Question

Question #689e9

Answer 1

The dilution factor is equal to `8`.

Explanation:

The dilution factor is simply the ratio between the final volume and the initial volume of the solution.

`color(blue)("DF" = V_"final"/V_"initial")`

You start with 3 mL of stock solution, which you mix with 3 mL of water in tube `A`. For this dilution you get

`V_"final" = "3 mL" + "3 mL" = "6 mL"`

The dilution factor will be

`DF_1 = V_"final"/V_"initial" = (6color(red)(cancel(color(black)("mL"))))/(3color(red)(cancel(color(black)("mL")))) = 2`

Now you take a 3-mL sample from the solution in tube `A`, and mix it with 3 mL of water in tube `B`.

The final volume will once again be `"6 mL"`, which means that you get the same dilution factor for this second dilution

`DF_2 = V_"final"/V_"initial" = (6color(red)(cancel(color(black)("mL"))))/(3color(red)(cancel(color(black)("mL")))) = 2`

Finally, you do the same thing for tube `C`. After you take a 3-mL sample from tube `B` and mix it with 3 mL of water in tube `C`, you will get the same dilution factor again

`DF_3 = V_"final"/V_"initial" = (6color(red)(cancel(color(black)("mL"))))/(3color(red)(cancel(color(black)("mL")))) = 2`

This means that you've essentially performed a serial dilution, for which multiple dilution steps have thesame dilution factor.

To get the overall dilution factor, you multiply the dilution factors you have for each successive step

`DF_"total" = DF_1 xx DF_2 xx DF_3`

`DF_"total" = 2 xx 2 xx 2 = color(green)(8)`

This means that you've performed a `1:8` dilution of the original stock solution.