# Question #23bd9

##### 1 Answer

#### Explanation:

The **dilution factor** can be calculated by dividing the **final volume** of the diluted solution by the **initial volume** of the aliquot

#color(blue)(|bar(ul(color(white)(a/a)"D.F." = V_"final"/V_"initial"color(white)(a/a)|)))#

Now, notice that you're essentially performing **two dilutions** here, one of the initial

The first aliquot is diluted from

#"D.F"_1 = (100 color(red)(cancel(color(black)("mL"))))/(3color(red)(cancel(color(black)("mL")))) = 33.3#

Next, you take a **Second dilution** will be

#"D.F"_2 = (100 color(red)(cancel(color(black)("mL"))))/(10color(red)(cancel(color(black)("mL")))) = 10#

The **overall dilution factor** for the initial solution will be

#"D.F"_"overall" = "D.F"_1 xx "D.F"_2#

In your case, you will have

#"D.F"_"overall" = 33.3 xx 10 = color(green)(|bar(ul(color(white)(a/a)333color(white)(a/a)|)))#

So, your goal here was to find the dilution factor of the *initial solution*, i.e. of the

One way to think about this is by assuming that instead of diluting a **first dilution**, you dilute the **entire** **by the same dilution factor** you had for your *second dilution*.

So, you diluted

#"D.F" = V_"final"/V_"initial" implies V_"final" = "D.F." xx V_"initial"#

In your case, you will have

#V_"final" = 10 xx "100 mL" = "1000 mL"#

So, if you dilute the **total volume** of

#"D.F"_"overall" = (1000color(red)(cancel(color(black)("mL"))))/(3color(red)(cancel(color(black)("mL")))) = color(green)(|bar(ul(color(white)(a/a)333color(white)(a/a)|)))#