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For Cr_2O_7^(2-) + 14 H^(+) + 6e^(-) to 2Cr^(+3) + 7H_2O, E^(@) = 1.33 V " At" [ Cr_2O_7^(2-)]=4.5 millimoles , [Cr^(+3)]=15 millimole , E is 1.067V. The pH of the solution is nearly equal to

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Solution :For the GIVEN reaction,
`Cr_(2)O_(7)^(2-)+14H^(+)+6e^(-) rarr 2Cr^(3+)+7H_(2)O`
`E=E^(@)-(2.303RT)/(nF)log. ("[Products]")/("[Reactants]")`
`1.067=1.33-(0.0591)/(6)log. ([Cr^(3+)]^(2)[H_(2)O]^(7))/([Cr_(2)O_(7)^(2-)][H^(+)]^(14))`
`1.067=1.33-9.85xx10^(-3)log. ([15xx10^(-3)]^(2)[1]^(7))/([4.5xx10^(-3)][H^(+)]^(14))`
`(-0.263)/(-9.85xx10^(-3))=2 log[15xx10^(-3)]-log[4.5xx10^(-3)]-14log[H^(+)]`
`26.7=2xx-1.82+2.34+14`pH
`26.7= - 3.64+ 2.34+14 ` pH
`14pH=26.7+3.64-2.34`
`pH=(28)/(14)=2`


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