Question

Potassium dichromate (K2Cr2O7) is a bright orange salt that can be converted to a blue-violet solution of Cr3+ ions. Under certain conditions, K2Cr2O7 reacts with ethanol (C2H5OH) to produce carbon dioxide gas. The legal definition of intoxication is a blood alcohol (C2H5OH) level of 0.08% by mass or higher. In a given case, 35.48 mL of 0.05182 M K2Cr2O7 was required to titrate a 50.02 g sample of blood. From the tested sample, should the person be arrested for a DUI?

Assume that only the ethanol reacts with the potassium dichromate.

C₂+H₅+OH (l) + K₂Cr₂O₇ (aq) ----> CO₂ (g) + K⁺+ Cr³⁺

Answer 1

The balance eqtaion is

C₂H₅OH (l) + 2K₂Cr₂O₇ (aq)+16H⁺ ----> 2CO₂ (g) + 4K⁺+ 4Cr³⁺ + 11H₂O

Given Molarity of K₂Cr₂O₇ is = 0.05182 M

         Volume of K₂Cr₂O₇ is = 35.48 mL

                                         = 35.48 x10 ^-3 L

Number of moles of K₂Cr₂O₇ is , n = Molarity x volume in L

                                                   = 0.05182 x 35.48 x10 ^-3 mol

                                                   = 1.84x10^-3 mol

Also given mass of blood sample is = 50.02 g

C₂H₅OH (l) + 2K₂Cr₂O₇ (aq)+16H⁺ ----> 2CO₂ (g) + 4K⁺+ 4Cr³⁺ + 11H₂O

According to the balanced equation ,

1 mole of C₂H₅OH reacts with 2 moles of K₂Cr₂O₇

Z mol of C₂H₅OH reacts with 1.84x10^-3 mol moles of K₂Cr₂O₇

of C₂H₅OH

Molar mass of C₂H₅OH = (2x12) + (6x1) + 16 = 46 g/mol

So mass of C₂H₅OH is , mass = number of moles x molar mass

                                             = 9.2x10 ^-4 mol x 46 g/mol

                                             = 0.042 g

Mass persent = [ mass of C₂H₅OH / mass of sample ]x 100

                    = [ 0.042 / 50.02 ] x 100

                    = 0.0845 %

Given The legal definition of intoxication is a blood alcohol (C₂H₅OH) level of 0.08% by mass or higher

Since the mass % we obtained is more than this 0.08%

Therefore we should arrest the person