Question

Question #31802

Answer 1

Here's how you can do that.

Explanation:

Your first goal here will be to determine how many grams of amoxicillin you need in order to have in your target solution.

A solution's parts per million concentration, ppm, expresses the number of grams of solute present in `10^6` grams of solvent. Simply put, a `"1 ppm"` solution will have `"1 g"` of solute in `10^6"g"` of solvent.

If you take water's density to be equal to `"1.0 g mL"^(-1)`, you can say that the target solution contains

`5 color(red)(cancel(color(black)("mL"))) * "1 g"/(1color(red)(cancel(color(black)("mL")))) = "5 g"`

of water. Notice that because your solution contains a very, very small amount o amoxicillin, you can safely assume that the mass of the solution is equal to the mass of the water.

Now, a `"20 ppm"` amoxicillin solution will contain `"20 g"` of amoxicillin for every `10^6"g"` of water. You can thus say that your sample will contain

`5 color(red)(cancel(color(black)("g water"))) * "20 g amoxicillin"/(10^6color(red)(cancel(color(black)("g water")))) = 1 * 10^(-4)"g amoxicillin"`

At this point, you should focus on determining the volume of amoxicillin solution that contains `1 * 10^(-4)"g"` of solute. Your stock solution is `1%"m/v"` amoxicillin, which basically means that it contains `"1 g"` of solute for every `"100 mL"` of solution.

You can thus say that you need

`1 * 10^(-4) color(red)(cancel(color(black)("g amoxicillin"))) * "100 mL stock"/(1color(red)(cancel(color(black)("g amoxicillin")))) = "0.01 mL stock"`

Therefore, you can prepare your solution by taking `"0.01 mL"` of your `"1% m/v"` amoxicillin stock solution and adding enough water to get the final volume to `"5 mL"`.

This will get you `"5 mL"` of `"20 ppm"` amoxicillin solution.