Question

Question #23bd9

Answer 1

`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)|)))`