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For the following electrochemical cell a...

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

A

-2

B

-1

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
(d) For a given electrochemical cell, the redox reaction is
`{:(At anode :, H_(2)(g) to 2H^(+)(aq)+2e^(-)),(At cathode :, M^(4+)(aq)+2e^(-) to M^(2+)(aq)):}/(" "H_(2)(g)+M^(4+)(aq) to M^(2+)(aq)+2H^(+)(aq))`
`E_(cell)=E_(cell)^(@)-(0.059)/(2)"log"([M_((aq))^(2+)][H^(+)]^(2))/([M^(4+)(aq)])`
`0.092=0.151-(0.059)/(2)"log"(10^(X)xx(H^(+))^(2))`
`0.092=0.151-(0.059)/(2)log(10^(X)xx1^(2))`
`0.092=0.151-0.0295("log "10^(X))`
`0.0295("log "10^(X))=0.151-0.0151-0.092=0.059`
`log10^(X)=(0.059)/(0.0295)=2`
`10^(X)="Antilog "2=10^(2)" or " X=2`
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