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

Nov 6, 2016

Here's how you can do that.

#### Explanation:

A 0.15%"v/v" concentration means that the given solution contains $\text{0.15 mL}$ of solute for every $\text{100 mL}$ of solution.

In this case, your solution will contain $\text{0.15 ML}$ of acetic acid in every $\text{199 mL}$ 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 $\text{250 mL}$ of acetic acid solution. The conversion factor will be

$\text{0.15 mL acetic acid"/"100 mL solution" color(white)(color(black)(larr)/color(black)(larr)) "what is needed goes on top"/"what is given goes on the bottom}$

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 $\text{0.035 mL}$ of acetic acid. The conversion factor will be

$\text{100 mL solution"/"0.15 mL acetic acid" color(white)(color(black)(larr)/color(black)(larr)) "what is needed goes on top"/"what is given goes on the bottom}$

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"