# Question #ff032

##### 1 Answer

#### Answer:

#### Explanation:

The thing to remember about **serial dilutions** is that the **total dilution factor** is the product of the individual dilution factors that you use for each dilution.

For a serial dilution that consists of

#color(blue)(ul(color(black)("DF"_ "total" = "DF"_ 1 xx "DF"_ 2 xx ... xx "DF"_ n)))#

Now, the **dilution factor** is simply the **ratio** that exists between

the volume of thediluted solutionand the volume of the concentrated solutionthe concentration of theconcentrated solutionand the concentration of thediluted solution

Mathematically, this is written as

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

In your case, you're working with a **total volume** of

#{(V_"diluted" = "100.00 mL"), (V_"concentrated" = "5.00 mL") :}#

This means that the dilution factor for **one dilution** will be

#"DF"_ 1 = (100.00 color(red)(cancel(color(black)("mL"))))/(5.00color(red)(cancel(color(black)("mL")))) = color(blue)(20)#

You can thus say that the concentration of the solution **after the first dilution** will be equal to

#c_"diluted 1" = c_"concentrated 1"/"DF"_ 1 #

#c_"diluted 1" = "5.00 M"/color(blue)(20) = "0.25 M"#

Now, you're doing **identical dilutions**, so you can sue the first equation to calculate the total dilution factor for this serial dilution

#"DF"_ "total" = "DF"_ 1 xx "DF"_ 1 xx "DF"_ 1#

#"DF"_ "total" = color(blue)(20) xx color(blue)(20) xx color(blue)(20) = color(blue)(8000)#

You can thus say that the concentration of the diluted solution **after the third and final dilution** will be

#c_"diluted 3" = c_"concentrated 1"/"DF"_ "total"#

#c_"diluted 3" = "5.00 M"/color(blue)(8000) = "0.000625 M" -># rounded to threesig figs

As you can see, the dilution factor for an individual dilution tells how **concentrated** the concentrated solution was compared with the diluted solution.

For a dilution factor of **times as concentrated** as the diluted solution.

After **times as concentrated** as the final diluted solution.