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"#