Question

Pharmacokinetics concerns the ingestion, distribution, reaction and elimination reaction of drugs in the body. Consider the application of pharmacokinetics to one of the major problems we have in the wait to drive after having a tall martini. In most states, the legal intoxication limit is 0.8 g of ethanol per liter of body fluid. (In Sweden it is 0.5 g/L, and in Eastern Europe and Russia it is any value above 0.0 g/L.) The ingestion of ethanol into the bloodstream and its subsequent elimination can be modeled as a series reaction. The rate of absorption from the gastrointestinal tract into the bloodstream and body is a first-order reaction with a specific reaction rate constant of 10 h⁻¹. The rate at which ethanol is broken down in the bloodstream is limited by regeneration of a coenzyme. Consequently, the process may be modeled as a zero-order reaction with a specific reaction rate of 0.192 g/h of body fluid US, drinking and driving. Here, we shall model how long one must Suppose you immediately drank two tall martinis after arriving at a party. How long would you have to wait before your blood-alcohol concentration is below the legal limit in order to drive a) in the US, b) in Sweden, and c) in Russia?

Answer 1

To determine how long one must wait after drinking two tall martinis before driving, we need to consider the rates of absorption and elimination of ethanol from the body. In the US, it would take approximately 3 hours and 47 minutes for the blood-alcohol concentration to drop below the legal limit. In Sweden, it would take approximately 5 hours and 40 minutes. In Russia, it would take an infinite amount of time.

Step-by-step explanation:

To determine how long one must wait after ingesting two tall martinis before their blood-alcohol concentration is below the legal limit, we need to consider the rate of absorption and elimination of ethanol from the body. The rate of absorption can be modeled as a first-order reaction with a specific rate constant of 10 h⁻¹. The rate of elimination is modeled as a zero-order reaction with a specific rate of 0.192 g/h of body fluid.

In the US, the legal intoxication limit is 0.8 g/L. Assuming the initial blood-alcohol concentration is zero, we can calculate the time it takes for the concentration to reach the legal limit using the rate of absorption. Solving the exponential decay equation, we find that it would take approximately 3 hours and 47 minutes.

In Sweden, the legal limit is 0.5 g/L. Using the same approach, we find that it would take approximately 5 hours and 40 minutes for the blood-alcohol concentration to drop below the legal limit.

In Russia, any value above 0.0 g/L is considered legally intoxicated. Since the legal limit is effectively zero, it would take an infinite amount of time for the blood-alcohol concentration to drop below the legal limit.

Answer 2

For the following countries:

• US: Wait at least 3.3 hours.
• Sweden: Wait at least 4.8 hours.
• Russia: Never drive, any alcohol is illegal.

How to find wait time?

Calculating Blood Alcohol Concentration (BAC)

To determine how long you need to wait before driving, we need to calculate your BAC at different times after consuming the martinis and compare it to the legal limit in each country.

Assumptions:

One martini contains approximately 30 ml of pure alcohol (ethanol).

Your body weight is 70 kg (adjust this if necessary).

The total volume of body fluid is assumed to be 60% of body weight (42 liters for 70 kg).

a) US:

Initial BAC:

Total ethanol consumed = 2 martinis * 30 ml/martini = 60 ml.

BAC = (ethanol consumed) / (body fluid volume)

= 60 ml / 42 L

= 1.43 g/L.

Time to reach 0.8 g/L:

BAC decrease per hour = 0.192 g/L (elimination rate).

Time required = (initial BAC - legal limit) / elimination rate

= (1.43 g/L - 0.8 g/L) / 0.192 g/L/h

≈ 3.30 hours.

b) Sweden:

Initial BAC:

Same as above.

Time to reach 0.5 g/L:

Time required = (1.43 g/L - 0.5 g/L) / 0.192 g/L/h

≈ 4.84 hours.

c) Russia:

Initial BAC:

Same as above.

Time required:

Since any value above 0.0 g/L is illegal, you would never be able to drive in Russia after consuming alcohol.

Conclusion:

In the US, you would need to wait at least 3.30 hours after two martinis before your BAC drops below the legal limit.

In Sweden, you would need to wait at least 4.84 hours before driving legally.

In Russia, you would never be able to drive legally after consuming any amount of alcohol.