Question #59098

1 Answer
Oct 12, 2015

Answer:

#1/30#

Explanation:

A good approach to have here is to take the dilutions one at a time.

The dilution factors of each dilution step will determine the overall dilution factor of the sample.

So, a dilution factor is simply the ratio between the initial volume of the sample and the final volume of the solution afterthe dilution takes place.

#"D.F." = V_"initial"/V_"final"#

So, you starting sample has a volume of #150mu"L"#. You know that you add this sample to a volume of #300mu""# of saline solution. This will be your first dilution step.

So, what is the final volume for this dilution?

#V_"final 1" = V_"initial 1" + V_"saline 1"#

#V_"final 1" = 150mu"L" + 300mu"L" = 450mu"L"#

The dilution factor for this first step will thus be

#"D.F"_1 = (150color(red)(cancel(color(black)(mu"L"))))/(450color(red)(cancel(color(black)(mu"L")))) = 1/3#

Now you take a #20mu"L# sample of this resulting solution and add it to, presumably, another #180mu"L"# of saline solution.

The initial volume for this second dilution is #20mu"L"#. The final volume will be

#V_"final 2" = V_"initial 2" + V_"saline 2"#

#V_"final 2" = 20mu"L" + 180mu"L" = 200mu"L"#

The dilution factor for this second step is

#"D.F"_2 = (20color(red)(cancel(color(black)(mu"L"))))/(200color(red)(cancel(color(black)(mu"L")))) = 1/10#

The total dilution factor will simply be the product of the two dilution factors that characterized the two dilution steps

#"D.F"_"total" = "D.F"_1 xx "D.F"_2#

#"D.F"_"total" = 1/3 xx 1/10 = color(green)(1/30)#