# Question 07012

Sep 11, 2016

$\text{303 cans}$

#### Explanation:

What you need to do here is to convert the caffeine concentration from milligrams per ounce, $\text{mg/oz}$, to grams per oz, $\text{g/oz}$.

This will then allow you to find the number of cans that must be consumed in order to get that lethal dose.

So, you know that you have

$\textcolor{p u r p \le}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 g" = 10^3"mg}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

This means that the concentration of a single can of soda is equivalent to

2.75 color(red)(cancel(color(black)("mg")))/"oz" * "1 g"/(10^3color(red)(cancel(color(black)("mg")))) = 2.75 * 10^(-3)"g/oz"

Next, use the known lethal dose to figure out how many ounces of soda would be needed

10.0 color(red)(cancel(color(black)("g"))) * "1 oz"/(2.75 * 10^(-3)color(red)(cancel(color(black)("g")))) = 3.636 * 10^3"oz"

Finally, use the fact that one can has a volume of $\text{12 oz}$ to determine the number of cans that would be needed

3.636 * 10^3 color(red)(cancel(color(black)("oz"))) * "1 can"/(12color(red)(cancel(color(black)("oz")))) = color(green)(bar(ul(|color(white)(a/a)color(black)("303 cans")color(white)(a/a)|)))#

I'll leave the answer rounded to three sig figs, but keep in mind that you only have two sig figs for the volume of a single can.

In this regard, the correct answer would be $3.0 \cdot {10}^{2}$ cans.