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)1.54V
(b)1.48V
(c)1.84V
(d)none of these

Options

A. `1.54V`
B. `1.48V`
C. `1.84V`
D. `1.51`

Answer

B

Explanation

Anode `H_(2(g))rarr2H^(+)(aq)+2e^(-)`
(i)Cathode `MnO_(4)^(-)+8H^(+)+5e^(-)rarrMn^(2+)+4H_(2)O`
(ii)
`(i)xx(5)`
`(ii)xx(2)`
`E=E^(o)-(0.06)/(10)log,([Mn^(2+)]^(2)[H^(+)]_(a)^(10))/([MnO_(4)^(-)][H^(+)]_(ca)^(16)P_(H2)^(5))`
`=1.51-(0.06)/(10)log,((10^(-2))^(2)xx(10^(-3))^(10))/((10^(-1))^(2)xx(10^(-2))^(16)(10^(-1))^(5))`
`=1.51-(0.06)/(10)log10^(5)`
`=1.51-0.03=1.48V`