# Question 07a44

Jan 18, 2017

Here's what I got.

#### Explanation:

The problem tells you that the correct dosage is

$\text{15 mg drug " -> " 1 kg}$

and that the patient has a mass of $\text{20 kg}$, so the first thing to do here is to calculate the total mass of drug that must be administered to the patient.

To do that, use the correct dosage as a conversion factor to take you from the mass of the patient to the mass of the drug

20 color(red)(cancel(color(black)("kg"))) * overbrace("15 mg drug"/(1color(red)(cancel(color(black)("kg")))))^(color(blue)("given by the problem")) = "300 mg drug"#

Now, assuming that your solution contains $\text{200 mg}$ of drug for every ${\text{5 cm}}^{3}$ of solution, you can use the given composition of the solution as conversion factor to take you from the mass of drug to the volume of the solution

$300 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{mg drug"))) * ("5 cm"^2color(white)(.)"solution")/(200color(red)(cancel(color(black)("mg drug")))) = color(darkgreen)(ul(color(black)("7.5 cm"^2color(white)(.)"solution}}}}$

I'll leave the answer rounded to two sig figs, but keep in mind that you only have one significant figure for your data.

SIDE NOTE If you only have $\text{200 mg}$ of drug dissolved in ${\text{5 cm}}^{3}$ of solution, then you can't really administer the $\text{300 g}$ of drug needed by the patient because you are $\text{100 mg}$ of drug short.

This is why I assumed that the solution contains $\text{200 mg}$ of drug for every ${\text{5 cm}}^{3}$ of solution.