# Question 76612

Jan 17, 2017

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

$\text{DF" = c_"stock"/c_"diluted" = V_"diluted"/V_"stock}$

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 $\text{99.99 mL}$. To find the volume of the diluted solution, you add the volume of diluent, which is the substance you're using to dilute the stock solution with.

${V}_{\text{diluted" = V_"stock" + V_"diluent}}$

You will have

${V}_{\text{diluted" = "99.99 mL" + "0.1 mL" = "100.09 mL}}$

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

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{DF} = 1}}}$

However, if the volume of the stock solution is $\text{0.1 mL}$ and the volume of the diluent is $\text{99.99 mL}$, the dilution factor 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

$\text{DF} = 10 , 000$