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

Options

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

Explanation

For the given electrochemical cell, the reactions are
At anode: `H_(2_((g))to 2H_((aq))^(+)+2e^(-)`
At cathode : `(M_((aq))^(4+)+2e^(-)to M_((aq))^(2+))/(H_(2_((g))+M_((aq))^(4+)to M_((aq))^(2+)+2H_((aq))^(+)))`
`E_(cell)=E_(cell)^(@)-0.059/2log. ((M^(2+))(H_((aq))^(+)))/([M^(4+)])`
`0.092=(E_(M^(4+)//M^(2+))^(@)-E_(H^(+)//H_2)^(@))-0.059/2log(10^(x) [H^(x)[H^(+)]^(2))`
`0.092=(0.151-0)-0.059/2log(10^(x) xx1^(2)`
`0.092=0.151-0.0295 log 10^(x)`
`log 10^(x)=0.059/0.0295=2`
`10^(x) ="Antilog" 2=10^(2) impliesx=2`