Breathalyzer is used to detect the alcohol content in the suspected drunk drivers. The ethanol in the exhaled breath is oxidized to ethanoic acid with an acidic solution of `K_(2)Cr_(2)O_(7)` as follows `:`
`underset(Ehanol)(3CH_(3)CH_(2)OH(aq))+2Cr_(2)O_(7)^(2-)(aq) +16H^(o+)(aq) rarr underset(Ethanoic ac i d)(3CH_(3)COH(aq))+4Cr^(3+)(aq)+11H_(2)O(l)`
The breathalyzer measures the colour change and produces a metre reading calibrated in the terms of blood alcohol content.
The `EMF` of the reaction when the concentration of all the species are `1.0M` and `pH` is `4.0` is

Options

A. `1.64`
B. `0.31`
C. `-1.01V`
D. `0.95V`

Answer

d

Explanation

`pH=4.0implies[H^(o+)]=10^(-4)M`.
`28H^(o+)+2Cr_(2)O_(7)^(2-)+12e^(-) rarr underset((Reduction at cathode))( 4Cr^(3+)+14H_(2)O)`
`:. n_(cell)=12` `[Take2.303(RT)/(F)=0.06]`
`E=E^(c-)._(cell)-(0.06)/(12)log .([CH_(3)COOH]^(3)[Cr^(3+)]^(4)[H_(2)O]^(11))/([CH_(3)CH_(2)OH]^(3)[Cr_(2)O_(7)^(2-)]^(2)[H^(o+)]^(16))`
`=1.27V-(1)/(200)log.((1)^(3)(1)^(4)(1)^(11))/((1)^(3)(1)^(2)(10^(-4))^(16))`
`=1.27V-(1)/(200)log[10^(64)]`
`=1.27-(1)/(200)xx64=1.27-0.32=0.95V`