# Question #76612

##### 1 Answer

Here's what I got.

#### Explanation:

The **dilution factor** is simply a measure of how concentrated the stock solution was compared with the diluted solution.

You can express the dilution factor as a ratio of concentrations **and** as a ratio of volumes

#"DF" = c_"stock"/c_"diluted" = V_"diluted"/V_"stock"#

As you can see, the dilution factor is equal to the ratio between the volume of the **diluted solution** and the volume of the **stock solution**.

In your case, the stock solution has a volume of **add** the volume of diluent, which is the substance you're using to dilute the stock solution with.

#V_"diluted" = V_"stock" + V_"diluent"#

You will have

#V_"diluted" = "99.99 mL" + "0.1 mL" = "100.09 mL"#

Therefore, the dilution factor will be

#"DF" = (100.09 color(red)(cancel(color(black)("mL"))))/(99.99color(red)(cancel(color(black)("mL")))) = 1.001#

However, you only have one significant figure for the volume of the diluent, so you must say that

#color(darkgreen)(ul(color(black)("DF" = 1)))#

However, if the volume of the stock solution is

#"DF" = (100.09 color(red)(cancel(color(black)("mL"))))/(0.1color(red)(cancel(color(black)("mL")))) = 10,009#

Rounded to one significant figure, you will have

#"DF" = 10,000#