What will be the emf for the given cell ?
`Pt|H_(2)(g,P_(1))|H^(+)(aq)|H_(2)(g,P_(2))|Pt`

Options

A. `(RT)/(f)ln(P_(1))/(P_(2))`
B. `(RT)/(2f)ln(P_(1))/(P_(2))`
C. `(RT)/(f)ln(P_(2))/(P_(1))`
D. None of these

Answer

B

Explanation

Anodic reaction: `H_(2)(P_(1))to2H^(+)`
Cathodic reaction: `2H^(+)toH_(2)(P_(2))`
`E_("cathode")=-(RT)/(2F)ln (P_(2))/([H^(+)]^(2)),E_("anode")=-(RT)/(2F)ln([H^(+)]^(2))/(P_(1))`
`E_("inf")=E_("anode")+E_("cathode")` ltBrgt `=-(RT)/(2F)ln((H^(+))^(2))/(P_(1))-(RT)/(2F)ln(P_(2))/((H^(+))^(2))`
`=-(RT)/(2F)ln(P_(2))/(P_(1))=(RT)/(2F)ln(P_(1))/(P_(2))`