Question #07a44

1 Answer
Jan 18, 2017

Answer:

Here's what I got.

Explanation:

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.