The `e.m.f` of the `M|M^(n+)(0.02 M)||H^(+)(1M)H_(2(g))(1 atm) pt` at `25^(@)C` is `0.81 V`. Calculate the valence of metal if `E_(M//M^(n+))^(@) = 0.76V`.

Explanation

`M rarr M^(n+)+n e`
`nH^(+)+n e rarr (n)/(2)H_(2)`
`E_(Cell) = E_(OP_(M//M^(n+))) + E_(RP_(H^(+)//H_(2)))`
`E_(OP_(M//M^(n+)))^(@) - (0.059)/(n)"log"[M^(n+)] + E_(RP_(H^(+)//H_(2)))^(@) + (0.059)/(n)log.([H^(+)]^(n))/([P_(H_(2))]^(n//2))`
`= 0.76 + (0.059)/(n)"log"([H^(+)]^(n))/([P_(H_(2))]^(n//2)[M^(n+1)])`
`0.81 = 0.76 + (0.059)/(n)"log"([1]^(n))/([1]^(n//2)[0.02])`
or `n = 2`