Question

Question #708f5

Answer 1

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)("(*)")`.