# Question 80d6a

Jul 28, 2016

$\text{DF} = 4$

#### Explanation:

The first thing to do here is make sure that the two volumes given to you are expressed using the same units.

You can convert microliters, $\mu \text{L}$, to milliliters, $\text{mL}$, by using the conversion factor

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 mL" = 10^3mu"L}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

In your case, the sample of urine will have a volume equivalent to

50 color(red)(cancel(color(black)(mu"L"))) * "1 mL"/(10^3color(red)(cancel(color(black)(mu"L")))) = "0.050 mL"

Now, the dilution factor is calculated by dividing the final volume of the solution, which is the volume of the diluted solution, by the initial volume of the solution, which is the volume of the concentrated solution.

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{DF" = V_"diluted"/V_"concentrated} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The volume of the diluted solution is equal to the volume of the concentrated sample, which in this case is urine, plus the volume of the diluent, which in this case is water

${V}_{\text{diluted" = V_"concentrated" + V_"diluent}}$

${V}_{\text{diluted" = "0.050 mL" + "0.150 mL" = "0.200 mL}}$

The dilution factor will thus be equal to

"DF" = (0.200 color(red)(cancel(color(black)("mL"))))/(0.050color(red)(cancel(color(black)("mL")))) = color(blue)(4)#

This tells you that the concentrated solution was $\textcolor{b l u e}{4}$ times more concentrated than the diluted solution.