Given below are the half -cell reactions
`Mn^(2+) + 2e^(-) rarr Mn, E^@ =- 1. 18 V`
`2 (Mn^(3+) = E^(-) rarr Mn^(2+)). E^@ = + 1.5 V`
The `E^@` for `Mn^(2+) rarr Mn+ 2 Mn^(3+)` will be.

Options

A. `-0.33` V , the reaction will occur
B. `-2.69 V` , the reaction will not occur
C. `-2.69 ` V , the reaction will occur
D. `-0.33` V , the reaction will not occur

Answer

B

Explanation

`Mn^(2+) + 2e^(-) to Mn , " " E^(@) = -1.18 V`
`DeltaG_(1)^(@) = - 2 F( - 1.18) = 2.36 V " " … (i)`
`Mn^(3+) + e^(-) to Mn^(2+) " " E^(@) = +1.51 V`
`Delta G_(2)^(@) = - F (1.51) = - 1.51 F " " … (ii)`
Eq. (i) - `2 xx` Eq. (ii)
`3 Mn^(2+) to Mn + 2 Mn^(3+)`
`Delta G_(3)^(@) = Delta G_(1)^(@) - 2 Delta G_(2)^(@)`
`= (2.36 - 2 xx (-1.51)] F `
`= 5.38 F `
But `Delta G_(3)^(@) = - 2 F E^(@)`
`E^(@) = - 2.69 V`
Since `E^(@)` value is negative , the reaction will not occur .