Question

Let the ED50 of a recreational drug be defined as the amount required for 50% of a test group to feel high or get a buzz. If the ED50 value of ethanol is 470 mg/kg body mass, what dose would a 70 kg party goer need to quickly consume in order to have a 50% chance of getting a buzz?If a bottle of beer contains about 13.9 g of ethanol, how many bottles of beer would a 70 kg party goer need to consume in order to have a 50% chance of getting a buzz?
If the lethal dose (LD50) for ethanol is 4,700 mg/kg, how many bottles of beer would a 70 kg party goer need to chug in order to have a 50% chance of dying?

A one liter bottle of Jack Daniels contains about 356 g of ethanol. How many 1.0 liter bottles of this whiskey would a 70 kg party goer need to chug in order to have a 50% chance of dying?

Answer 1

Explanation:

1) The ED50 value of ethanol = 470 mg per kg of person body = 470 mg/kg

Mass of person = 70 kg

Amount of ethanol required by person of 70 kg to get buzz:

$70 kg\times 470 mg/kg=32,900 mg$

A 70 kg party goer need to quickly consume in order to have a 50% chance of getting a buzz is 32,900 mg of ethanol.

Mass of ethanol in beer bottle = 13.9 g

Amount of ethanol required by person of 70 kg to get buzz:

$70 kg\times 470 mg/kg=32,900 mg =32.9 g$

1 mg = 0.001 mg

Bottles of beer would a 70 kg party goer need to consume:

$=\frac{32.9 g}{13.9 g}=2.367\approx 2$

Bottles of beer would a 70 kg party goer need to consume a 50% chance of getting a buzz is 2.

2)The LD50 value of ethanol = 4,700 mg per kg of person body = 4,700 mg/kg

Mass of person = 70 kg

Amount of ethanol required by person of 70 kg  to have a 50% chance of dying:

$70 kg\times 4,700 mg/kg=329,000 mg$

A 70 kg party goer need to quickly consume in order to have a 50% chance of dying is 329,000 mg of ethanol.

Mass of ethanol in Jack Daniels bottle = 356 g

Amount of ethanol required by person of 70 kg  to have a 50% chance of dying:

$70 kg\times 4,700 mg/kg=329.000 mg =329 g$

1 mg = 0.001 mg

Bottles of Jack Daniels would a 70 kg party goer need to consume to have a 50% chance of dying:

$=\frac{329 g}{356 g}=0.923\approx 1$

Bottles of  Jack Daniels would a 70 kg party goer need to consume to have a 50% chance of dying is 1.