19.03.2023 - 13:54

# A typical martini glass weighs 5.0 oz (142 g) and the alcohol content is 30% by mass. About 15% of the alcohol in the martini passes directly into the bloodstream (blood volume = 7.0 L in an adult). Consider an adult who drinks two martinis with lunch. Es

Question:

A typical martini glass weighs {eq}\rm 5.0 oz (142 g) {/eq} and the alcohol content is {eq}\rm 30% {/eq} by mass. About {eq}\rm 15% {/eq} of the alcohol in the martini passes directly into the bloodstream (blood volume = {eq}\rm 7.0 L {/eq} in an adult). Consider an adult who drinks two martinis with lunch. Estimate the blood alcohol concentration in this person after two martinis have been consumed. An adult with a blood alcohol concentration of {eq}\rm 3.0 \times 10^{-3} g/mL {/eq} or more is considered in toxicated. Is this person intoxicated?

• April 10, 2023 в 20:15

To estimate the blood alcohol concentration in the person after consuming two martinis, we need to first calculate the amount of alcohol consumed.

Each martini contains 30% alcohol by mass, and the weight of each martini is 142 g, so the amount of alcohol in one martini is:

0.3 x 142 g = 42.6 g

Thus, two martinis contain:

2 x 42.6 g = 85.2 g

Of the 85.2 g of alcohol consumed, only 15% passes directly into the bloodstream. So the amount of alcohol that enters the bloodstream after drinking two martinis is:

0.15 x 85.2 g = 12.78 g

Now, we need to calculate the blood alcohol concentration (BAC) in the person. BAC is usually expressed in terms of the mass of alcohol per unit volume of blood. We know that the adult has a blood volume of 7.0 L, which is equivalent to 7000 mL.

So, the BAC can be calculated as:

BAC = (mass of alcohol in bloodstream) / (blood volume)

BAC = 12.78 g / 7000 mL

BAC = 1.826 x 10^-3 g/mL

This BAC is below the legal limit for driving in most countries, which is typically around 0.05% or 0.08% (0.0005 or 0.0008 g/mL). However, the question asks if the person is intoxicated at a BAC of 3.0 x 10^-3 g/mL or more. Since the calculated BAC is lower than this threshold, the person is not considered intoxicated.

Therefore, drinking two martinis with lunch will not lead to intoxication in an adult with a blood volume of 7.0 L. However, it is important to note that individual tolerance to alcohol can vary and that driving or operating heavy machinery after drinking any amount of alcohol is not recommended.