If the following half cells have `E^(@)` values as
`A^(3+) + e^(-) to A^(2-) , E^(@) = y_(2) V`
`A^(2+) + 2e^(-) to A , E^(@) = - y_(1) V`
The `E^(@)` of the half cell `A^(3+) + 3e to A` will be

Options

A. `(2y_(1) - y_(2))/(3)`
B. `(y_(2) - 2y_(1))/(3)`
C. `2y_(1) - 3 y_(2)`
D. `y_(2) - 2 y_(1)`

Answer

B

Explanation

(i) `A^(3+) + e^(-) to A^(2+) , Delta G_(1) = - 1 F y_(2)`
(ii) `A^(2+) + 2e^(-) to A , Delta G_2 = -2 F(-y_(1)) = 2 F y_(1)`
Add , (i) and (ii) we get
`A^(3+) + 3e^(-) to A ,`
`Delta G_(3) = Delta G_(1) + DeltaG_(2)`
`- 3 FE^(@) = - Fy_(2) + 2 Fy_(1)`
`-3 FE^(@) = -F (y_(2) - y_(1))`
`F^(@) = (y_(2) - 2y_(1))/(3)`