For the following electrochemical cell at `298K`
`Pt(s)+H_(2)(g,1"bar") |H^(+) (aq,1M)||M^(4+)(aq),M^(2+)(aq)|Pt(s)`
`E_(cell) = 0.092 V` when `([M^(2+)(aq)])/([M^(4+)(aq)])=10^(x)`
Given, `E_(M^(4+)//M^(2+))^(@) = 0.151V, 2.303 (RT)/(F) = 0.059`
The value of x is-

Options

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

Answer

D

Explanation

At anode: `H_(2)(g) hArr 2H^(+)(aq) +2e^(-)`
At cathode: `M^(4+)(aq) +2e^(-) hArr M^(2+) (aq)`
Net cell reaction: `H_(2)(g) +M^(4+)(aq) hArr`
`2H^(+) (aq) +M^(2+)(aq)`
Now,
`E_(cell) = (E_(M^(4+)//M^(2+))^(@)-E_(H^(+)//H_(2))^(@))-(0.059)/(n)log.([H^(+)]^(2)[M^(2+)])/(P_(H_(2))[M^(4+)])`
or, `0.092 = (0.151 -0) -(0.059)/(2)log.(1^(2)xx[M^(2+)])/(1xx[M^(4+)])`
`:. ([M^(2+)])/([M^(4+)]) = 10^(2) rArr x = 2`