Question #ff032

1 Answer
Jan 12, 2017

Answer:

#"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.