Question

Question #ff032

Answer 1

`"0.000625 M"`

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 `n` dilutions, you have

`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 the diluted solution and the volume of the concentrated solution
• the concentration of the concentrated solution and the concentration of the diluted solution

Mathematically, this is written as

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

In your case, you're working with a `"5.00-mL"` aliquot that is being diluted to a total volume of `"100.00 mL"`. You will have

`{(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 `3` 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 three sig 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 `color(blue)(20)`, we get that the concentrated solution was `color(blue)(20)` times as concentrated as the diluted solution.

After `3` such dilutions, we got to a point where the concentration of the initial solution, i.e. the concentrated sample, was `color(blue)(8000)` times as concentrated as the final diluted solution.