Question #07a44

The problem tells you that the correct dosage is

`"15 mg drug " -> " 1 kg"`

and that the patient has a mass of `"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 `"200 mg"` of drug for every `"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 color(red)(cancel(color(black)("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 `"200 mg"` of drug dissolved in `"5 cm"^3` of solution, then you can't really administer the `"300 g"` of drug needed by the patient because you are `"100 mg"` of drug short.

This is why I assumed that the solution contains `"200 mg"` of drug for every `"5 cm"^3` of solution.