Question

In the following process of disproportionation
`2CIO_(3)^(-)hArrCiO_(2)^(-)+CIO_(4)^(-)`
`E_(CIO_(4)^(-)//CIO_(3)^(-))^(@)=+0.36V,E_(CIO_(3)^(-)//CIO_(2)^(-))^(@)=+0.33V`
If initial concentration of chloride ion was 0.1M, calculate the equilibrium concentration of perchlorate ion.

Answer 1

The two reactions of the given reaction will be
`CIO_(3)^(-)(aq)+H_(2)O(l)toCIO_(4)^(-)(aq)+2H^(+)(aq)+2e^(-)`
`underline(" "CI_(3)^(-)(aq)+2H^(+)(aq)+2e^(-)toCIO_(2)^(-)(aq)+H_(2)O(l)" ")`
Adding `2CIO_(3)^(-)(aq)hArrCIO_(2)^(-)(aq)+CIO_(4)(aq)`
`E_(cell)^(@)=0.33-0.36=-0.03V`
`E=E^(@)-(0.059)/(n)logQ`
At equilibrium, `E=0,Q=K_(eq)`. also n=2, hence
`0=-0.03-(0.059)/(2)logK_(eq)`
or `logK_(eq)=-(0.03xx2)/(0.059)=-1=overline(1)` or `K_(eq)=0.1`
`{:(,2CIO_(3)^(-)(aq),hArr,CIO_(3)^(-)(aq),+,CIO_(4)^(-)(aq)),("Initial conc.",0.1M,,0,,0),("At eqm.",0.1-2x,,x,,x):}`
`K=(x xx x)/((0.1-2x)^(2))=0.1` or `(x)/(0.1-2x)=sqrt(0.1)=0.316`
or `x=0.0316-0.632` or `1.632x=0.0316` or `x=0.0194M`