For the following electrochemical cell at 298 K,
`pt (s) |H_(2) (g, 1 " bar" )|H^(+) (aq.), M^(2+) (aq.)| Pt (s)`
`E_("cell") = 0.92 V` when `([M^(2+) (aq.)])/([M^(4+) (aq.)]) = 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

`E_(cell)^(@)=E_(M^(4+)//M^(2+))^(@)-E_(H^(+)//H_(2))^(@)`
`=(+0.151-0)=0.151` volt
`{:(H_(2)(g) rarr 2H^(+) +2e^(-)),(M^(4+)+2e^(-) rarr M^(2+)),(ulbar(M^(4+)+H_(2)(g) hArr M^(2+) +2H^(+))" "n=2):}`
`Q= ([M^(2+)][H^(+)]^(2))/([M^(4+)][H_(2)])=([M^(2+)]xx1^(2))/([M^(4+)]xx1)`
`=([M^(2+)])/([M^(4+)])=10^(x)`
Using Nernst equation :
`E=E^(@)-0.059/n log [10^(x)]`
`0.092=0.151-0.059/2 xx x`
`x=2`