([P_(H_(2))]^(1//2))/([H^(+)])`
D. `E^(@) =(RT)/(F)In K_(w)`

Answer

A