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For the following electrochemical cell a...

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-

A

`-2`

B

`-1`

C

`1`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
D
Anode: `H_(2)-2ehArr2H^(+)`
`underline("Cathode: "M^(4+)+2ehArrM^(2+))`
Net cell reaction: `H_(2)+M^(4+)hArr2H^(+)+M^(2+)`
`E_(cell)=E_(cell)^(0)-(0.059)/(2)"log"([H^(+)]^(2)[M^(2+)])/([M^(4+)]xxP_(H_(2)))`
`0.092=0.151-(0.059)/(2)log10^(x)`
`0.092=0.151-(0.059)/(2)x`
`(0.059x)/(2)=0.151-0.092`
`0.059x=0.059xx2impliesx=2`.
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