An aqueous solution containing `0.1M Fe^(3+)` and `0.01 M Fe^(2+)` was titrated with a concentrated solution of `NaOH` at `30^(@)C` , so that changes in volumes were negligible. Assuming that the new species formed during titration are `Fe(OH)_(3)` and `Fe(OH)_(2)` only.
Given `E^(c-)._(Fe^(3+)|Fe^(2+))=0.80V, `
`K_(spFe(OH)_(3))=10^(-37), ` and `K_(sp Fe(OH)_(2))=10^(-19)`
The redox potential of `Fe^(3+)|Fe^(2+)` electrode at `pH=6` is
(a)`0.8V`
(b)`0.5V`
(c)`0.2V`
(d)`0.1V`

Options

A. `0.8V`
B. `0.5V`
C. `0.2V`
D. `0.1V`

Answer

c

Explanation

`Fe^(3+)+e^(-) rarr Fe^(2+)" "E^(c-)=0.80V`
When `Fe(OH)_(3)` precipitates , `K_(sp)=[Fe^(3+)[overset(c-)(O)H]^(3)`
`:. [Fe^(3+)]=(K_(sp))/([overset(c-)(O)H]^(3))=(10^(-37))/([overset(c-)(O)H]^(3))`
When `Fe(OH)_(2)` precipitates , `K_(sp)=[Fe^(3+)[overset(c-)(O)H]^(2)`
`:. [Fe^(2+)]=(K_(sp))/([overset(c-)(O)H]^(2))=(10^(-19))/([overset(c-)(O)H]^(2))`
At `pH=6`
`E(cell)=E^(c-)._(cell)-(0.06)/(1) log .([Fe^(2+)])/([Fe^(3+)])`
`=0.80-0.06log .(K_(sp)of Fe(OH)_(2)//[overset(c-)(O)H]^(2))/(K_(sp)of Fe(OH)_(3)//[overset(c-)(O)H]^(3))`
`=0.08-0.06log .(10^(-19)//(10^(-8))^(2))/(10^(-37)//(10^(-8))^(3))`
`=0.80-0.06log .(10^(-19)xx10^(-24))/(10^(-37)xx10^(-16))`
`=0.80-0.06log 10^(10)`
`=0.80-0.06xx10=0.2V`