If a person has a BAC (blood alcohol concentration) of 0.08% v/v, would it be considered higher than the legal limit if the legal limit was 0.08 g/dL? (The density of ethanol is 0.789g/ mL)

To determine whether the BAC is higher than the legal limit, we need to convert the BAC from one unit to the other so that we can make a valid comparison.

First, let's convert the BAC from the given unit of 0.08% v/v to a common unit for comparison. BAC is usually expressed in grams per deciliter (g/dL), so we need to convert the percentage to grams.

The BAC is given as a percentage by volume (v/v), which means that it represents the grams of ethanol in 100 mL of blood. To convert it to grams per deciliter (g/dL), we need to consider the density of ethanol.

Given:
BAC = 0.08% v/v
Density of ethanol = 0.789 g/mL

First, we need to convert the percentage to a decimal:

0.08% = 0.08/100 = 0.0008

Next, we need to find the volume of blood represented by the given BAC. To do this, we divide the BAC by the density:

Volume of blood in mL = BAC / density
Volume of blood in mL = 0.0008 / 0.789
Volume of blood in mL ≈ 0.001013 mL

Now, we convert the blood volume from mL to dL (since the legal limit is given in g/dL):

Volume of blood in dL = Volume of blood in mL / 100
Volume of blood in dL = 0.001013 mL / 100
Volume of blood in dL ≈ 0.00001013 dL

Finally, to compare the BAC to the legal limit, we need to convert the blood volume in deciliters to grams:

BAC in g/dL = Volume of blood in dL * density
BAC in g/dL = 0.00001013 dL * 0.789 g/mL
BAC in g/dL ≈ 0.00000799 g/dL

The BAC of 0.08% v/v is equivalent to approximately 0.00000799 g/dL.

Comparing this value to the legal limit of 0.08 g/dL, we can conclude that the BAC of 0.08% v/v is significantly lower than the legal limit of 0.08 g/dL.