# Question 59098

Oct 12, 2015

$\frac{1}{30}$

#### 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.

$\text{D.F." = V_"initial"/V_"final}$

So, you starting sample has a volume of $150 \mu \text{L}$. 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?

${V}_{\text{final 1" = V_"initial 1" + V_"saline 1}}$

${V}_{\text{final 1" = 150mu"L" + 300mu"L" = 450mu"L}}$

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 $180 \mu \text{L}$ of saline solution.

The initial volume for this second dilution is $20 \mu \text{L}$. The final volume will be

${V}_{\text{final 2" = V_"initial 2" + V_"saline 2}}$

${V}_{\text{final 2" = 20mu"L" + 180mu"L" = 200mu"L}}$

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

${\text{D.F"_"total" = "D.F"_1 xx "D.F}}_{2}$

$\text{D.F"_"total} = \frac{1}{3} \times \frac{1}{10} = \textcolor{g r e e n}{\frac{1}{30}}$