Question #23bd9

1 Answer
May 8, 2016

Answer:

#333#

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 #"3-mL"# aliquot and one of a #"10-mL"# aliquot.

The first aliquot is diluted from #"3 mL"# to #"100 mL"#, which is equivalent to a dilution factor of

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

Next, you take a #"10-mL"# sample of this diluted solution and dilute it to #"100 mL"#. The dilution factor for the 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 #"3-mL"# aliquot.

One way to think about this is by assuming that instead of diluting a #"10-mL"# sample of the solution that resulted from the first dilution, you dilute the entire #"100 mL"# by the same dilution factor you had for your second dilution.

So, you diluted #"10 mL"# to #"100 mL"#, which is equivalent to a dilution factor of #10#. Using the same dilution factor for the entire #"100 mL"# sample would get you

#"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 #"3-mL"# aliquot to a total volume of #"1000 mL"#, you'll once again get a dilution factor 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)|)))#