Question

Question #07012

Answer 1

`"303 cans"`

Explanation:

What you need to do here is to convert the caffeine concentration from milligrams per ounce, `"mg/oz"`, to grams per oz, `"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

`color(purple)(bar(ul(|color(white)(a/a)color(black)("1 g" = 10^3"mg")color(white)(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 `"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 * 10^2` cans.