[dumakey1212]

An individual’s blood alcohol content (% alcohol in blood as measured mass per
volume = mass of alcohol per volume of blood) was 0.15. If we assume the individual
drank all of the alcohol at once (i.e. no metabolism of alcohol by the body), the total
volume of blood for the individual was 1.5 gallons, and the individual was drinking
Maker’s Mark (130 proof), what volume of Maker’s Mark was consumed?

I would assume you'd just multiply 0.15 by 1.5 gallons to determine what percent of her blood is alcohol. Then I'd imagine you'd divide this new number (0.225 gallons) by 0.65 (percent alcohol by volume of Maker's Mark) to determine the total amount of Maker's Mark originally consumed. Is this wrong?

[Borek]

0.15% is 0.0015.

[billnotgatez]

http://en.wikipedia.org/wiki/Blood_alcohol_content

[dumakey1212]

Alright, change 0.225 to 0.0025. Is this right now?

[Borek]

Logic looks right.

[DrCMS]

No I'm not sure the logic is not right.  The BAC is m/v% while the proof of a drink is I think v/v%.

[Borek]

I decided to silently ignore the problem - as it would require checking the densities and what is really meant by proof (from what I know it is country dependent).

[dumakey1212]

No I'm not sure the logic is not right.  The BAC is m/v% while the proof of a drink is I think v/v%.

How do I convert from m/v% to v/v%?

[billnotgatez]

@dumakey1212
The WIKI I linked previously discusses formulas
http://en.wikipedia.org/wiki/Blood_alcohol_content
But I am not sure when they are doing m/v or v/v in some of the tables
and the the tables talk about 80 proof

Additionally WIKI says

The average adult has a blood volume of roughly 5 liters (1.3 gal)

http://en.wikipedia.org/wiki/Blood

When I GOOGLED the question

how to convert m/v to v/v for ethano

l
one of the links was this
http://au.answers.yahoo.com/question/index?qid=20110320020539AAu6Zfa

@everyone else
I can see the confusion
even here in the forum there are post that state
~m/v if commonly used except with alcohol which is v/v
percent is so confusing

[Archer]

I have probably come to this discussion far too late for the person who has posted the original question and for that I apologise, but I thought I would post this so anyone searching for this in the future may find it helpful.

Firstly you need to convert all of your data to metric, considering that a gallon is different in different parts of the world this is essential.

The formula used is the Widmark equation:

a =cpr

where
a = mass of alchol drunk (g)
c = blood alcohol level (g/L)
p = weight of the drinker (kg)
r = widmark factor (L/kg)

(note that the units balance on either side of the equation)

The Widmark factor (r) 0.68 L/kg for men and 0.55 L/kg  for women as women tend to have slightly higher % body fat than men.

There are alternative factors (r) which use BMI for a more accurate volume of distribution (See Forrest equation or Watson equation) what you should use it what you have been taught.

As you know the % w/v then you can calculate this as g/L

Once you have calculated the weight of the alcohol consumed you must convert it to the volume of alcohol by dividing by the density of ethanol (0.789 g/ml).

Once you have this value you have to divide it by the concentration of ethanol in the drink (% by volume) and multiply by 100 to provide the volume drunk.

I hope this helps and again I am sorry that you probably needed this for an assignment two months ago.