Question

Question

Background information:

- The molecular weight of ethanol (C2H5OH) is 46.1 and the density of absolute (100%) ethanol = 0.79 g/mL.

- Assume that a 80 kg person contains 48 L of ‘water’. Ignore the metabolism, and assume the water content of the person remains constant.

- The legal limit for a driver’s blood alcohol in Australia is 50 mg of ethanol per 100 mL of blood (referred to as a blood alcohol content (BAC) of 0.05%).

a.) During a romantic candlelight dinner a 80 kg person drinks a bottle (750 mL) of D’Arenberg The Old Bloke & Three Young Blondes in the space of 3 hours. Ethanol is metabolised at a constant rate of 120 mg per hour per kg body weight, regardless of its concentration.

i. What is their blood alcohol content (mg/100 mL blood) at the end of the dinner?

ii. How long will it take for their blood alcohol level to fall below the legal limit (0.05%)?

Postscript: Fortunately, their partner was the designated driver. He/she enjoyed the meal, but only drank water, and drove the couple home safely, soundly and legally.

Answer 1

i) volume of alcohol intake by the person=750ml

Alcohol content in red wine in excess=14.5% (by volume)

density of 100% alcohol=0.79g/ml

So, the density of 14.5% alcohol(in red wine)=(0.79/100)*14.5=0.11g/ml

Amount of alcohol intake by the person=750ml*density of alcohol=750 ml*0.11g/ml*(1000mg/g)=82500 mg

rate of metabolism of alcohol=120mg/kg.h

Amount of alcohol metabolized=rate*body weight*time=(120mg/kg.h)*80kg*3h=28800mg

remaining alcohol in blood=82500 mg-28800mg=53700mg

So, blood alcohol content=amount of alcohol in the blood/body fluid volume=53700mg/48L=1118.75mg/L

blood alcohol content (mg/100 mL blood)=(1118.75mg/L)*(10^-3L/ml)*100ml=111.875mg/100ml

2)legal limit of blood alcohol=50mg/100ml=0.05mg/ml

So,the person's legal blood alcohol limit=0.05mg/ml *48L*1000ml/L=2400mg

Amount of alcohol in the person's blood after dinner=53700 mg

Amount that needs to be metabolized further to meet the legal limit=53700mg-2400mg=51300mg

rate of metabolism of alcohol=120mg/kg.h

Rate of metabolism for 80 kg person=120mg/kg.h *80kg=9600mg/h

Thus ,time taken for metabolism of 51300mg alcohol=51300mg/(9600mg/h)=5.3 h

Hence, time required for his blood alcohol level to fall below the legal limit (0.05%)=5.3 hours