For `Cr_(2)O_(7)^(2)+14 H^(+)+6e^(-)rarr2Cr^(3+)+7H_(2)O`
`E^(@)=1.33 V.At 298 k, [Cr_(2)O_(7)^(2-)] =4.5` millimole
`[Cr^(3+)]=15` millimole ,E is 1.067 v The pH of the solution is nearly eual to

Explanation

For the given reaction,
`Cr_(2)O_(7)^(2-)+14H^(+)+6e^(-)to2Cr^(3+)+7H_(2)O`
`E=E^(@)=-(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))=2log(15xx10^(-3))-log(4.5xx10^(-3))-14log(H^(+))`
`26.7=2(-1.82)+2.34+14pH` or `pH=(28)/(14)=2`.