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

The reactions occurring in the cell are
At anode: `H_(2)(g)to2H^(+)(aq)+2e^(-)`
`underline("At cathode: "M^(4+)(aq)+2e^(-)toM^(2+)(aq))`
Overall reaction: `H_(2)(g)+M^(4+)(aq)toM^(2+)(aq)+2H^(+)(aq)`
`E_(cell)=E_(cell)^(@)-(0.059)/(2)"log"([M^(2+)][H^(+)]^(2))/([M^(4+)])`
`E_(cell)^(@)-E_(M^(4+)//M^(2+))^(@)-E_(H^(+)//H_(2))^(@)`
`=0.151-0=0.151V`
`therefore0.092=0.151-(0.059)/(2)log(10^(x)xx1^(2))`
or `0.092=0.151-0.0295log10^(x)`
or `0.0295log10^(x)=0.151-0.092=0.059`
or `log10^(x)=(0.059)/(0.0295)=2`
`therefore10^(x)`=Antilog `2=10^(2)thereforex=2`