For the following electrochemical cell at 298 k<
`Pt_(s) H_(g)(1bar)| H^(+)_(1M)||M _(aq)^(4+)`, `+(aq)^(2+) |Pt_(s)E _(cell) = 0.092V` When `([M_(aq)^(2+)])/([M_(aq)^(4+)] )=10^(X)`.
Given : `E_(M^(4+)//M^(2+))^(@) = 0.151 V`, `2.303(RT)/(F) = 0.059V ]`
The value of X is ,

Options

A. `-2`
B. `-1`
C. 1
D. 2

Answer

D

Explanation

`Pt (s) |H_(2) (g)` ( 1 bar) |`H^+ (aq) , (1 M) ||M^(4+) (aq) , M^(2+) (aq) |Pt (s)`
The cell is reaction is :` H_2 + M^(4+) (aq) to 2 H^(+) (aq) + M^(2+) (aq)`
`E_(cell) = E_(cell)^(@) - (0.059)/(n) "log" ([H^(+)]^(2) [M^(2+) (aq)])/(P_(H_(2)) . [M^(4+)(aq)])`
`E_(cell)^(@) = E_(M^(4+) |M^(2+))^(@) - E_(H^(+) |H_(2))^(@) = 0.151 - 0 = 0.151` V
`[H^(+)] = 1 , E_(cell) = 0.092 V , p_(H_(2)) = 1` 1 bar = x = 2
`therefore 0.092 = 0.151 - (0.059)/(2) "log" ([1]^(2) [M^(2+) (aq)])/([1] [M^(4+)(aq)])`
`0.092 - 0.151 = - (0.059)/(2) "log" ([M^(2+) (aq)])/([M^(4+)(aq)]) - 0.059 = - (0.059)/(2) "log" ([M^(2+) (aq)])/([M^(4+) (aq)])`
or `log ([M^(2+) (aq)])/([M^(4+) (aq)]) = 2`
or `([M^(2+) (aq)]) /([M^(4+) (aq)]) = 10^(2) = 10^(x) ` or x = 2