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)In(p_(1))/(p_(2))`
B. `(RT)/(2F)In(p_(1))/(p_(2))`
C. `(RT)/(F)In(p_(1))/(p_(2))`
D. None of these.

Answer

B

Explanation

R.H.S. : `2H^(+)+2e^(-)rarrH_(2)(P_(2))`
L.H.S. : `H_(2)(P_(1))rarr2H^(+)+2e^(-)`
Over all reaction: `H_(2)(P_(1)) H_(2)(P_(2))`
`E=E^(@)+(RT)/(nF)"In"(P_(2))/(P_(1))=0-(RT)/(2F)"In"(P_(2))/(P_(1))`
`=(RT)/(2F)"in"(P_(1))/(P_(2))`.