QuestionHow many 100 g drinks of a liquid with 120 g ethylene glycol in 550 g total would an 80 kg victim need for toxicity?

Studdy Solution

STEP 1

Assumptions1. The total weight of the liquid in the container is550g. The weight of ethylene glycol in the liquid is120g3. Each drink contains100g of the liquid4. The weight of the victim is80kg5. The toxic level of ethylene glycol is reached when the victim consumes1.5g of ethylene glycol per kg of body weight

STEP 2

First, we need to find the concentration of ethylene glycol in the liquid. We can do this by dividing the weight of ethylene glycol by the total weight of the liquid.
$Concentration = \frac{Weight\, of\, ethylene\, glycol}{Total\, weight\, of\, liquid}$

STEP 3

Now, plug in the given values for the weight of ethylene glycol and the total weight of the liquid to calculate the concentration.
$Concentration = \frac{120g}{550g}$

STEP 4

Calculate the concentration of ethylene glycol in the liquid.
$Concentration = \frac{120g}{550g} =0.2181818$

STEP 5

Now that we have the concentration of ethylene glycol in the liquid, we can find out how much ethylene glycol is in each drink. We can do this by multiplying the concentration by the weight of the liquid in each drink.
$Ethylene\, glycol\, per\, drink = Concentration \\times Weight\, of\, liquid\, per\, drink$

STEP 6

Plug in the values for the concentration and the weight of the liquid per drink to calculate the amount of ethylene glycol per drink.
$Ethylene\, glycol\, per\, drink =0.2181818 \\times100g$

STEP 7

Calculate the amount of ethylene glycol in each drink.
$Ethylene\, glycol\, per\, drink =0.218181 \\times100g =21.81818g$

STEP 8

Now that we have the amount of ethylene glycol in each drink, we can find out how many drinks the victim needs to consume to reach the toxic level. We can do this by dividing the toxic level of ethylene glycol (1.5g per kg of body weight) by the amount of ethylene glycol in each drink.
$Number\, of\, drinks = \frac{Toxic\, level}{Ethylene\, glycol\, per\, drink}$

STEP 9

Plug in the values for the toxic level (.5g per kg of body weight) and the amount of ethylene glycol per drink to calculate the number of drinks.
$Number\, of\, drinks = \frac{.5g/kg \\times80kg}{21.81818g}$

STEP 10

Calculate the number of drinks the victim needs to consume to reach the toxic level.
$Number\, of\, drinks = \frac{.5g/kg \\times80kg}{21.81818g} =5.5$ Since the number of drinks must be an integer, the victim would need to consume6 drinks to reach the toxic level of ethylene glycol.

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