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

Options

A. 2
B. 3
C. 5
D. 4

Answer

A

Explanation

`E = E^(@) - (0.0591)/(n) "log" ([Cr^(3+)]^(2))/([Cr_(2) O_(7)^(2-)] [H^(+)]^(14))`
`1.067 = 1.33 - (0.0591)/(6) "log" ((15 xx 10^(-3))^(2))/((4.5 xx 10^(-3))[H^(+)]^(14))`
`1.067 = 1.33 - 0.0098 log (50 xx 10^(-3))/([H^(+)]^(14))`
`0.0098 log (50 xx 10^(-3))/([H^(+)]^(14)) = 1.33 - 1.067 = 0.263 V`
log `(50 xx 10^(-3))/([H^(+)]^(14)) = (0.263)/(0.0098) = 26.83`
log `(50 xx 10^(-3)) - log [H^(+)]^(14) = 26.83`
`-1.3 - 14 log [H^(+)] = 26.83`
`-14 log [H^(+)] = 26.83 + 1.3 = 28.13`
or `- log [H^(+)] = (28.13)/(14) = 2.01`
`therefore pH = 2`