Question #708f5

1 Answer
Jan 17, 2017

Answer:

Here's what I got.

Explanation:

You know that you are starting with a #0.4%# solution, presumably a mass by volume percent concentration, that you dilute by a factor of #10#.

Before the dilution, the initial solution contained #"0.4 g"# of solute, which is your drug, for every #"100 cm"^3# of solution.

When you dilute this solution by a factor of #10#, you ensure that the same amount of solution, let's say #"100 cm"^3#, contains #10# times less solute than the original solution. In other words, the starting solution must be #10# times more concentrated than the diluted solution.

This means that after the dilution, the solution will contain

#"0.4 g"/10 = "0.04 g"#

of drug for every #"100 cm"^3# of solution. To make the calculations easier, convert this to milligrams of drug

#0.04 color(red)(cancel(color(black)("g"))) * (10^3"mg")/(1color(red)(cancel(color(black)("g")))) = "40 mg"#

Therefore, you can say that for the diluted solution, you have

#"40 mg drug " -> " 100 cm"^3 color(white)(.)"solution" " "color(orange)("(*)")#

Now, the patient received #"120 mg"# of this drug in #3# doses, meaning that you have

#"120 mg drug"/"3 doses" = "40 mg drug / dose"#

You can thus say that the patient received #"40 mg"# of drug per dose and that each dose had a volume of #"100 cm"^3#, as shown by relation #color(orange)("(*)")#.