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Determine the potential of the following...

Determine the potential of the following cell:
`Pt|H_2(g,0.1 "bar")|H^+(aq,10^(-3)M"||"MnO_4^-)(aq),0.1M)`
`Mn^(2+)(aq,0.01M),H^+(aq,0.01M)|Pt`
Given : `E_(MnO_4^(-)|Mn^(2+))^(@)=1.51V`

A

1.54 V

B

1.48 V

C

1.84 V

D

1.68 V

Text Solution

Verified by Experts

The correct Answer is:
B
Anode : `H_(2)(g)rarr2H^(+)(aq)+2e^(-),E^(@)=0.0V`
Cathode : `MnO_(4)^(-)(aq)+8H^(+)(aq)+5e^(-)rarrMn^(2+)(aq)+4H_(2)O(l),E^(@)+1.51V`
`E_(cell)=E_("RP(RHS))-E_(RP(LHS))`
`rArr[1.51-(0.06)/(5)log.([Mn^(2+)])/([MnO_(4)^(-)][H^(+)]^(8))]`
`-[0-(0.06)/(2)log.(P_(H_(2)))/([H^(+)]^(2))]`
`=1.51-[(0.06)/(5) log. (0.001)/(0.1xx(10^(-2))^(8))]+(0.06)/(2)log.[(0.1)/((10^(-3))^(2))]`
`=1.48V`
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