Question

Question #59098

Answer 1

`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)`