A cell contains two hydrogen electrodes. The negative electrode is in contact with a solution of `10^(-6) M` hydrogen ions. The emf of the cell is 0.118 volt at `25^(@)C`. Calculate the concentration of hydrogen ions at the positive electrode.

Explanation

The cell may be written as :
`H_(2) | H^(+) (10^(-6) M) || H^(+) (M_(1)) | H_(2)`
Applying Nernst equation ,
`E = E^(+) - (0.059)/(1) "log" ([H^(+)]_("anode"))/([H^(+)]_("cathode"))`
`0.118 = 0 - (0.059)/(1) "log" ((10^(-6)))/(M_(1))`
log `(10^(-6))/(M_(1)) = (0.118)/(0.059) = -2`
`(10^(-6))/(M_(1)) = 10^(-2)`
or `M_(1) = 10^(-4) M`