What is the approximate bac of a 160 pound man who consumes five 12-oz beers in two hours
The Correct Answer and Explanation is:
To determine the approximate Blood Alcohol Concentration (BAC) of a 160-pound man who consumes five 12-ounce beers in two hours, we can use the Widmark Formula for BAC calculation:
[
BAC = \frac{{\text{{Alcohol Consumed in grams}}}}{{\text{{Body Weight in grams}} \times r}} – \text{{Alcohol Elimination per Hour}} \times \text{{Time}}
]
Where:
- Alcohol consumed: Each 12-ounce beer contains approximately 0.6 ounces of pure alcohol. So, five beers will provide:
[
5 \text{{ beers}} \times 0.6 \text{{ ounces of alcohol}} = 3 \text{{ ounces of alcohol}}.
]
Converting ounces to grams (1 ounce = 28.35 grams):
[
3 \text{{ ounces}} \times 28.35 = 85.05 \text{{ grams of alcohol}}.
] - Body weight: A 160-pound man weighs approximately 72.57 kg (since 1 pound = 0.4536 kg).
[
160 \text{{ pounds}} \times 0.4536 = 72.57 \text{{ kg}}.
]
In grams, this is:
[
72.57 \text{{ kg}} \times 1000 = 72,570 \text{{ grams}}.
] - Widmark factor (r): For men, the average value of r is 0.68.
- Time: The drinking occurred over 2 hours, and alcohol is typically eliminated from the body at a rate of about 0.015% per hour.
Step-by-step BAC Calculation:
- Alcohol Consumed:
[
85.05 \text{{ grams of alcohol}}.
] - Body Weight in Grams:
[
72,570 \text{{ grams}}.
] - BAC Calculation (ignoring alcohol elimination initially):
[
BAC = \frac{{85.05}}{{72,570 \times 0.68}} = 0.0017 \text{{ or }} 0.17\%.
] - Alcohol Elimination: Over 2 hours, the person would eliminate about 0.03% of alcohol (0.015% per hour × 2 hours).
- Final BAC:
[
0.17\% – 0.03\% = 0.14\%.
]
Conclusion:
The approximate BAC for this 160-pound man after consuming five 12-ounce beers over two hours is 0.14%. This BAC is above the legal driving limit in many places (0.08%), indicating that the individual would be impaired.