# Question #689e9

##### 1 Answer

The dilution factor is equal to

#### Explanation:

The dilution factor is simply the ratio between the **final volume** and the **initial volume** of the solution.

#color(blue)("DF" = V_"final"/V_"initial")#

You start with **3 mL** of stock solution, which you mix with **3 mL** of water in tube

#V_"final" = "3 mL" + "3 mL" = "6 mL"#

The dilution factor will be

#DF_1 = V_"final"/V_"initial" = (6color(red)(cancel(color(black)("mL"))))/(3color(red)(cancel(color(black)("mL")))) = 2#

Now you take a **3-mL** sample from the solution in tube **3 mL** of water in tube

The final volume will once again be

#DF_2 = V_"final"/V_"initial" = (6color(red)(cancel(color(black)("mL"))))/(3color(red)(cancel(color(black)("mL")))) = 2#

Finally, you do the same thing for tube **3-mL** sample from tube **3 mL** of water in tube

#DF_3 = V_"final"/V_"initial" = (6color(red)(cancel(color(black)("mL"))))/(3color(red)(cancel(color(black)("mL")))) = 2#

This means that you've essentially performed a serial dilution, for which multiple dilution steps have the*same dilution factor*.

To get the **overall dilution factor**, you multiply the dilution factors you have for each successive step

#DF_"total" = DF_1 xx DF_2 xx DF_3#

#DF_"total" = 2 xx 2 xx 2 = color(green)(8)#

This means that you've performed a