Question #689e9

1 Answer
Sep 6, 2015

Answer:

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.