How do you write conversion factors that correspond to the following concentration: 0.15% (v/v) acetic acid?

A `0.15%"v/v"` concentration means that the given solution contains `"0.15 mL"` of solute for every `"100 mL"` of solution.

In this case, your solution will contain `"0.15 ML"` of acetic acid in every `"199 mL"` of solution. You can thus say that the volume by volume percent concentration can be written as

`0.15%"v/v" = "0.15 mL acetic acid"/"100 mL solution"`

To use this as a conversion factor, rearrange keeping in mind that

• what is given by the probme goes on the bottom, i.e. as the denomiantor
• what must be calcualted goes on top, i.e. as the numerator

So, let's say that you want to find the amount of solute present in `"250 mL"` of acetic acid solution. The conversion factor will be

`"0.15 mL acetic acid"/"100 mL solution" color(white)(color(black)(larr)/color(black)(larr)) "what is needed goes on top"/"what is given goes on the bottom"`

You will have

`250 color(red)(cancel(color(black)("mL solution"))) * "0.15 mL acetic acid"/(100color(red)(cancel(color(black)("mL solution")))) = "0.38 mL acetic acid"`

Now let's say that you want to figure out what volume of solution will contain `"0.035 mL"` of acetic acid. The conversion factor will be

`"100 mL solution"/"0.15 mL acetic acid" color(white)(color(black)(larr)/color(black)(larr)) "what is needed goes on top"/"what is given goes on the bottom"`

You will have

`0.035 color(red)(cancel(color(black)("mL acetic acid"))) * "100 mL solution"/(0.15 color(red)(cancel(color(black)("mL acetic acid")))) = "23 mL solution"`